NUMAR CORP
SC 13D, 1997-06-19
OIL & GAS FIELD MACHINERY & EQUIPMENT
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                                 UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549


                                 SCHEDULE 13D

                   Under the Securities Exchange Act of 1934


                               NUMAR CORPORATION
  ---------------------------------------------------------------------------
                               (Name of Issuer)

                    COMMON STOCK, PAR VALUE $.01 PER SHARE
  ---------------------------------------------------------------------------
                        (Title of Class of Securities)

                                   67052E105
                                  ----------
                                (CUSIP Number)


                             Walter J. Mostek, Jr.
                          Drinker Biddle & Reath LLP
                        1000 Westlakes Drive, Suite 300
                               Berwyn, PA 19312
                                (610) 993-2200
  ---------------------------------------------------------------------------
                 (Name, Address and Telephone Number of Person
               Authorized to Receive Notices and Communications)

                                 June 9, 1997
  ---------------------------------------------------------------------------
            (Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this
schedule because of Rule 13d-1(b)(3) or (4), check the following box [ ].
<PAGE>
 
                                  SCHEDULE 13D

- ----------------------------                       -----------------------------
CUSIP No. 67052E105                                  Page 2 of 13 Pages
- --------------------------------------------------------------------------------

1     NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
 
      Dr. Melvin N. Miller
- --------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                  (a) [ ]
                                                                         (b) [X]
- --------------------------------------------------------------------------------
3     SEC USE ONLY

- --------------------------------------------------------------------------------
4     SOURCE OF FUNDS*

      Not applicable.

- --------------------------------------------------------------------------------
5     CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO 
      ITEMS 2(d) OR 2(e)                                                     [ ]
- --------------------------------------------------------------------------------
6     CITIZENSHIP OR PLACE OF ORGANIZATION
 
      United States of America

- --------------------------------------------------------------------------------
                         7  SOLE VOTING POWER       
                            362,143
                        --------------------------------------------------------
   NUMBER OF SHARES      8  SHARED VOTING POWER                       
     BENEFICIALLY           -0-                    
     OWNED BY EACH      --------------------------------------------------------
   REPORTING PERSON      9  SOLE DISPOSITIVE POWER 
         WITH               362,143               
                        --------------------------------------------------------
                         9  SHARED DISPOSITIVE POWER                          
                            -0-                     
                        --------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 362,143
- --------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES* [ ]
- --------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) 4.2% (approximate)
- --------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON* IN
- --------------------------------------------------------------------------------

                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
          INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
      (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.
<PAGE>
 
                                  SCHEDULE 13D

- ----------------------------                       -----------------------------
CUSIP No. 67052E105                                  Page 3 of 13 Pages
- --------------------------------------------------------------------------------

1     NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
 
      Seymour G. Mandell
- --------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                  (a) [ ]
                                                                         (b) [X]
- --------------------------------------------------------------------------------
3     SEC USE ONLY

- --------------------------------------------------------------------------------
4     SOURCE OF FUNDS*

      Not applicable.

- --------------------------------------------------------------------------------
5     CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO 
      ITEMS 2(d) OR 2(e)                                                     [ ]
- --------------------------------------------------------------------------------
6     CITIZENSHIP OR PLACE OF ORGANIZATION
 
      United States of America

- --------------------------------------------------------------------------------
                         7  SOLE VOTING POWER       
                            175,396
                        --------------------------------------------------------
   NUMBER OF SHARES      8  SHARED VOTING POWER                       
     BENEFICIALLY           -0-                    
     OWNED BY EACH      --------------------------------------------------------
   REPORTING PERSON      9  SOLE DISPOSITIVE POWER 
         WITH               175,396
                        --------------------------------------------------------
                         9  SHARED DISPOSITIVE POWER                          
                            -0-                     
                        --------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 175,396
- --------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES* [ ]
- --------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) 2.0% (approximate)
- --------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON* IN
- --------------------------------------------------------------------------------

                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
          INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
      (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.
<PAGE>
 
                                  SCHEDULE 13D

- ----------------------------                       -----------------------------
CUSIP No. 67052E105                                  Page 4 of 13 Pages
- --------------------------------------------------------------------------------

1     NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
 
      Barry M. Davis
- --------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                  (a) [ ]
                                                                         (b) [X]
- --------------------------------------------------------------------------------
3     SEC USE ONLY

- --------------------------------------------------------------------------------
4     SOURCE OF FUNDS*

      Not applicable.

- --------------------------------------------------------------------------------
5     CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO 
      ITEMS 2(d) OR 2(e)                                                     [ ]
- --------------------------------------------------------------------------------
6     CITIZENSHIP OR PLACE OF ORGANIZATION
 
      United States of America

- --------------------------------------------------------------------------------
                         7  SOLE VOTING POWER       
                            23,283
                        --------------------------------------------------------
   NUMBER OF SHARES      8  SHARED VOTING POWER                       
     BENEFICIALLY           700,486
     OWNED BY EACH      --------------------------------------------------------
   REPORTING PERSON      9  SOLE DISPOSITIVE POWER 
         WITH               23,283               
                        --------------------------------------------------------
                         9  SHARED DISPOSITIVE POWER                          
                            700,486
                        --------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 723,769
- --------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES* [ ]
- --------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) 7.8% (approximate)
- --------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON* IN
- --------------------------------------------------------------------------------

                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
          INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
      (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.
<PAGE>
 
                                  SCHEDULE 13D

- ----------------------------                       -----------------------------
CUSIP No. 67052E105                                  Page 5 of 13 Pages
- --------------------------------------------------------------------------------

1     NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
 
      Dr. James H. Simons
- --------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                  (a) [ ]
                                                                         (b) [X]
- --------------------------------------------------------------------------------
3     SEC USE ONLY

- --------------------------------------------------------------------------------
4     SOURCE OF FUNDS*

      Not applicable.

- --------------------------------------------------------------------------------
5     CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO 
      ITEMS 2(d) OR 2(e)                                                     [ ]
- --------------------------------------------------------------------------------
6     CITIZENSHIP OR PLACE OF ORGANIZATION
 
      United States of America

- --------------------------------------------------------------------------------
                         7  SOLE VOTING POWER       
                            13,934
                        --------------------------------------------------------
   NUMBER OF SHARES      8  SHARED VOTING POWER                       
     BENEFICIALLY           -0-                    
     OWNED BY EACH      --------------------------------------------------------
   REPORTING PERSON      9  SOLE DISPOSITIVE POWER 
         WITH               13,934
                        --------------------------------------------------------
                         9  SHARED DISPOSITIVE POWER                          
                            -0-                     
                        --------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 13,934
- --------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES* [ ]
- --------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) 0.2% (approximate)
- --------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON* IN
- --------------------------------------------------------------------------------

                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
          INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
      (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.
<PAGE>
 
                                  SCHEDULE 13D

- ----------------------------                       -----------------------------
CUSIP No. 67052E105                                  Page 6 of 13 Pages
- --------------------------------------------------------------------------------

1     NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
 
      Davis Venture Partners, L.P.
- --------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                  (a) [_]
                                                                         (b) [X]
- --------------------------------------------------------------------------------
3     SEC USE ONLY

- --------------------------------------------------------------------------------
4     SOURCE OF FUNDS*

      Not applicable.

- --------------------------------------------------------------------------------
5     CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO 
      ITEMS 2(d) OR 2(e)                                                     [_]
- --------------------------------------------------------------------------------
6     CITIZENSHIP OR PLACE OF ORGANIZATION
 
      Oklahoma, United States of America

- --------------------------------------------------------------------------------
                         7  SOLE VOTING POWER       
                            700,486
                        --------------------------------------------------------
   NUMBER OF SHARES      8  SHARED VOTING POWER                       
     BENEFICIALLY           -0-                    
     OWNED BY EACH      --------------------------------------------------------
   REPORTING PERSON      9  SOLE DISPOSITIVE POWER 
         WITH               700,486
                        --------------------------------------------------------
                        10  SHARED DISPOSITIVE POWER                          
                            -0-                     
- --------------------------------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 700,486
- --------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES* [_]
- --------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) 8.1% (approximate)
- --------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON* PN
- --------------------------------------------------------------------------------

                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
          INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
      (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.
<PAGE>
 
                                  SCHEDULE 13D

- ----------------------------                       -----------------------------
CUSIP No. 67052E105                                  Page 7 of 13 Pages
- --------------------------------------------------------------------------------

1     NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
 
      Bermuda Trust Company Limited
- --------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                  (a) [_]
                                                                         (b) [X]
- --------------------------------------------------------------------------------
3     SEC USE ONLY

- --------------------------------------------------------------------------------
4     SOURCE OF FUNDS*

      Not applicable.

- --------------------------------------------------------------------------------
5     CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO 
      ITEMS 2(d) OR 2(e)                                                     [_]
- --------------------------------------------------------------------------------
6     CITIZENSHIP OR PLACE OF ORGANIZATION
 
      Bermuda

- --------------------------------------------------------------------------------
                         7  SOLE VOTING POWER       
                            900,000
                        --------------------------------------------------------
   NUMBER OF SHARES      8  SHARED VOTING POWER                       
     BENEFICIALLY           -0-                    
     OWNED BY EACH      --------------------------------------------------------
   REPORTING PERSON      9  SOLE DISPOSITIVE POWER 
         WITH               900,000
                        --------------------------------------------------------
                        10  SHARED DISPOSITIVE POWER                          
                            -0-                     
- --------------------------------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 900,000
- --------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES* [_]
- --------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) 10.4% (approximate)
- --------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON* OO
- --------------------------------------------------------------------------------

                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
          INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
      (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.
<PAGE>
 
          This Schedule 13D (the "statement") is being filed as an original
filing with the Securities and Exchange Commission by Dr. Melvin N. Miller,
Seymour G. Mandell, Barry M. Davis, Dr. James H. Simons, Davis Venture Partners,
L.P. and Bermuda Trust Company Limited, as trustee of the Lord Jim Trust, in
connection with the proposed merger (the "Merger") of Halliburton M.S. Corp.
("Merger Sub"), a Delaware corporation and wholly owned subsidiary of
Halliburton Company ("Halliburton") with and into NUMAR Corporation ("Issuer").
The statement is being filed with respect to various Voting Agreements between
Halliburton and the Reporting Persons who beneficially own an aggregate of
2,154,450 shares of common stock of the Issuer (or approximately 25.0% of the
total outstanding shares of common stock of the Issuer).

Item 1.  Security and Issuer.
         --------------------

          This statement relates to the common stock, par value $.01 per share
(the "Common Stock"), of the Issuer.  The Issuer is a Pennsylvania corporation
and has its principal executive offices located at 508 Lapp Road, Malvern, PA
19355.

Item 2.  Identity and Background.
         ------------------------

          The Reporting Persons for this statement are Dr. Melvin N. Miller,
Seymour G. Mandell, Barry M. Davis, Dr. James H. Simons, Davis Venture Partners,
L.P. (the "Partnership") and Bermuda Trust Company Limited, as trustee of the
Lord Jim Trust (the "Trustee").

          The Partnership is an Oklahoma limited partnership and the address of
its principal business and principal office is 320 South Boston, Suite 1000,
Tulsa, Oklahoma 74103.  The principal business of the Partnership is investing
venture capital in various businesses.  The Trustee is a Bermuda corporation and
the address of its principal business and principal office is 6 Front Street,
Hamilton, Bermuda.  The principal business of the Trustee is providing trust and
related services.

          The names, business or residence addresses and present principal
occupations of the (i) general partners of the Partnership (each of whom is a
United States citizen and one of whom is Mr. Davis), (ii) directors and
executive officers of the Trustee and (iii) Messrs. Mandell and Davis and Drs.
Miller and Simons (each of whom is a United States citizen), is attached on
Schedule I. Except for Thomas F. Hawkins and Karen M. Malcolm, each of the
directors and executive officers of the Trustee is a citizen of Bermuda. Mr.
Hawkins is a United States citizen. Ms. Malcolm is a citizen of the United
Kingdom. During the last five years neither the Reporting Persons nor such
persons have been convicted in a criminal proceeding (excluding traffic
violations or similar misdemeanors) and have not been a party to a civil
proceeding of a judicial or administrative body of competent jurisdiction
resulting in a judgment, decree or final order enjoining future violations of,
or prohibiting or mandating activities subject to, federal or state securities
laws or finding any violation with respect to such laws.

          On June 9, 1997, Halliburton and Merger Sub entered into an Agreement
and Plan of Merger (the "Merger Agreement") with the Issuer providing for the
merger of Merger Sub with and into the Issuer, with the Issuer continuing as the
Surviving Corporation (as defined in the Merger Agreement).

          On June 9, 1997, the Reporting Persons entered into Voting Agreements
(the "Voting Agreements") with Halliburton.  Certain provisions of the Voting
Agreements, a form of which is attached hereto as Exhibit 1, are summarized in
Item 4 below.

          As a result of the execution of the Voting Agreements, the Reporting
Persons may be deemed, for purposes of Section 13(d) of the Securities and
Exchange Act of 1934, as amended (the "Exchange Act"), to have formed a "group"
with Halliburton.  Each of the Reporting Persons expressly declares that the
filing of this statement on Schedule 13D shall not be construed as an admission
by it, for the purposes of Section 13(d) or Section 13(g) of the Exchange Act,
that it has formed a group or that it has any shared voting or dispositive power
over any shares of Common Stock of the Issuer by virtue thereof.
<PAGE>
 
Item 3.  Source and Amount of Funds or Other Consideration.
         --------------------------------------------------

          The Reporting Persons have not paid any amount of funds or other
consideration to the Issuer or any other person in connection with entering into
the Voting Agreements.


Item 4.  Purpose of Transaction.
         -----------------------

          The purpose of the transactions described herein is to consummate the
proposed Merger.  There can be no assurance, however, that the proposed Merger
will be consummated or as to the timing or exact terms thereof.

          On June 9, 1997 the Reporting Persons entered into the Voting
Agreements with Halliburton.  Pursuant to the Voting Agreements, the Reporting
Persons severally agreed (i) to vote certain shares of Common Stock beneficially
owned or controlled by him or it (the "Shares") at any meeting of shareholders
of the Issuer called to consider and vote to approve the Merger Agreement and
the Merger and/or the transactions contemplated thereby; (ii) not to initiate,
solicit or encourage, or take any other action to facilitate, any inquiries or
the making of any proposal that constitutes, or that may reasonably be expected
to lead to, any merger, consolidation, share exchange, business combination or
similar transaction involving the Issuer or any of its "Significant
Subsidiaries" (as defined in the Merger Agreement), or a sale, lease, exchange,
transfer or other disposition of 50% or more of the assets of the Issuer and its
subsidiaries, or the acquisition by a person or group of beneficial ownership or
the right to acquire beneficial ownership of 50% or more of the outstanding
common shares of the Issuer or a substantial portion of the Issuer's assets (a
"Competing Transaction"), other than transactions contemplated by the Merger
Agreement; (iii) not to enter into discussions or negotiate with any person or
entity in furtherance of the inquiries specified in subclause (ii) or to obtain
a Competing Transaction, or to authorize or permit any of its representatives to
take any such action; and (iv) not to, and not to permit any company, trust or
other entity controlled by him or it, to sell, transfer, pledge or otherwise
dispose of, or grant a proxy with respect to, any of the Shares or to grant any
option or enter into any other agreement or arrangement with respect thereto,
other than pursuant to the Merger.  The Voting Agreements will terminate upon
the earlier of December 31, 1997 or the termination of the Merger Agreement.
The foregoing summary of the Voting Agreements is qualified in its entirety by
reference to a form of the Voting Agreements included as Exhibit 1 to this
Schedule 13D and incorporated herein in its entirety by reference.  All Voting
Agreements that were entered into are substantially identical to the form of 
Voting Agreement included as Exhibit 1.

          Except as set forth herein or as provided in the Voting Agreements,
the Reporting Persons do not have any current plans or proposals that relate to
or would result in (i) the acquisition by any person of shares of the Issuer or
the disposition of shares of the Issuer; (ii) an extraordinary corporate
transaction, such as a merger, reorganization or liquidation; (iii) a sale or
transfer of any material amount of assets of the Issuer; (iv) any change in the
present board of directors or management of the Issuer, including any plans or
proposals to change the number or term of directors or to fill any vacancies on
the board; (v) any material change in the present capitalization or dividend
policy of the Issuer; (vi) any other material change in the Issuer's business or
corporate structure; (vii) any change in the Issuer's charter or bylaws, or
instruments corresponding thereto, or other actions that may impede the
acquisition of control of the Issuer by any person; (viii) causing a class of
securities of the Issuer to be delisted from a national securities exchange or
to cease to be authorized to be quoted in an inter-dealer quotation system of a
registered national securities association; (ix) a class of equity securities of
the Issuer becoming eligible for termination of registration pursuant to Section
12(g)(4) of the Exchange Act; or (x) any action similar to any of those
enumerated above.

                                      -2-
<PAGE>
 
Item 5.  Interest in Securities of the Issuer.
         -------------------------------------

          (a) The Reporting Persons beneficially own securities of the Issuer as
follows:  Dr. Miller beneficially owns 341,351 Shares (or approximately 4.2% of
the outstanding Shares), of which 209,101 may be acquired pursuant to the
exercise of vested options; Mr. Mandell beneficially owns 175,396 Shares (or
approximately 2.0% of the outstanding Shares), of which 5,000 may be acquired
pursuant to the exercise of vested options; Mr. Davis beneficially owns 723,769
Shares inclusive of 700,486 Shares owned by the Partnership (or approximately
7.8% of the outstanding Shares), of which 5,000 may be acquired pursuant to the
exercise of vested options; Dr. Simons beneficially owns 13,934 Shares (or
approximately 0.2% of the outstanding Shares), of which 4,500 may be acquired
pursuant to the exercise of vested options; the Partnership beneficially owns
700,486 Shares (or approximately 8.1% of the outstanding Shares); and the
Trustee beneficially owns 900,000 Shares (or approximately 10.4% of the
outstanding Shares).

          (b) Each of the Reporting Persons has the sole power to vote and the
sole power to dispose of that number of Shares specified as being beneficially
owned by him or it in paragraph (a) of this Item 5.

          (c) Pursuant to the Issuer's 1994 Stock Incentive Plan, options to
purchase Shares, all of which were immediately exercisable upon issuance at
$19.75 per Share, were automatically granted on May 14, 1997 to the following
Reporting Persons and in the following amounts: 2,500 to Mr. Davis, 2,500 to Mr.
Mandell and 2,500 to Dr. Simons.

          (d)  Not applicable.

          (e)  Not applicable.

Item 6.  Contracts, Arrangements, Understandings or Relationships With
         -------------------------------------------------------------
Respect to Securities of the Issuer.
- ------------------------------------

          The Reporting Persons have entered into the Voting Agreements with
Halliburton.  The Voting Agreements will terminate upon the earlier of December
31, 1997 or the termination of the Merger Agreement.

          A form of the Voting Agreements is included as Exhibit 1 to this
Schedule 13D and is incorporated herein by reference.  See Item 4.



Item 7.  Material to be Filed as Exhibits.
         ---------------------------------

         A form of the Voting Agreements, dated June 9, 1997, by and between
Halliburton Company and the persons named therein.

                                      -3-
<PAGE>
 
                                   SIGNATURES
                                   ----------

          After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.


Dated:  June 19, 1997

                             /s/ Dr. Melvin N. Miller
                             ------------------------
                             Dr. Melvin N. Miller


                             /s/ Seymour G. Mandell
                             ------------------------
                             Seymour G. Mandell


                             /s/ Barry M. Davis
                             ------------------------
                             Barry M. Davis


                             /s/ Dr. James H. Simons
                             ------------------------
                             Dr. James H. Simons



                             Davis Venture Partners, L.P.


 
                             By: /s/ Barry M. Davis
                                ---------------------
                                 Name:  Barry M. Davis
                                 Title: Managing General Partner



                             Bermuda Trust Company Limited



                             By: /s/ Susan Gibbons
                                ---------------------
                                Name:  Susan Gibbons
                                Title: Trust Officer


                                      -4-
<PAGE>
 
                                   SCHEDULE I
                                   ----------

<TABLE> 
<CAPTION> 

Name, Business or Residence
Addresses                                 Principal Occupation
- -------------------------                 --------------------
<S>                                       <C> 
Melvin N. Miller, Ph.D.                   President, Chief Executive Officer
508 Lapp Road                             and Chairman of the Issuer
Malvern, PA 19355
 
Barry M. Davis                            Managing General Partner of the
320 South Boston                          Partnership
Suite 1000
Tulsa, OK 74103
 
Seymour G. Mandell                        President of MGM Consulting
1735 Market Street                        Corporation
Suite 3410
Philadelphia, PA 19103
 
James H. Simons                           Chairman and Chief Executive
800 Third Avenue                          Officer of Renaissance Technologies
New York, NY 10022                        Corporation
 
 
Phillip Tuttle                            General Partner of the Partnership
320 South Boston
Suite 1000
Tulsa, OK 74103

Elmer Wilkening                           General Partner of the Partnership
320 South Boston
Suite 1000
Tulsa, OK 74103
 
Michael Stone                             General Partner of the Partnership
320 South Boston
Suite 1000
Tulsa, OK 74103

*Elden H. Trimingham                      Chairman of the Trustee

*David E. Wilkinson                       Deputy Chairman of the Trustee

*Luis A. Douglas                          President and Director of the Trustee

*Cummings V. Zuill                        Director of the Trustee and an officer
                                          of the Bank of Bermuda

*Karen M. Malcolm                         Vice President and Director of the 
                                          Trustee

*William F. Maycock                       Director of the Trustee and an officer
                                          of the Bank of Bermuda

*Judith P. Doidge                         Secretary of the Trustee

*Thomas F. Hawkins                        Vice President of the Trustee

*David T. Smith                           Vice President of the Trustee

*Susan Gibbons                            Trust Officer for the Trustee


*Business address is 6 Front Street, Hamilton, Bermuda.

</TABLE> 

<PAGE>
 
                                                                     EXHIBIT 2.C

                               VOTING AGREEMENT


     VOTING AGREEMENT ("Agreement") dated as of June 9, 1997, between
Halliburton Company, a Delaware corporation (the "Acquiror"), and Davis Venture
Partners, L.P. (the "Shareholder"), a holder of common shares, par value $0.01
per share, of NUMAR Corporation, a Pennsylvania corporation (the "Company").

                                   RECITALS:

     The Shareholder beneficially owns an aggregate of 700,486 common shares
(together with any additional common shares as to which beneficial ownership is
acquired by any member of the Shareholder Group described below, the "Company
Shares"), par value $0.01 per share ("Company Common Shares"), of the Company.

     The Acquiror is prepared to enter into an Agreement and Plan of Merger with
the Company (the "Plan") providing for the merger of a wholly owned subsidiary
of Acquiror with and into the Company and the conversion in such merger of each
Company Common Share into the number of shares of the Common Stock, par value
$2.50 per share, of the Acquiror set forth in the Plan (the "Merger").

     To facilitate the Merger, the Shareholder is willing to enter into certain
arrangements with respect to the Company Shares.

     NOW, THEREFORE, in consideration of the premises set forth above, the
mutual promises set forth below, and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties hereto
agree as follows:

1.   Shareholder's Support of the Merger. From the date hereof until December
31, 1997, or, if earlier, termination of the Plan:

          (a) Except as contemplated by the Plan or hereby, neither the
     Shareholder nor any Person controlled by the Shareholder, other than the
     Company and its subsidiaries (collectively, the "Shareholder Group"), will,
     directly or indirectly, sell, transfer, pledge or otherwise dispose of, or
     grant a proxy with respect to, any Company Shares to any Person other than
     any member of the Shareholder Group or the Acquiror or its designee, or
     grant an option with respect to any of the Company Shares or enter into any
     other agreement or arrangement with respect to any of the Company Shares.

          (b) The Shareholder agrees that the Shareholder will vote, and will
     cause each member of the Shareholder Group to vote, all Company Shares
     entitled to vote and beneficially owned by such Persons (i) in favor of the
     Merger and (ii), subject to the provisions of paragraph (c) below, against
     any combination proposal or other matter that may
<PAGE>
 
     (in the reasonable opinion of the Acquiror) interfere or be inconsistent
     with the Merger (including without limitation a Competing Transaction).

          (c) The Shareholder agrees that, if requested by the Acquiror in
     writing in order to facilitate the Merger, the Shareholder will not, and
     will cause each member of the Shareholder Group not to, attend or vote any
     Company Shares beneficially owned by any such Person at any annual or
     special meeting of shareholders or execute any written consent of
     shareholders

          (d) Neither the Shareholder nor any other member of the Shareholder
     Group will initiate, solicit or encourage (including by way of furnishing
     information or assistance), or take any other action to facilitate, any
     inquiries or the making of any proposal that constitutes, or that may
     reasonably be expected to lead to, any merger, consolidation, share
     exchange, business combination or similar transaction involving the Company
     or any of its Significant Subsidiaries, a sale, lease, exchange, transfer
     or other disposition of 50% or more of the assets of the Company and its
     subsidiaries, taken as a whole, in a single transaction or series of
     transactions, the acquisition by a Person or Group of beneficial ownership
     or the right to acquire beneficial ownership of 50% or more of the
     outstanding Company Common Shares, whether by tender offer, exchange offer
     or otherwise, or the acquisition in any manner, directly or indirectly, of
     a material equity interest in any voting securities of, or a substantial
     portion of the assets of, the Company or any of its Significant
     Subsidiaries, other than the transactions contemplated by the Plan (a
     "Competing Transaction"), or enter into discussions or negotiate with any
     Person in furtherance of such inquiries or to obtain a Competing
     Transaction, or agree to or endorse any Competing Transaction, or authorize
     or permit any of the officers, directors or employees of the Shareholder or
     any member of the Shareholder Group or any investment banker, financial
     advisor, attorney, accountant or other representative retained by the
     Shareholder or any other member of the Shareholder Group to take any such
     action. The Shareholder shall promptly notify the Acquiror of all relevant
     terms of any such inquiries or proposals received by such Shareholder or
     any other member of the Shareholder Group or by any such officer, director,
     employee, investment banker, financial advisor, attorney, accountant or
     other representative relating to any of such matters and, if such inquiry
     or proposal is in writing, such Shareholder shall deliver or cause to be
     delivered to the Acquiror a copy of such inquiry or proposal.

          (e) The Shareholder hereby consents to the Acquiror's announcement in
     any press release, public filing, advertisement or other document, that the
     Shareholder has entered into this Agreement.

          (f) To the extent inconsistent with the provisions of this Section 1,
     the Shareholder hereby revokes, and will cause each member of the
     Shareholder Group to revoke, any and all proxies with respect to such
     member's Company Common Shares or any other voting securities of the
     Company.
 

                                      -2-
<PAGE>
 
2.   Miscellaneous

     (a) The Shareholder, on the one hand, and the Acquiror, on the other,
acknowledge and agree that irreparable damage would occur if any of the
provisions of this Agreement were not performed in accordance with their
specific terms or were otherwise breached.  It is accordingly agreed that the
parties hereto shall be entitled to an injunction or injunctions to prevent
breaches of the provisions of this Agreement and to enforce specifically the
terms and provisions hereof in any court of the United States or any state
thereof having jurisdiction, in addition to any other remedies to which they may
be entitled at law or equity.

     (b) Descriptive headings are for convenience only and shall not control or
affect the meaning or construction of any provision of this Agreement.

     (c) All notices, consents, requests, instructions, approvals and other
communications provided for herein shall be validly given, made or served, if in
writing and delivered personally, by telecopier (subject to receipt of
electronic confirmation) or sent by registered mail, postage prepaid:

     If to the Acquiror:

         Halliburton Company
         3600 Lincoln Plaza
         500 N. Akard Street
         Dallas, Texas  75201-3391
         Attention: Lester L. Coleman
                    Executive Vice President
                      and General Counsel
         Telecopier No.:  (214) 978-2658

         with a copy to:

                    Vinson & Elkins L.L.P.
                    First City Tower
                    1001 Fannin
                    Houston, Texas  77002-6760
                    Attention:  William E. Joor III
                    Telecopier No.:  (713) 758-2346

                                      -3-
<PAGE>
 
         If to the Shareholder:

               Davis Venture Partners, L.P.
               320 South Boston, Suite 1000
               Tulsa, Oklahoma  74103
               Attention:  Barry M. Davis
               Telecopier No.:  (918) 582-3404

or to such other address or telecopier number as any party may, from time to
time, designate in a written notice given in a like manner.  Notice given by
telecopier shall be deemed delivered on the day the sender receives telecopier
confirmation that such notice was received at the telecopier number of the
addressee.  Notice given by mail as set out above shall be deemed delivered
three days after the date the same is postmarked.

     (d) From and after the termination of this Agreement, the covenants of the
parties set forth herein shall be of no further force or effect and the parties
shall be under no further obligation with respect thereto.

     (e) For purposes of this Agreement, the following terms shall have the
following meanings:

         (i)   Affiliate.  "Affiliate" shall have the meaning ascribed to it in
               ---------                                                       
     Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
     in effect on the date hereof.

         (ii)  Associate.  "Associate" shall have the meaning ascribed to it in
               --------- 
     Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
     in effect on the date hereof.

         (iii) Beneficial Owner.  A person shall be deemed a "beneficial owner"
               ----------------                                                
     of or to have "beneficial ownership" of Company Shares in accordance with
     the interpretations of the term "beneficial ownership" as defined in Rule
     13-d(3) under the Exchange Act, as in effect on the date hereof, provided
     that a person shall be deemed to be the beneficial owner of, and to have
     beneficial ownership of, Company Shares that such Person or any Affiliate
     of such Person has the right to acquire (whether such right is exercisable
     immediately or only after the passage of time) pursuant to any agreement,
     arrangement or understanding or upon the exercise of conversion rights,
     exchange rights, warrant, options or otherwise.

         (iv)  Exchange Act.  "Exchange Act" shall mean the Securities Exchange
               -------------  
     Act of 1934, as amended.

                                      -4-
<PAGE>
 
         (v)   Person.  A "Person" shall mean any individual, firm, corporation,
               ------                                                           
     partnership, trust, limited liability company or other entity.

         (vi)  Significant Subsidiary.  "Significant Subsidiary" shall have the
               ----------------------                                          
     meaning ascribed to it in Rule 1-02 of SEC Regulation S-X as in effect on
     the date hereof.

     (g) The Shareholder hereby represents and warrants to the Acquiror as
follows:  The Shareholder has full power and authority to enter into this
Agreement; neither the execution or delivery of this Agreement nor the
consummation of the transactions contemplated herein will (i) conflict with or
result in a breach, default or violation of (A) any of the terms, provisions or
conditions of the certificate of incorporation or bylaws of any member of the
Shareholder Group or (B) any agreement, proxy, document, instrument, judgment,
decree, order, governmental permit, certificate, license, law, statute, rule or
regulation to which any member of the Shareholder Group is a party or to which
it is subject, (ii) result in the creation of any lien, charge or other
encumbrance on any Company Common Shares or (iii) require any member of the
Shareholder Group to obtain the consent of any private nongovernmental third
party; and no consent, action, approval or authorization of, or registration,
declaration or filing with, any governmental department, commission, agency or
other instrumentality or any other person or entity is required to authorize, or
is otherwise required in connection with, the execution and delivery of this
Agreement (with the exception of an amended Schedule 13D to be filed by the
Shareholder pursuant to the Exchange Act) or the Shareholder's performance of
the terms of this Agreement or the validity or enforceability of this Agreement.

     (h) This Agreement shall be binding upon, and inure to the benefit of, the
parties hereto and their respective heirs, personal representatives, successors,
assigns and Affiliates, but shall not be assignable by either party hereto
without the prior written consent of the other party hereto.

     (i) No party may waive any of the terms or conditions of this Agreement
except by a duly signed writing referring to the specific provision to be
waived.

     (j) This Agreement shall be governed by, and construed in accordance with,
the laws of the State of Texas, regardless of the laws that might otherwise
govern under applicable principles of conflicts of law; provided, however, that
any matter involving the internal corporate affairs of any party hereto shall be
governed by the provisions of the Business Corporation Law of the Commonwealth
of Pennsylvania.

     (k) This Agreement constitutes the entire agreement, and supersedes all
other and prior agreements and understandings, both written and oral, among the
parties hereto and their Affiliates.

                                      -5-
<PAGE>
 
     (l) This Agreement may be executed in two or more counterparts, each of
which shall be deemed an original but all of which shall constitute one and the
same instrument.

                                      -6-
<PAGE>
 
     IN WITNESS WHEREOF, the Shareholder and the Acquiror have each caused this
Agreement to be duly executed by an officer or other Person, thereunto duly
authorized, all as of the day and year first above written.

                                 HALLIBURTON COMPANY


                                 By: /s/ Lester L. Coleman
                                    ------------------------------
                                    Lester L. Coleman
                                    Executive Vice President and General Counsel
 

                                 DAVIS VENTURE PARTNERS, L.P.


                                 By: /s/ Barry M. Davis
                                    ------------------------------      
                                    Barry M. Davis
                                    General Partner
 
 

                                      -7-
<PAGE>
 
                               VOTING AGREEMENT


     VOTING AGREEMENT ("Agreement") dated as of June 9, 1997, between
Halliburton Company, a Delaware corporation (the "Acquiror"), and Melvin N.
Miller (the "Shareholder"), a holder of common shares, par value $0.01 per
share, of NUMAR Corporation, a Pennsylvania corporation (the "Company").

                                   RECITALS:

     The Shareholder beneficially owns an aggregate of 334,143 common shares
(together with any additional common shares as to which beneficial ownership is
acquired by any member of the Shareholder Group described below, the "Company
Shares"), par value $0.01 per share ("Company Common Shares"), of the Company.

     The Acquiror is prepared to enter into an Agreement and Plan of Merger with
the Company (the "Plan") providing for the merger of a wholly owned subsidiary
of Acquiror with and into the Company and the conversion in such merger of each
Company Common Share into the number of shares of the Common Stock, par value
$2.50 per share, of the Acquiror set forth in the Plan (the "Merger").

     To facilitate the Merger, the Shareholder is willing to enter into certain
arrangements with respect to the Company Shares.

     NOW, THEREFORE, in consideration of the premises set forth above, the
mutual promises set forth below, and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties hereto
agree as follows:

1.   Shareholder's Support of the Merger. From the date hereof until December
31, 1997, or, if earlier, termination of the Plan:

          (a) Except as contemplated by the Plan or hereby, neither the
     Shareholder nor any Person controlled by the Shareholder, other than the
     Company and its subsidiaries (collectively, the "Shareholder Group"), will,
     directly or indirectly, sell, transfer, pledge or otherwise dispose of, or
     grant a proxy with respect to, any Company Shares to any Person other than
     any member of the Shareholder Group or the Acquiror or its designee, or
     grant an option with respect to any of the Company Shares or enter into any
     other agreement or arrangement with respect to any of the Company Shares.

          (b) The Shareholder agrees that the Shareholder will vote, and will
     cause each member of the Shareholder Group to vote, all Company Shares
     entitled to vote and beneficially owned by such Persons (i) in favor of the
     Merger and (ii), subject to the provisions of paragraph (c) below, against
     any combination proposal or other matter that may 
<PAGE>
 
     (in the reasonable opinion of the Acquiror) interfere or be inconsistent
     with the Merger (including without limitation a Competing Transaction).

          (c) The Shareholder agrees that, if requested by the Acquiror in
     writing in order to facilitate the Merger, the Shareholder will not, and
     will cause each member of the Shareholder Group not to, attend or vote any
     Company Shares beneficially owned by any such Person at any annual or
     special meeting of shareholders or execute any written consent of
     shareholders

          (d) Neither the Shareholder nor any other member of the Shareholder
     Group will initiate, solicit or encourage (including by way of furnishing
     information or assistance), or take any other action to facilitate, any
     inquiries or the making of any proposal that constitutes, or that may
     reasonably be expected to lead to, any merger, consolidation, share
     exchange, business combination or similar transaction involving the Company
     or any of its Significant Subsidiaries, a sale, lease, exchange, transfer
     or other disposition of 50% or more of the assets of the Company and its
     subsidiaries, taken as a whole, in a single transaction or series of
     transactions, the acquisition by a Person or Group of beneficial ownership
     or the right to acquire beneficial ownership of 50% or more of the
     outstanding Company Common Shares, whether by tender offer, exchange offer
     or otherwise, or the acquisition in any manner, directly or indirectly, of
     a material equity interest in any voting securities of, or a substantial
     portion of the assets of, the Company or any of its Significant
     Subsidiaries, other than the transactions contemplated by the Plan (a
     "Competing Transaction"), or enter into discussions or negotiate with any
     Person in furtherance of such inquiries or to obtain a Competing
     Transaction, or agree to or endorse any Competing Transaction, or authorize
     or permit any of the officers, directors or employees of the Shareholder or
     any member of the Shareholder Group or any investment banker, financial
     advisor, attorney, accountant or other representative retained by the
     Shareholder or any other member of the Shareholder Group to take any such
     action. The Shareholder shall promptly notify the Acquiror of all relevant
     terms of any such inquiries or proposals received by such Shareholder or
     any other member of the Shareholder Group or by any such officer, director,
     employee, investment banker, financial advisor, attorney, accountant or
     other representative relating to any of such matters and, if such inquiry
     or proposal is in writing, such Shareholder shall deliver or cause to be
     delivered to the Acquiror a copy of such inquiry or proposal.

          (e) The Shareholder hereby consents to the Acquiror's announcement in
     any press release, public filing, advertisement or other document, that the
     Shareholder has entered into this Agreement.

          (f) To the extent inconsistent with the provisions of this Section 1,
     the Shareholder hereby revokes, and will cause each member of the
     Shareholder Group to revoke, any and all proxies with respect to such
     member's Company Common Shares or any other voting securities of the
     Company.

                                      -2-
<PAGE>
 
2.   Miscellaneous

     (a) The Shareholder, on the one hand, and the Acquiror, on the other,
acknowledge and agree that irreparable damage would occur if any of the
provisions of this Agreement were not performed in accordance with their
specific terms or were otherwise breached.  It is accordingly agreed that the
parties hereto shall be entitled to an injunction or injunctions to prevent
breaches of the provisions of this Agreement and to enforce specifically the
terms and provisions hereof in any court of the United States or any state
thereof having jurisdiction, in addition to any other remedies to which they may
be entitled at law or equity.

     (b) Descriptive headings are for convenience only and shall not control or
affect the meaning or construction of any provision of this Agreement.

     (c) All notices, consents, requests, instructions, approvals and other
communications provided for herein shall be validly given, made or served, if in
writing and delivered personally, by telecopier (subject to receipt of
electronic confirmation) or sent by registered mail, postage prepaid:

     If to the Acquiror:

         Halliburton Company
         3600 Lincoln Plaza
         500 N. Akard Street
         Dallas, Texas  75201-3391
         Attention: Lester L. Coleman
                    Executive Vice President
                      and General Counsel
         Telecopier No.:  (214) 978-2658

         with a copy to:

               Vinson & Elkins L.L.P.
               First City Tower
               1001 Fannin
               Houston, Texas  77002-6760
               Attention:  William E. Joor III
               Telecopier No.:  (713) 758-2346

                                      -3-
<PAGE>
 
          If to the Shareholder:

               Melvin N. Miller
               c/o NUMAR Corporation
               508 Lapp Road
               Malvern, Pennsylvania  19355
               Telecopier No.:  (610) 644-8131

or to such other address or telecopier number as any party may, from time to
time, designate in a written notice given in a like manner.  Notice given by
telecopier shall be deemed delivered on the day the sender receives telecopier
confirmation that such notice was received at the telecopier number of the
addressee.  Notice given by mail as set out above shall be deemed delivered
three days after the date the same is postmarked.

     (d) From and after the termination of this Agreement, the covenants of the
parties set forth herein shall be of no further force or effect and the parties
shall be under no further obligation with respect thereto.

     (e) For purposes of this Agreement, the following terms shall have the
following meanings:

         (i)    Affiliate.  "Affiliate" shall have the meaning ascribed to it in
                ----------                                                     
Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
in effect on the date hereof.

         (ii)   Associate.  "Associate" shall have the meaning ascribed to it in
                ---------- 
Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
in effect on the date hereof.

         (iii)  Beneficial Owner.  A person shall be deemed a "beneficial owner"
                -----------------                                              
of or to have "beneficial ownership" of Company Shares in accordance with
the interpretations of the term "beneficial ownership" as defined in Rule
13-d(3) under the Exchange Act, as in effect on the date hereof, provided
that a person shall be deemed to be the beneficial owner of, and to have
beneficial ownership of, Company Shares that such Person or any Affiliate
of such Person has the right to acquire (whether such right is exercisable
immediately or only after the passage of time) pursuant to any agreement,
arrangement or understanding or upon the exercise of conversion rights,
exchange rights, warrant, options or otherwise.

         (iv)   Exchange Act.  "Exchange Act" shall mean the Securities Exchange
                ------------- 
Act of 1934, as amended.

         (v)    Person.  A "Person" shall mean any individual, firm, 
                ------   
corporation, partnership, trust, limited liability company or other entity.

                                      -4-
<PAGE>
 
         (vi) Significant Subsidiary.  "Significant Subsidiary" shall have the
              ----------------------                                          
     meaning ascribed to it in Rule 1-02 of SEC Regulation S-X as in effect on
     the date hereof.

     (g) The Shareholder hereby represents and warrants to the Acquiror as
follows:  The Shareholder has full power and authority to enter into this
Agreement; neither the execution or delivery of this Agreement nor the
consummation of the transactions contemplated herein will (i) conflict with or
result in a breach, default or violation of (A) any of the terms, provisions or
conditions of the certificate of incorporation or bylaws of any member of the
Shareholder Group or (B) any agreement, proxy, document, instrument, judgment,
decree, order, governmental permit, certificate, license, law, statute, rule or
regulation to which any member of the Shareholder Group is a party or to which
it is subject, (ii) result in the creation of any lien, charge or other
encumbrance on any Company Common Shares or (iii) require any member of the
Shareholder Group to obtain the consent of any private nongovernmental third
party; and no consent, action, approval or authorization of, or registration,
declaration or filing with, any governmental department, commission, agency or
other instrumentality or any other person or entity is required to authorize, or
is otherwise required in connection with, the execution and delivery of this
Agreement (with the exception of an amended Schedule 13D to be filed by the
Shareholder pursuant to the Exchange Act) or the Shareholder's performance of
the terms of this Agreement or the validity or enforceability of this Agreement.

     (h) This Agreement shall be binding upon, and inure to the benefit of, the
parties hereto and their respective heirs, personal representatives, successors,
assigns and Affiliates, but shall not be assignable by either party hereto
without the prior written consent of the other party hereto.

     (i) No party may waive any of the terms or conditions of this Agreement
except by a duly signed writing referring to the specific provision to be
waived.

     (j) This Agreement shall be governed by, and construed in accordance with,
the laws of the State of Texas, regardless of the laws that might otherwise
govern under applicable principles of conflicts of law; provided, however, that
any matter involving the internal corporate affairs of any party hereto shall be
governed by the provisions of the Business Corporation Law of the Commonwealth
of Pennsylvania.

     (k) This Agreement constitutes the entire agreement, and supersedes all
other and prior agreements and understandings, both written and oral, among the
parties hereto and their Affiliates.

     (l) This Agreement may be executed in two or more counterparts, each of
which shall be deemed an original but all of which shall constitute one and the
same instrument.

                                      -5-
<PAGE>
 
     IN WITNESS WHEREOF, the Shareholder has executed this Agreement and the
Acquiror has caused this Agreement to be duly executed by an officer, thereunto
duly authorized, all as of the day and year first above written.

                                 HALLIBURTON COMPANY


                                 By: /s/ Lester L. Coleman
                                    ----------------------------
                                    Lester L. Coleman
                                    Executive Vice President and General Counsel
 
                                 SHAREHOLDER

                                 /s/ Melvin N. Miller
                                 ------------------------------- 
                                 Melvin N. Miller

                                      -7-
 
<PAGE>
 
                               VOTING AGREEMENT


     VOTING AGREEMENT ("Agreement") dated as of June 9, 1997, between
Halliburton Company, a Delaware corporation (the "Acquiror"), and Barry M. Davis
(the "Shareholder"), a holder of common shares, par value $0.01 per share, of
NUMAR Corporation, a Pennsylvania corporation (the "Company").

                                   RECITALS:

     The Shareholder beneficially owns an aggregate of 723,144 common shares
(together with any additional common shares as to which beneficial ownership is
acquired by any member of the Shareholder Group described below, the "Company
Shares"), par value $0.01 per share ("Company Common Shares"), of the Company.

     The Acquiror is prepared to enter into an Agreement and Plan of Merger with
the Company (the "Plan") providing for the merger of a wholly owned subsidiary
of Acquiror with and into the Company and the conversion in such merger of each
Company Common Share into the number of shares of the Common Stock, par value
$2.50 per share, of the Acquiror set forth in the Plan (the "Merger").

     To facilitate the Merger, the Shareholder is willing to enter into certain
arrangements with respect to the Company Shares.

     NOW, THEREFORE, in consideration of the premises set forth above, the
mutual promises set forth below, and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties hereto
agree as follows:

1.   Shareholder's Support of the Merger.  From the date hereof until
December 31, 1997, or, if earlier, termination of the Plan:

          (a) Except as contemplated by the Plan or hereby, neither the
     Shareholder nor any Person controlled by the Shareholder, other than the
     Company and its subsidiaries (collectively, the "Shareholder Group"), will,
     directly or indirectly, sell, transfer, pledge or otherwise dispose of, or
     grant a proxy with respect to, any Company Shares to any Person other than
     any member of the Shareholder Group or the Acquiror or its designee, or
     grant an option with respect to any of the Company Shares or enter into any
     other agreement or arrangement with respect to any of the Company Shares.

          (b) The Shareholder agrees that the Shareholder will vote, and will
     cause each member of the Shareholder Group to vote, all Company Shares
     entitled to vote and beneficially owned by such Persons (i) in favor of the
     Merger and (ii), subject to the provisions of paragraph (c) below, against
     any combination proposal or other matter that may 
<PAGE>
 
     (in the reasonable opinion of the Acquiror) interfere or be inconsistent
     with the Merger (including without limitation a Competing Transaction).

          (c) The Shareholder agrees that, if requested by the Acquiror in
     writing in order to facilitate the Merger, the Shareholder will not, and
     will cause each member of the Shareholder Group not to, attend or vote any
     Company Shares beneficially owned by any such Person at any annual or
     special meeting of shareholders or execute any written consent of
     shareholders

          (d) Neither the Shareholder nor any other member of the Shareholder
     Group will initiate, solicit or encourage (including by way of furnishing
     information or assistance), or take any other action to facilitate, any
     inquiries or the making of any proposal that constitutes, or that may
     reasonably be expected to lead to, any merger, consolidation, share
     exchange, business combination or similar transaction involving the Company
     or any of its Significant Subsidiaries, a sale, lease, exchange, transfer
     or other disposition of 50% or more of the assets of the Company and its
     subsidiaries, taken as a whole, in a single transaction or series of
     transactions, the acquisition by a Person or Group of beneficial ownership
     or the right to acquire beneficial ownership of 50% or more of the
     outstanding Company Common Shares, whether by tender offer, exchange offer
     or otherwise, or the acquisition in any manner, directly or indirectly, of
     a material equity interest in any voting securities of, or a substantial
     portion of the assets of, the Company or any of its Significant
     Subsidiaries, other than the transactions contemplated by the Plan (a
     "Competing Transaction"), or enter into discussions or negotiate with any
     Person in furtherance of such inquiries or to obtain a Competing
     Transaction, or agree to or endorse any Competing Transaction, or authorize
     or permit any of the officers, directors or employees of the Shareholder or
     any member of the Shareholder Group or any investment banker, financial
     advisor, attorney, accountant or other representative retained by the
     Shareholder or any other member of the Shareholder Group to take any such
     action. The Shareholder shall promptly notify the Acquiror of all relevant
     terms of any such inquiries or proposals received by such Shareholder or
     any other member of the Shareholder Group or by any such officer, director,
     employee, investment banker, financial advisor, attorney, accountant or
     other representative relating to any of such matters and, if such inquiry
     or proposal is in writing, such Shareholder shall deliver or cause to be
     delivered to the Acquiror a copy of such inquiry or proposal.

          (e) The Shareholder hereby consents to the Acquiror's announcement in
     any press release, public filing, advertisement or other document, that the
     Shareholder has entered into this Agreement.

          (f) To the extent inconsistent with the provisions of this Section 1,
     the Shareholder hereby revokes, and will cause each member of the
     Shareholder Group to revoke, any and all proxies with respect to such
     member's Company Common Shares or any other voting securities of the
     Company.

                                      -2-
<PAGE>
 
2.   Miscellaneous

     (a) The Shareholder, on the one hand, and the Acquiror, on the other,
acknowledge and agree that irreparable damage would occur if any of the
provisions of this Agreement were not performed in accordance with their
specific terms or were otherwise breached.  It is accordingly agreed that the
parties hereto shall be entitled to an injunction or injunctions to prevent
breaches of the provisions of this Agreement and to enforce specifically the
terms and provisions hereof in any court of the United States or any state
thereof having jurisdiction, in addition to any other remedies to which they may
be entitled at law or equity.

     (b) Descriptive headings are for convenience only and shall not control or
affect the meaning or construction of any provision of this Agreement.

     (c) All notices, consents, requests, instructions, approvals and other
communications provided for herein shall be validly given, made or served, if in
writing and delivered personally, by telecopier (subject to receipt of
electronic confirmation) or sent by registered mail, postage prepaid:

     If to the Acquiror:

               Halliburton Company
               3600 Lincoln Plaza
               500 N. Akard Street
               Dallas, Texas  75201-3391
               Attention:  Lester L. Coleman
                          Executive Vice President
                              and General Counsel
               Telecopier No.:  (214) 978-2658

               with a copy to:

                    Vinson & Elkins L.L.P.
                    First City Tower
                    1001 Fannin
                    Houston, Texas  77002-6760
                    Attention:  William E. Joor III
                    Telecopier No.:  (713) 758-2346

                                      -3-
<PAGE>
 
     If to the Shareholder:


               Davis Venture Partners, L.P.
               320 South Boston, Suite 1000
               Tulsa, Oklahoma  74103
               Attention: Barry M.Davis 
               Telecopier No.:  (918) 582-3404
 
or to such other address or telecopier number as any party may, from time to
time, designate in a written notice given in a like manner.  Notice given by
telecopier shall be deemed delivered on the day the sender receives telecopier
confirmation that such notice was received at the telecopier number of the
addressee.  Notice given by mail as set out above shall be deemed delivered
three days after the date the same is postmarked.

     (d) From and after the termination of this Agreement, the covenants of the
parties set forth herein shall be of no further force or effect and the parties
shall be under no further obligation with respect thereto.

     (e) For purposes of this Agreement, the following terms shall have the
following meanings:

         (i)   Affiliate.  "Affiliate" shall have the meaning ascribed to it in
               ---------                                                       
     Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
     in effect on the date hereof.

         (ii)  Associate.  "Associate" shall have the meaning ascribed to it in
               ---------
     Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
     in effect on the date hereof.

         (iii) Beneficial Owner.  A person shall be deemed a "beneficial owner"
               ----------------                                                
     of or to have "beneficial ownership" of Company Shares in accordance with
     the interpretations of the term "beneficial ownership" as defined in Rule
     13-d(3) under the Exchange Act, as in effect on the date hereof, provided
     that a person shall be deemed to be the beneficial owner of, and to have
     beneficial ownership of, Company Shares that such Person or any Affiliate
     of such Person has the right to acquire (whether such right is exercisable
     immediately or only after the passage of time) pursuant to any agreement,
     arrangement or understanding or upon the exercise of conversion rights,
     exchange rights, warrant, options or otherwise.

         (iv)  Exchange Act.  "Exchange Act" shall mean the Securities Exchange
               ------------
Act of 1934, as amended.

                                      -4-
<PAGE>
 
         (v)   Person.  A "Person" shall mean any individual, firm, corporation,
               ------                                                           
     partnership, trust, limited liability company or other entity.

         (vi)  Significant Subsidiary.  "Significant Subsidiary" shall have the
               ----------------------                                          
     meaning ascribed to it in Rule 1-02 of SEC Regulation S-X as in effect on
     the date hereof.

     (g) The Shareholder hereby represents and warrants to the Acquiror as
follows:  The Shareholder has full power and authority to enter into this
Agreement; neither the execution or delivery of this Agreement nor the
consummation of the transactions contemplated herein will (i) conflict with or
result in a breach, default or violation of (A) any of the terms, provisions or
conditions of the certificate of incorporation or bylaws of any member of the
Shareholder Group or (B) any agreement, proxy, document, instrument, judgment,
decree, order, governmental permit, certificate, license, law, statute, rule or
regulation to which any member of the Shareholder Group is a party or to which
it is subject, (ii) result in the creation of any lien, charge or other
encumbrance on any Company Common Shares or (iii) require any member of the
Shareholder Group to obtain the consent of any private nongovernmental third
party; and no consent, action, approval or authorization of, or registration,
declaration or filing with, any governmental department, commission, agency or
other instrumentality or any other person or entity is required to authorize, or
is otherwise required in connection with, the execution and delivery of this
Agreement (with the exception of an amended Schedule 13D to be filed by the
Shareholder pursuant to the Exchange Act) or the Shareholder's performance of
the terms of this Agreement or the validity or enforceability of this Agreement.

     (h) This Agreement shall be binding upon, and inure to the benefit of, the
parties hereto and their respective heirs, personal representatives, successors,
assigns and Affiliates, but shall not be assignable by either party hereto
without the prior written consent of the other party hereto.

     (i) No party may waive any of the terms or conditions of this Agreement
except by a duly signed writing referring to the specific provision to be
waived.

     (j) This Agreement shall be governed by, and construed in accordance with,
the laws of the State of Texas, regardless of the laws that might otherwise
govern under applicable principles of conflicts of law; provided, however, that
any matter involving the internal corporate affairs of any party hereto shall be
governed by the provisions of the Business Corporation Law of the Commonwealth
of Pennsylvania.

     (k) This Agreement constitutes the entire agreement, and supersedes all
other and prior agreements and understandings, both written and oral, among the
parties hereto and their Affiliates.

                                      -5-
<PAGE>
 
     (l) This Agreement may be executed in two or more counterparts, each of
which shall be deemed an original but all of which shall constitute one and the
same instrument.

                                      -6-
<PAGE>
 
     IN WITNESS WHEREOF, the Shareholder has executed this Agreement and the
Acquiror has caused this Agreement to be duly executed by an officer, thereunto
duly authorized, all as of the day and year first above written.

                                 HALLIBURTON COMPANY


                                 By:/s/ Lester L. Coleman
                                    ------------------------------
                                    Lester L. Coleman
                                    Executive Vice President and General Counsel
 
                                 SHAREHOLDER

                                 /s/ Barry M. Davis
                                 --------------------------------
                                 Barry M. Davis

                                      -7-
<PAGE>
 
                               VOTING AGREEMENT


     VOTING AGREEMENT ("Agreement") dated as of June 9, 1997, between
Halliburton Company, a Delaware corporation (the "Acquiror"), and Seymour G.
Mandell (the "Shareholder"), a holder of common shares, par value $0.01 per
share, of NUMAR Corporation, a Pennsylvania corporation (the "Company").

                                   RECITALS:

     The Shareholder beneficially owns an aggregate of 174,771 common shares
(together with any additional common shares as to which beneficial ownership is
acquired by any member of the Shareholder Group described below, the "Company
Shares"), par value $0.01 per share ("Company Common Shares"), of the Company.

     The Acquiror is prepared to enter into an Agreement and Plan of Merger with
the Company (the "Plan") providing for the merger of a wholly owned subsidiary
of Acquiror with and into the Company and the conversion in such merger of each
Company Common Share into the number of shares of the Common Stock, par value
$2.50 per share, of the Acquiror set forth in the Plan (the "Merger").

     To facilitate the Merger, the Shareholder is willing to enter into certain
arrangements with respect to the Company Shares.

     NOW, THEREFORE, in consideration of the premises set forth above, the
mutual promises set forth below, and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties hereto
agree as follows:

1.   Shareholder's Support of the Merger. From the date hereof until December
31, 1997, or, if earlier, termination of the Plan:

          (a) Except as contemplated by the Plan or hereby, neither the
     Shareholder nor any Person controlled by the Shareholder, other than the
     Company and its subsidiaries (collectively, the "Shareholder Group"), will,
     directly or indirectly, sell, transfer, pledge or otherwise dispose of, or
     grant a proxy with respect to, any Company Shares to any Person other than
     any member of the Shareholder Group or the Acquiror or its designee, or
     grant an option with respect to any of the Company Shares or enter into any
     other agreement or arrangement with respect to any of the Company Shares.

          (b) The Shareholder agrees that the Shareholder will vote, and will
     cause each member of the Shareholder Group to vote, all Company Shares
     entitled to vote and beneficially owned by such Persons (i) in favor of the
     Merger and (ii), subject to the provisions of paragraph (c) below, against
     any combination proposal or other matter that may
<PAGE>
 
     (in the reasonable opinion of the Acquiror) interfere or be inconsistent
     with the Merger (including without limitation a Competing Transaction).

          (c) The Shareholder agrees that, if requested by the Acquiror in
     writing in order to facilitate the Merger, the Shareholder will not, and
     will cause each member of the Shareholder Group not to, attend or vote any
     Company Shares beneficially owned by any such Person at any annual or
     special meeting of shareholders or execute any written consent of
     shareholders

          (d) Neither the Shareholder nor any other member of the Shareholder
     Group will initiate, solicit or encourage (including by way of furnishing
     information or assistance), or take any other action to facilitate, any
     inquiries or the making of any proposal that constitutes, or that may
     reasonably be expected to lead to, any merger, consolidation, share
     exchange, business combination or similar transaction involving the Company
     or any of its Significant Subsidiaries, a sale, lease, exchange, transfer
     or other disposition of 50% or more of the assets of the Company and its
     subsidiaries, taken as a whole, in a single transaction or series of
     transactions, the acquisition by a Person or Group of beneficial ownership
     or the right to acquire beneficial ownership of 50% or more of the
     outstanding Company Common Shares, whether by tender offer, exchange offer
     or otherwise, or the acquisition in any manner, directly or indirectly, of
     a material equity interest in any voting securities of, or a substantial
     portion of the assets of, the Company or any of its Significant
     Subsidiaries, other than the transactions contemplated by the Plan (a
     "Competing Transaction"), or enter into discussions or negotiate with any
     Person in furtherance of such inquiries or to obtain a Competing
     Transaction, or agree to or endorse any Competing Transaction, or authorize
     or permit any of the officers, directors or employees of the Shareholder or
     any member of the Shareholder Group or any investment banker, financial
     advisor, attorney, accountant or other representative retained by the
     Shareholder or any other member of the Shareholder Group to take any such
     action. The Shareholder shall promptly notify the Acquiror of all relevant
     terms of any such inquiries or proposals received by such Shareholder or
     any other member of the Shareholder Group or by any such officer, director,
     employee, investment banker, financial advisor, attorney, accountant or
     other representative relating to any of such matters and, if such inquiry
     or proposal is in writing, such Shareholder shall deliver or cause to be
     delivered to the Acquiror a copy of such inquiry or proposal.

          (e) The Shareholder hereby consents to the Acquiror's announcement in
     any press release, public filing, advertisement or other document, that the
     Shareholder has entered into this Agreement.

          (f) To the extent inconsistent with the provisions of this Section 1,
     the Shareholder hereby revokes, and will cause each member of the
     Shareholder Group to revoke, any and all proxies with respect to such
     member's Company Common Shares or any other voting securities of the
     Company.
 
                                      -2-
<PAGE>
 
2.   Miscellaneous

     (a) The Shareholder, on the one hand, and the Acquiror, on the other,
acknowledge and agree that irreparable damage would occur if any of the
provisions of this Agreement were not performed in accordance with their
specific terms or were otherwise breached.  It is accordingly agreed that the
parties hereto shall be entitled to an injunction or injunctions to prevent
breaches of the provisions of this Agreement and to enforce specifically the
terms and provisions hereof in any court of the United States or any state
thereof having jurisdiction, in addition to any other remedies to which they may
be entitled at law or equity.

     (b) Descriptive headings are for convenience only and shall not control or
affect the meaning or construction of any provision of this Agreement.

     (c) All notices, consents, requests, instructions, approvals and other
communications provided for herein shall be validly given, made or served, if in
writing and delivered personally, by telecopier (subject to receipt of
electronic confirmation) or sent by registered mail, postage prepaid:

     If to the Acquiror:

               Halliburton Company
               3600 Lincoln Plaza
               500 N. Akard Street
               Dallas, Texas  75201-3391
               Attention:  Lester L. Coleman
                          Executive Vice President
                              and General Counsel
               Telecopier No.:  (214) 978-2658

               with a copy to:

                    Vinson & Elkins L.L.P.
                    First City Tower
                    1001 Fannin
                    Houston, Texas  77002-6760
                    Attention:  William E. Joor III
                    Telecopier No.:  (713) 758-2346

                                      -3-
<PAGE>
 
     If to the Shareholder:

               Melvin N. Miller  
               c/o NUMAR Corporation
               508 Lapp Road
               Malvern, Pennsylvania 19355
               Telecopier No.:  (610) 644-8131
 
or to such other address or telecopier number as any party may, from time to
time, designate in a written notice given in a like manner.  Notice given by
telecopier shall be deemed delivered on the day the sender receives telecopier
confirmation that such notice was received at the telecopier number of the
addressee.  Notice given by mail as set out above shall be deemed delivered
three days after the date the same is postmarked.

     (d) From and after the termination of this Agreement, the covenants of the
parties set forth herein shall be of no further force or effect and the parties
shall be under no further obligation with respect thereto.

     (e) For purposes of this Agreement, the following terms shall have the
following meanings:

         (i)   Affiliate.  "Affiliate" shall have the meaning ascribed to it in
               ---------                                                       
     Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
     in effect on the date hereof.

         (ii)  Associate.  "Associate" shall have the meaning ascribed to it in
               ---------  
     Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
     in effect on the date hereof.

         (iii) Beneficial Owner.  A person shall be deemed a "beneficial owner"
               ----------------                                                
     of or to have "beneficial ownership" of Company Shares in accordance with
     the interpretations of the term "beneficial ownership" as defined in Rule
     13-d(3) under the Exchange Act, as in effect on the date hereof, provided
     that a person shall be deemed to be the beneficial owner of, and to have
     beneficial ownership of, Company Shares that such Person or any Affiliate
     of such Person has the right to acquire (whether such right is exercisable
     immediately or only after the passage of time) pursuant to any agreement,
     arrangement or understanding or upon the exercise of conversion rights,
     exchange rights, warrant, options or otherwise.

         (iv)  Exchange Act.  "Exchange Act" shall mean the Securities Exchange
               ------------
Act of 1934, as amended.

                                      -4-
<PAGE>
 
         (v)   Person.  A "Person" shall mean any individual, firm, corporation,
               ------                                                           
     partnership, trust, limited liability company or other entity.

         (vi)  Significant Subsidiary.  "Significant Subsidiary" shall have the
               ----------------------                                          
     meaning ascribed to it in Rule 1-02 of SEC Regulation S-X as in effect on
     the date hereof.

     (g) The Shareholder hereby represents and warrants to the Acquiror as
follows:  The Shareholder has full power and authority to enter into this
Agreement; neither the execution or delivery of this Agreement nor the
consummation of the transactions contemplated herein will (i) conflict with or
result in a breach, default or violation of (A) any of the terms, provisions or
conditions of the certificate of incorporation or bylaws of any member of the
Shareholder Group or (B) any agreement, proxy, document, instrument, judgment,
decree, order, governmental permit, certificate, license, law, statute, rule or
regulation to which any member of the Shareholder Group is a party or to which
it is subject, (ii) result in the creation of any lien, charge or other
encumbrance on any Company Common Shares or (iii) require any member of the
Shareholder Group to obtain the consent of any private nongovernmental third
party; and no consent, action, approval or authorization of, or registration,
declaration or filing with, any governmental department, commission, agency or
other instrumentality or any other person or entity is required to authorize, or
is otherwise required in connection with, the execution and delivery of this
Agreement (with the exception of an amended Schedule 13D to be filed by the
Shareholder pursuant to the Exchange Act) or the Shareholder's performance of
the terms of this Agreement or the validity or enforceability of this Agreement.

     (h) This Agreement shall be binding upon, and inure to the benefit of, the
parties hereto and their respective heirs, personal representatives, successors,
assigns and Affiliates, but shall not be assignable by either party hereto
without the prior written consent of the other party hereto.

     (i) No party may waive any of the terms or conditions of this Agreement
except by a duly signed writing referring to the specific provision to be
waived.

     (j) This Agreement shall be governed by, and construed in accordance with,
the laws of the State of Texas, regardless of the laws that might otherwise
govern under applicable principles of conflicts of law; provided, however, that
any matter involving the internal corporate affairs of any party hereto shall be
governed by the provisions of the Business Corporation Law of the Commonwealth
of Pennsylvania.

     (k) This Agreement constitutes the entire agreement, and supersedes all
other and prior agreements and understandings, both written and oral, among the
parties hereto and their Affiliates.

                                      -5-
<PAGE>
 
     (l) This Agreement may be executed in two or more counterparts, each of
which shall be deemed an original but all of which shall constitute one and the
same instrument.

                                      -6-
<PAGE>
 
     IN WITNESS WHEREOF, the Shareholder has executed this Agreement and the
Acquiror has caused this Agreement to be duly executed by an officer, thereunto
duly authorized, all as of the day and year first above written.


                                 HALLIBURTON COMPANY


                                 By:/s/ Lester L. Coleman
                                    ------------------------------
                                    Lester L. Coleman
                                    Executive Vice President and General Counsel
 
                                 SHAREHOLDER

                                 /s/ Seymour G. Mandell
                                 ---------------------------------
                                 Seymour G. Mandell

                                      -6-
<PAGE>
 
                               VOTING AGREEMENT


     VOTING AGREEMENT ("Agreement") dated as of June 9, 1997, between
Halliburton Company, a Delaware corporation (the "Acquiror"), and James H.
Simons (the "Shareholder"), a holder of common shares, par value $0.01 per
share, of NUMAR Corporation, a Pennsylvania corporation (the "Company").

                                   RECITALS:

     The Shareholder beneficially owns an aggregate of 13,434 common shares
(together with any additional common shares as to which beneficial ownership is
acquired by any member of the Shareholder Group described below, the "Company
Shares"), par value $0.01 per share ("Company Common Shares"), of the Company.

     The Acquiror is prepared to enter into an Agreement and Plan of Merger with
the Company (the "Plan") providing for the merger of a wholly owned subsidiary
of Acquiror with and into the Company and the conversion in such merger of each
Company Common Share into the number of shares of the Common Stock, par value
$2.50 per share, of the Acquiror set forth in the Plan (the "Merger").

     To facilitate the Merger, the Shareholder is willing to enter into certain
arrangements with respect to the Company Shares.

     NOW, THEREFORE, in consideration of the premises set forth above, the
mutual promises set forth below, and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties hereto
agree as follows:

1.   Shareholder's Support of the Merger. From the date hereof until December
31, 1997, or, if earlier, termination of the Plan:

          (a) Except as contemplated by the Plan or hereby, neither the
     Shareholder nor any Person controlled by the Shareholder, other than the
     Company and its subsidiaries (collectively, the "Shareholder Group"), will,
     directly or indirectly, sell, transfer, pledge or otherwise dispose of, or
     grant a proxy with respect to, any Company Shares to any Person other than
     any member of the Shareholder Group or the Acquiror or its designee, or
     grant an option with respect to any of the Company Shares or enter into any
     other agreement or arrangement with respect to any of the Company Shares.

          (b) The Shareholder agrees that the Shareholder will vote, and will
     cause each member of the Shareholder Group to vote, all Company Shares
     entitled to vote and beneficially owned by such Persons (i) in favor of the
     Merger and (ii), subject to the provisions of paragraph (c) below, against
     any combination proposal or other matter that may 
<PAGE>
 
     (in the reasonable opinion of the Acquiror) interfere or be inconsistent
     with the Merger (including without limitation a Competing Transaction).

          (c) The Shareholder agrees that, if requested by the Acquiror in
     writing in order to facilitate the Merger, the Shareholder will not, and
     will cause each member of the Shareholder Group not to, attend or vote any
     Company Shares beneficially owned by any such Person at any annual or
     special meeting of shareholders or execute any written consent of
     shareholders

          (d) Neither the Shareholder nor any other member of the Shareholder
     Group will initiate, solicit or encourage (including by way of furnishing
     information or assistance), or take any other action to facilitate, any
     inquiries or the making of any proposal that constitutes, or that may
     reasonably be expected to lead to, any merger, consolidation, share
     exchange, business combination or similar transaction involving the Company
     or any of its Significant Subsidiaries, a sale, lease, exchange, transfer
     or other disposition of 50% or more of the assets of the Company and its
     subsidiaries, taken as a whole, in a single transaction or series of
     transactions, the acquisition by a Person or Group of beneficial ownership
     or the right to acquire beneficial ownership of 50% or more of the
     outstanding Company Common Shares, whether by tender offer, exchange offer
     or otherwise, or the acquisition in any manner, directly or indirectly, of
     a material equity interest in any voting securities of, or a substantial
     portion of the assets of, the Company or any of its Significant
     Subsidiaries, other than the transactions contemplated by the Plan (a
     "Competing Transaction"), or enter into discussions or negotiate with any
     Person in furtherance of such inquiries or to obtain a Competing
     Transaction, or agree to or endorse any Competing Transaction, or authorize
     or permit any of the officers, directors or employees of the Shareholder or
     any member of the Shareholder Group or any investment banker, financial
     advisor, attorney, accountant or other representative retained by the
     Shareholder or any other member of the Shareholder Group to take any such
     action. The Shareholder shall promptly notify the Acquiror of all relevant
     terms of any such inquiries or proposals received by such Shareholder or
     any other member of the Shareholder Group or by any such officer, director,
     employee, investment banker, financial advisor, attorney, accountant or
     other representative relating to any of such matters and, if such inquiry
     or proposal is in writing, such Shareholder shall deliver or cause to be
     delivered to the Acquiror a copy of such inquiry or proposal.

          (e) The Shareholder hereby consents to the Acquiror's announcement in
     any press release, public filing, advertisement or other document, that the
     Shareholder has entered into this Agreement.

          (f) To the extent inconsistent with the provisions of this Section 1,
     the Shareholder hereby revokes, and will cause each member of the
     Shareholder Group to revoke, any and all proxies with respect to such
     member's Company Common Shares or any other voting securities of the
     Company.
 
                                      -2-
<PAGE>
 
2.   Miscellaneous

     (a) The Shareholder, on the one hand, and the Acquiror, on the other,
acknowledge and agree that irreparable damage would occur if any of the
provisions of this Agreement were not performed in accordance with their
specific terms or were otherwise breached.  It is accordingly agreed that the
parties hereto shall be entitled to an injunction or injunctions to prevent
breaches of the provisions of this Agreement and to enforce specifically the
terms and provisions hereof in any court of the United States or any state
thereof having jurisdiction, in addition to any other remedies to which they may
be entitled at law or equity.

     (b) Descriptive headings are for convenience only and shall not control or
affect the meaning or construction of any provision of this Agreement.

     (c) All notices, consents, requests, instructions, approvals and other
communications provided for herein shall be validly given, made or served, if in
writing and delivered personally, by telecopier (subject to receipt of
electronic confirmation) or sent by registered mail, postage prepaid:

          If to the Acquiror:

               Halliburton Company
               3600 Lincoln Plaza
               500 N. Akard Street
               Dallas, Texas  75201-3391
               Attention: Lester L. Coleman
                          Executive Vice President
                              and General Counsel
               Telecopier No.:  (214) 978-2658

               with a copy to:

                    Vinson & Elkins L.L.P.
                    First City Tower
                    1001 Fannin
                    Houston, Texas  77002-6760
                    Attention:  William E. Joor III
                    Telecopier No.:  (713) 758-2346

                                      -3-
<PAGE>
 
          If to the Shareholder:

               James H. Simons
               c/o Renaissance Technologies
               800 Third Avenue
               New York, New York  10022
 
or to such other address or telecopier number as any party may, from time to
time, designate in a written notice given in a like manner.  Notice given by
telecopier shall be deemed delivered on the day the sender receives telecopier
confirmation that such notice was received at the telecopier number of the
addressee.  Notice given by mail as set out above shall be deemed delivered
three days after the date the same is postmarked.

     (d) From and after the termination of this Agreement, the covenants of the
parties set forth herein shall be of no further force or effect and the parties
shall be under no further obligation with respect thereto.

     (e) For purposes of this Agreement, the following terms shall have the
following meanings:

         (i)   Affiliate.  "Affiliate" shall have the meaning ascribed to it in
               ----------                                                       
     Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
     in effect on the date hereof.

         (ii)  Associate.  "Associate" shall have the meaning ascribed to it in
               ----------
     Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
     in effect on the date hereof.

         (iii) Beneficial Owner.  A person shall be deemed a "beneficial owner"
               -----------------                                                
     of or to have "beneficial ownership" of Company Shares in accordance with
     the interpretations of the term "beneficial ownership" as defined in Rule
     13-d(3) under the Exchange Act, as in effect on the date hereof, provided
     that a person shall be deemed to be the beneficial owner of, and to have
     beneficial ownership of, Company Shares that such Person or any Affiliate
     of such Person has the right to acquire (whether such right is exercisable
     immediately or only after the passage of time) pursuant to any agreement,
     arrangement or understanding or upon the exercise of conversion rights,
     exchange rights, warrant, options or otherwise.

         (iv)  Exchange Act.  "Exchange Act" shall mean the Securities Exchange
               ------------- 
     Act of 1934, as amended.

         (v)   Person.  A "Person" shall mean any individual, firm, corporation,
               -------                                                         
     partnership, trust, limited liability company or other entity.

                                      -4-
<PAGE>
 
         (vi) Significant Subsidiary.  "Significant Subsidiary" shall have the
              ----------------------                                          
     meaning ascribed to it in Rule 1-02 of SEC Regulation S-X as in effect on
     the date hereof.

     (g) The Shareholder hereby represents and warrants to the Acquiror as
follows:  The Shareholder has full power and authority to enter into this
Agreement; neither the execution or delivery of this Agreement nor the
consummation of the transactions contemplated herein will (i) conflict with or
result in a breach, default or violation of (A) any of the terms, provisions or
conditions of the certificate of incorporation or bylaws of any member of the
Shareholder Group or (B) any agreement, proxy, document, instrument, judgment,
decree, order, governmental permit, certificate, license, law, statute, rule or
regulation to which any member of the Shareholder Group is a party or to which
it is subject, (ii) result in the creation of any lien, charge or other
encumbrance on any Company Common Shares or (iii) require any member of the
Shareholder Group to obtain the consent of any private nongovernmental third
party; and no consent, action, approval or authorization of, or registration,
declaration or filing with, any governmental department, commission, agency or
other instrumentality or any other person or entity is required to authorize, or
is otherwise required in connection with, the execution and delivery of this
Agreement (with the exception of an amended Schedule 13D to be filed by the
Shareholder pursuant to the Exchange Act) or the Shareholder's performance of
the terms of this Agreement or the validity or enforceability of this Agreement.

     (h) This Agreement shall be binding upon, and inure to the benefit of, the
parties hereto and their respective heirs, personal representatives, successors,
assigns and Affiliates, but shall not be assignable by either party hereto
without the prior written consent of the other party hereto.

     (i) No party may waive any of the terms or conditions of this Agreement
except by a duly signed writing referring to the specific provision to be
waived.

     (j) This Agreement shall be governed by, and construed in accordance with,
the laws of the State of Texas, regardless of the laws that might otherwise
govern under applicable principles of conflicts of law; provided, however, that
any matter involving the internal corporate affairs of any party hereto shall be
governed by the provisions of the Business Corporation Law of the Commonwealth
of Pennsylvania.

     (k) This Agreement constitutes the entire agreement, and supersedes all
other and prior agreements and understandings, both written and oral, among the
parties hereto and their Affiliates.

     (l) This Agreement may be executed in two or more counterparts, each of
which shall be deemed an original but all of which shall constitute one and the
same instrument.

                                      -5-
<PAGE>
 
     IN WITNESS WHEREOF, the Shareholder has executed this Agreement and the
Acquiror has caused this Agreement to be duly executed by an officer, thereunto
duly authorized, all as of the day and year first above written.

                                 HALLIBURTON COMPANY


                                 By:/s/ Lester L. Coleman
                                    -----------------------------
                                    Lester L. Coleman
                                    Executive Vice President and General Counsel
 
                                 SHAREHOLDER


                                 /s/ James H. Simons 
                                 --------------------------------
                                 James H. Simons

                                      -6-
 
<PAGE>
 
                               VOTING AGREEMENT


     VOTING AGREEMENT ("Agreement") dated as of June 9, 1997, between
Halliburton Company, a Delaware corporation (the "Acquiror"), and Bermuda Trust
Company Limited, as Trustee of the Lord Jim Trust (the "Shareholder"), a holder
of common shares, par value $0.01 per share, of NUMAR Corporation, a
Pennsylvania corporation (the "Company").

                                   RECITALS:

     The Shareholder beneficially owns an aggregate of 900,000 common shares
(together with any additional common shares as to which beneficial ownership is
acquired by any member of the Shareholder Group described below, the "Company
Shares"), par value $0.01 per share ("Company Common Shares"), of the Company.

     The Acquiror is prepared to enter into an Agreement and Plan of Merger with
the Company (the "Plan") providing for the merger of a wholly owned subsidiary
of Acquiror with and into the Company and the conversion in such merger of each
Company Common Share into the number of shares of the Common Stock, par value
$2.50 per share, of the Acquiror set forth in the Plan (the "Merger").

     To facilitate the Merger, the Shareholder is willing to enter into certain
arrangements with respect to the Company Shares.

     NOW, THEREFORE, in consideration of the premises set forth above, the
mutual promises set forth below, and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties hereto
agree as follows:

1.   Shareholder's Support of the Merger. From the date hereof until December
31, 1997, or, if earlier, termination of the Plan:

          (a) Except as contemplated by the Plan or hereby, neither the
     Shareholder nor any Person controlled by the Shareholder, other than the
     Company and its subsidiaries (collectively, the "Shareholder Group"), will,
     directly or indirectly, sell, transfer, pledge or otherwise dispose of, or
     grant a proxy with respect to, any Company Shares to any Person other than
     any member of the Shareholder Group or the Acquiror or its designee, or
     grant an option with respect to any of the Company Shares or enter into any
     other agreement or arrangement with respect to any of the Company Shares.

          (b) The Shareholder agrees that the Shareholder will vote, and will
     cause each member of the Shareholder Group to vote, all Company Shares
     entitled to vote and beneficially owned by such Persons (i) in favor of the
     Merger and (ii), subject to the provisions of paragraph (c) below, against
     any combination proposal or other matter that may 
<PAGE>
 
     (in the reasonable opinion of the Acquiror) interfere or be inconsistent
     with the Merger (including without limitation a Competing Transaction).

          (c) The Shareholder agrees that, if requested by the Acquiror in
     writing in order to facilitate the Merger, the Shareholder will not, and
     will cause each member of the Shareholder Group not to, attend or vote any
     Company Shares beneficially owned by any such Person at any annual or
     special meeting of shareholders or execute any written consent of
     shareholders

          (d) Neither the Shareholder nor any other member of the Shareholder
     Group will initiate, solicit or encourage (including by way of furnishing
     information or assistance), or take any other action to facilitate, any
     inquiries or the making of any proposal that constitutes, or that may
     reasonably be expected to lead to, any merger, consolidation, share
     exchange, business combination or similar transaction involving the Company
     or any of its Significant Subsidiaries, a sale, lease, exchange, transfer
     or other disposition of 50% or more of the assets of the Company and its
     subsidiaries, taken as a whole, in a single transaction or series of
     transactions, the acquisition by a Person or Group of beneficial ownership
     or the right to acquire beneficial ownership of 50% or more of the
     outstanding Company Common Shares, whether by tender offer, exchange offer
     or otherwise, or the acquisition in any manner, directly or indirectly, of
     a material equity interest in any voting securities of, or a substantial
     portion of the assets of, the Company or any of its Significant
     Subsidiaries, other than the transactions contemplated by the Plan (a
     "Competing Transaction"), or enter into discussions or negotiate with any
     Person in furtherance of such inquiries or to obtain a Competing
     Transaction, or agree to or endorse any Competing Transaction, or authorize
     or permit any of the officers, directors or employees of the Shareholder or
     any member of the Shareholder Group or any investment banker, financial
     advisor, attorney, accountant or other representative retained by the
     Shareholder or any other member of the Shareholder Group to take any such
     action. The Shareholder shall promptly notify the Acquiror of all relevant
     terms of any such inquiries or proposals received by such Shareholder or
     any other member of the Shareholder Group or by any such officer, director,
     employee, investment banker, financial advisor, attorney, accountant or
     other representative relating to any of such matters and, if such inquiry
     or proposal is in writing, such Shareholder shall deliver or cause to be
     delivered to the Acquiror a copy of such inquiry or proposal.

          (e) The Shareholder hereby consents to the Acquiror's announcement in
     any press release, public filing, advertisement or other document, that the
     Shareholder has entered into this Agreement.

          (f) To the extent inconsistent with the provisions of this Section 1,
     the Shareholder hereby revokes, and will cause each member of the
     Shareholder Group to revoke, any and all proxies with respect to such
     member's Company Common Shares or any other voting securities of the
     Company.
 
                                      -2-
<PAGE>
 
2.   Miscellaneous

     (a) The Shareholder, on the one hand, and the Acquiror, on the other,
acknowledge and agree that irreparable damage would occur if any of the
provisions of this Agreement were not performed in accordance with their
specific terms or were otherwise breached.  It is accordingly agreed that the
parties hereto shall be entitled to an injunction or injunctions to prevent
breaches of the provisions of this Agreement and to enforce specifically the
terms and provisions hereof in any court of the United States or any state
thereof having jurisdiction, in addition to any other remedies to which they may
be entitled at law or equity.

     (b) Descriptive headings are for convenience only and shall not control or
affect the meaning or construction of any provision of this Agreement.

     (c) All notices, consents, requests, instructions, approvals and other
communications provided for herein shall be validly given, made or served, if in
writing and delivered personally, by telecopier (subject to receipt of
electronic confirmation) or sent by registered mail, postage prepaid:

          If to the Acquiror:

                   Halliburton Company
                   3600 Lincoln Plaza
                   500 N. Akard Street
                   Dallas, Texas  75201-3391
                   Attention:  Lester L. Coleman
                               Executive Vice President
                                 and General Counsel
                   Telecopier No.:  (214) 978-2658

                   with a copy to:

                           Vinson & Elkins L.L.P.
                           First City Tower
                           1001 Fannin
                           Houston, Texas  77002-6760
                           Attention:  William E. Joor III
                           Telecopier No.:  (713) 758-2346

                                      -3-
<PAGE>
 
          If to the Shareholder:

                  Murdoch & Co.
                  c/o Bank of Bermuda
                  Compass Point
                  9 Bermuda Road
                  Hamilton, Bermuda
                  Attention:  Susan Gibbons
                  Telecopier No.:  (441) 295-9991

or to such other address or telecopier number as any party may, from time to
time, designate in a written notice given in a like manner.  Notice given by
telecopier shall be deemed delivered on the day the sender receives telecopier
confirmation that such notice was received at the telecopier number of the
addressee.  Notice given by mail as set out above shall be deemed delivered
three days after the date the same is postmarked.

     (d) From and after the termination of this Agreement, the covenants of the
parties set forth herein shall be of no further force or effect and the parties
shall be under no further obligation with respect thereto.

     (e) For purposes of this Agreement, the following terms shall have the
following meanings:

         (i) Affiliate.  "Affiliate" shall have the meaning ascribed to it in
             ---------                                                       
     Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
     in effect on the date hereof.

         (ii) Associate.  "Associate" shall have the meaning ascribed to it in
              --------- 
     Rule 12b-2 of the General Rules and Regulations under the Exchange Act, as
     in effect on the date hereof.

          (iii) Beneficial Owner.  A person shall be deemed a "beneficial owner"
                ----------------                                                
     of or to have "beneficial ownership" of Company Shares in accordance with
     the interpretations of the term "beneficial ownership" as defined in Rule
     13-d(3) under the Exchange Act, as in effect on the date hereof, provided
     that a person shall be deemed to be the beneficial owner of, and to have
     beneficial ownership of, Company Shares that such Person or any Affiliate
     of such Person has the right to acquire (whether such right is exercisable
     immediately or only after the passage of time) pursuant to any agreement,
     arrangement or understanding or upon the exercise of conversion rights,
     exchange rights, warrant, options or otherwise.

          (iv) Exchange Act.  "Exchange Act" shall mean the Securities Exchange
               ------------ 
     Act of 1934, as amended.

                                      -4-
<PAGE>
 
          (v)  Person.  A "Person" shall mean any individual, firm, corporation,
               -------                                                         
     partnership, trust, limited liability company or other entity.

          (vi) Significant Subsidiary.  "Significant Subsidiary" shall have the
               -----------------------                                          
     meaning ascribed to it in Rule 1-02 of SEC Regulation S-X as in effect on
     the date hereof.

     (g) The Shareholder hereby represents and warrants to the Acquiror as
follows:  The Shareholder has full power and authority to enter into this
Agreement; neither the execution or delivery of this Agreement nor the
consummation of the transactions contemplated herein will (i) conflict with or
result in a breach, default or violation of (A) any of the terms, provisions or
conditions of the certificate of incorporation or bylaws of any member of the
Shareholder Group or (B) any agreement, proxy, document, instrument, judgment,
decree, order, governmental permit, certificate, license, law, statute, rule or
regulation to which any member of the Shareholder Group is a party or to which
it is subject, (ii) result in the creation of any lien, charge or other
encumbrance on any Company Common Shares or (iii) require any member of the
Shareholder Group to obtain the consent of any private nongovernmental third
party; and no consent, action, approval or authorization of, or registration,
declaration or filing with, any governmental department, commission, agency or
other instrumentality or any other person or entity is required to authorize, or
is otherwise required in connection with, the execution and delivery of this
Agreement (with the exception of an amended Schedule 13D to be filed by the
Shareholder pursuant to the Exchange Act) or the Shareholder's performance of
the terms of this Agreement or the validity or enforceability of this Agreement.

     (h) This Agreement shall be binding upon, and inure to the benefit of, the
parties hereto and their respective heirs, personal representatives, successors,
assigns and Affiliates, but shall not be assignable by either party hereto
without the prior written consent of the other party hereto.

     (i) No party may waive any of the terms or conditions of this Agreement
except by a duly signed writing referring to the specific provision to be
waived.

     (j) This Agreement shall be governed by, and construed in accordance with,
the laws of the State of Texas, regardless of the laws that might otherwise
govern under applicable principles of conflicts of law; provided, however, that
any matter involving the internal corporate affairs of any party hereto shall be
governed by the provisions of the Business Corporation Law of the Commonwealth
of Pennsylvania.

     (k) This Agreement constitutes the entire agreement, and supersedes all
other and prior agreements and understandings, both written and oral, among the
parties hereto and their Affiliates.

                                      -5-
<PAGE>
 
     (l) This Agreement may be executed in two or more counterparts, each of
which shall be deemed an original but all of which shall constitute one and the
same instrument.

                                      -6-
<PAGE>
 
     IN WITNESS WHEREOF, the Shareholder and the Acquiror have each caused this
Agreement to be duly executed by an officer or other Person, thereunto duly
authorized, all as of the day and year first above written.

                                 HALLIBURTON COMPANY


                                 By:/s/ Lester L. Coleman
                                    ------------------------------------------- 
                                    Lester L. Coleman
                                    Executive Vice President and General Counsel
 
                                 BERMUDA TRUST COMPANY LIMITED,
                                    as Trustee of the Lord Jim Trust


                                  By:/s/ Susan E. Gibbons
                                     ------------------------------------------
                                Name:  Susan E. Gibbons
                                Title: Trust Officer

                                     -7- 

<PAGE>
                                                                      EXHIBIT 99

 
                                  SCHEDULE 13D

- ----------------------------                       -----------------------------
CUSIP No. 67052E105                                  Page 2 of 13 Pages
- --------------------------------------------------------------------------------

1     NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
 
- --------------------------------------------------------------------------------
2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                  (a) [ ]
                                                                         (b) [X]
- --------------------------------------------------------------------------------
3     SEC USE ONLY

- --------------------------------------------------------------------------------
4     SOURCE OF FUNDS*

      Not applicable.

- --------------------------------------------------------------------------------
5     CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO 
      ITEMS 2(d) OR 2(e)                                                     [ ]
- --------------------------------------------------------------------------------
6     CITIZENSHIP OR PLACE OF ORGANIZATION
 
      United States of America

- --------------------------------------------------------------------------------
                         7  SOLE VOTING POWER       
                            362,143
                        --------------------------------------------------------
   NUMBER OF SHARES      8  SHARED VOTING POWER                       
     BENEFICIALLY           -0-                    
     OWNED BY EACH      --------------------------------------------------------
   REPORTING PERSON      9  SOLE DISPOSITIVE POWER 
         WITH               362,143               
                        --------------------------------------------------------
                         9  SHARED DISPOSITIVE POWER                          
                            -0-                     
                        --------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 362,143
- --------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES* [ ]
- --------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) 4.2% (approximate)
- --------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON* IN
- --------------------------------------------------------------------------------

                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
          INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
      (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.


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