WILLIAMS COMPANIES INC
SC 13G, 1999-02-12
NATURAL GAS TRANSMISSION
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<PAGE>
 
                                 UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549

                                 SCHEDULE 13G

                  Under the Securities Exchange Act of 1934*


                              Williams Companies
- --------------------------------------------------------------------------------
                               (Name of Issuer)


                                 Common Stock
- --------------------------------------------------------------------------------
                        (Title of Class of Securities)

                                   969457100
- --------------------------------------------------------------------------------
                                (CUSIP Number)


                               December 31, 1998
- --------------------------------------------------------------------------------
            (Date of Event Which Requires Filing of this Statement)

Check appropriate box to designate the rule pursuant to which this Schedule is
filed:

    [X] Rule 13d-1(b)

    [_] Rule 13d-1(c)

    [_] Rule 13d-1(d)

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).

                               Page 1 of 4 Pages
<PAGE>
 
- -----------------------                                 
  CUSIP NO.  969457100              13G                 
- -----------------------                                 
 
- ------------------------------------------------------------------------------
      NAME OF REPORTING PERSON
 1    S.S. or I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
                                                                                
      Barrow, Hanley, Mewhinney & Strauss, Inc.
             752403190
- ------------------------------------------------------------------------------
      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
 2                                                              (a) [_]
                                                                (b) [_]
                                                 
- ------------------------------------------------------------------------------
      SEC USE ONLY
 3
 

- ------------------------------------------------------------------------------
      CITIZENSHIP OR PLACE OF ORGANIZATION
 4                                 
      A Neveda corporation

- ------------------------------------------------------------------------------
                          SOLE VOTING POWER
                     5                                                       
     NUMBER OF            4,991,526 shares
 
      SHARES       -----------------------------------------------------------
                          SHARED VOTING POWER
   BENEFICIALLY      6       
                          22,899,105 shares
     OWNED BY
                   -----------------------------------------------------------
       EACH               SOLE DISPOSITIVE POWER
                     7       
    REPORTING             27,890,631 shares
 
      PERSON       -----------------------------------------------------------
                          SHARED DISPOSITIVE POWER
       WITH          8       
                          ---
- ------------------------------------------------------------------------------
      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
 9                           
      27,890,631 shares
- ------------------------------------------------------------------------------
      CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*
10           
                                                                    [_]
 
- ------------------------------------------------------------------------------
      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
11           
      6.5%

- ------------------------------------------------------------------------------
      TYPE OF REPORTING PERSON*
12           
      IA

- ------------------------------------------------------------------------------

                     *SEE INSTRUCTIONS BEFORE FILLING OUT!

                               Page 2 of 4 Pages
<PAGE>
 
SCHEDULE 13G
- ------------


Item 1(a)  Name of Issuer:
                Williams Companies

     1(b)  Address of Issuer's Principal Executive Offices:
                One Williams Center
                Tulsa, OK  74172

Item 2(a)  Name of Person Filing:
                Barrow, Hanley, Mewhinney & Strauss, Inc.

     2(b)  Address of Principal Business Office or, if none, Residence:
                One McKinney Plaza
                3232 McKinney Avenue, 15th Floor
                Dallas, TX  75204-2429

     2(c)  Citizenship:
                A Nevada corporation

     2(d)  Title of Class of Securities:
                Common Stock

     2(e)  CUSIP Number:
                969457100

Item 3     If this statement is filed pursuant to Rules 13d-1(b), or 13d-2(b):
                The reporting person is an Investment Adviser registered under
                Section 203 of the Investment Advisers Act of 1940.

Item 4     Ownership:

      4(a) Amount beneficially owned:
                 27,890,631 shares

     4(b)  Percent of Class:
                 6.5%

     4(c)  Number of shares as to which such person has:

           (i) Sole power to vote or to direct the vote:
                      4,991,526 shares

                               Page 3 of 4 Pages
<PAGE>
 
           (ii) Shared power to vote or to direct the vote:
                     22,899,105 shares

           (iii) Sole power to dispose or to direct the disposition of:
                     27,890,631 shares

           (iv) Shared power to dispose or to direct the disposition of:
                     --

Item 5     Ownership of Five Percent or Less of a Class:
                Not Applicable.

Item 6     Ownership of More than Five Percent on Behalf of Another Person:
                The right to receive or the power to direct the receipt of
                dividends from, or the proceeds from the sale of, the common
                stock is held by certain clients of the reporting person, none
                of which has such right or power with respect to five percent or
                more of the common stock.

Item 7     Identification and Classification of the Subsidiary which Acquired
           the Security Being Reported on by the Parent Holding Company:
                Not Applicable.

Item 8     Identification and Classification of Members of the Group:
                Not Applicable.

Item 9     Notice of Dissolution of Group:
                Not Applicable.

Item 10    Certification:

           By signing below the undersigned certifies that, to the best of its
           knowledge and belief, the securities referred to above were acquired
           in the ordinary course of business and were not acquired for the
           purpose of and do not have the effect of changing or influencing the
           control of the issuer of such securities and were not acquired in
           connection with or as a participant in any transaction having such
           purpose or effect.

After reasonable inquiry and to the best of its knowledge and belief, the
undersigned certifies that the information set forth in this statement is true,
complete and correct.

                                 BARROW, HANLEY, MEWHINNEY &
                                 STRAUSS, INC.


                                 By: /s/ Bryant M. Hanley, Jr.
                                    Name: Bryant M. Hanley, Jr.
                                    Title:   President

February 11, 1999

                               Page 4 of 4 Pages


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