MESA ROYALTY TRUST/TX
SC 13D/A, 1999-06-18
OIL ROYALTY TRADERS
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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                 Schedule 13D**

                    Under the Securities Exchange Act of 1934
                               (Amendment No. 13)*

                               Mesa Royalty Trust
                                 (Name of Issuer)

                          Units of Beneficial Interest
                          (Title of Class of Securities)

                                    590660106
                                  (Cusip Number)

                               J. Taylor Crandall
                           201 Main Street, Suite 3100
                             Fort Worth, Texas 76102
                                  (817) 390-8500
                  (Name, Address and Telephone Number of Person
                Authorized to Receive Notices and Communications)

                                  June 16, 1999
             (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(e), 13d-1(f)  or  13d-1(g),  check  the
following box [ ].

*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).

**The  total number of units reported herein is 790,000 units, which constitutes
approximately  42.4%  of the total number of units outstanding.   All  ownership
percentages set forth herein assume that there are 1,863,590 units outstanding.
<PAGE>
1.   Name of Reporting Person:

     Alpine Capital, L.P.

2.   Check the Appropriate Box if a Member of a Group:

                                                  (a) /   /

                                                  (b) / X /

3.   SEC Use Only

4.   Source of Funds: WC

5.   Check  box if Disclosure of Legal Proceedings is Required Pursuant to Items
     2(d) or 2(e):
                                                  /   /

6.   Citizenship or Place of Organization: Texas


               7.   Sole Voting Power: 740,216 (1)
Number of
Units
Beneficially   8.   Shared Voting Power: -0-
Owned By
Each
Reporting      9.   Sole Dispositive Power: 740,216 (1)
Person
With
               10.  Shared Dispositive Power: -0-

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     740,216

12.  Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                  /   /


13.  Percent of Class Represented by Amount in Row (11):  39.7%


14.  Type of Reporting Person: PN

- ------------
(1)  Power  is  exercised through its two general partners, Robert W. Bruce  III
     and Algenpar, Inc.
<PAGE>
1.   Name of Reporting Person:

     Robert W. Bruce III

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: USA


               7.   Sole Voting Power: -0-
Number of
Units
Beneficially   8.   Shared Voting Power: 790,000 (1)
Owned By
Each
Reporting      9.   Sole Dispositive Power: -0-
Person
With
               10.  Shared Dispositive Power: 790,000 (1)

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     790,000 (1)

12.  Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                  /   /

13.  Percent of Class Represented by Amount in Row (11):  42.4%

14.  Type of Reporting Person: IN
- -------------
(1)  Solely  in  his capacity as one of two general partners of Alpine  Capital,
     L.P., with respect to 740,216 units, and in his capacity as a principal  of
     The  Robert  Bruce  Management  Co.,  Inc.,  which  has  shared  investment
     discretion  over units owned by The Anne T. and Robert M. Bass  Foundation,
     with respect to 49,784 units.
<PAGE>
1.   Name of Reporting Person:

     Algenpar, Inc.

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: Texas


               7.   Sole Voting Power: -0-
Number of
Units
Beneficially   8.   Shared Voting Power: 740,216 (1)(2)
Owned By
Each
Reporting      9.   Sole Dispositive Power: -0-
Person
With
               10.  Shared Dispositive Power: 740,216 (1)(2)

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     740,216 (2)

12.  Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                  /   /

13.  Percent of Class Represented by Amount in Row (11):  39.7%

14.  Type of Reporting Person: CO

- ------------
(1)  Power is exercised through its President, J. Taylor Crandall.
(2)  Solely  in  its capacity as one of two general partners of Alpine  Capital,
     L.P.

<PAGE>
1.   Name of Reporting Person:

     J. Taylor Crandall

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: USA


               7.   Sole Voting Power: -0-
Number of
Units
Beneficially   8.   Shared Voting Power: 790,000 (1)
Owned By
Each
Reporting      9.   Sole Dispositive Power: -0-
Person
With
               10.  Shared Dispositive Power: 790,000 (1)

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     790,000 (1)

12.  Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                  /   /

13.  Percent of Class Represented by Amount in Row (11): 42.4%


14.  Type of Reporting Person: IN

- ------------
(1)  Solely in his capacity as President and sole stockholder of Algenpar, Inc.,
     which  is one of two general partners of Alpine Capital, L.P., with respect
     to  740,216  units, and in his capacity as a director of The  Anne  T.  and
     Robert M. Bass Foundation, with respect to 49,784 units.

<PAGE>
1.   Name of Reporting Person:

     The Anne T. and Robert M. Bass Foundation

2.   Check the Appropriate Box if a Member of a Group:

                                                  (a) /   /

                                                  (b) / X /

3.   SEC Use Only


4.   Source of Funds: Working Capital

5.   Check  box if Disclosure of Legal Proceedings is Required Pursuant to Items
     2(d) or 2(e):

                                                  /   /


6.   Citizenship or Place of Organization: Texas


               7.   Sole Voting Power:  49,784 (1)
Number of
Units
Beneficially   8.   Shared Voting Power: -0-
Owned By
Each
Reporting      9.   Sole Dispositive Power:  49,784 (1)
Person
With
               10.  Shared Dispositive Power: -0-

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     49,784

12.  Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                  /   /

13.  Percent of Class Represented by Amount in Row (11):  2.7%

14.  Type of Reporting Person: CO
- ------------
(1)  Power  is  exercised through its three directors, Anne T. Bass,  Robert  M.
     Bass and J. Taylor Crandall and through Robert W. Bruce III in his capacity
     as  a  principal of The Robert Bruce Management Co., Inc., which has shared
     investment  discretion over units owned by The Anne T. and Robert  M.  Bass
     Foundation.

<PAGE>
1.   Name of Reporting Person:

     Anne T. Bass

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: USA


               7.   Sole Voting Power: -0-
Number of
Units
Beneficially   8.   Shared Voting Power:  49,784 (1)
Owned By
Each
Reporting      9.   Sole Dispositive Power: -0-
Person
With
               10.  Shared Dispositive Power:  49,784 (1)

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     49,784 (1)

12.  Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                  /   /


13.  Percent of Class Represented by Amount in Row (11):  2.7%


14.  Type of Reporting Person: IN

- ------------
(1)  Solely  in  her  capacity as a director of The Anne T. and Robert  M.  Bass
     Foundation.

<PAGE>
1.   Name of Reporting Person:

     Robert M. Bass

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: USA


               7.   Sole Voting Power: -0-
Number of
Units
Beneficially   8.   Shared Voting Power:  49,784 (1)
Owned By
Each
Reporting      9.   Sole Dispositive Power: -0-
Person
With
               10.  Shared Dispositive Power:  49,784 (1)

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     49,784 (1)

12.  Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                  /   /


13.  Percent of Class Represented by Amount in Row (11):  2.7%


14.  Type of Reporting Person: IN

- ------------
(1)  Solely  in  his  capacity as a director of The Anne T. and Robert  M.  Bass
     Foundation.

<PAGE>
     Pursuant  to  Rule  13d-2(a) of Regulation 13D-G of the General  Rules  and
Regulations  under the Securities Exchange Act of 1934, as amended (the  "Act"),
the  undersigned hereby amend their Schedule 13D Statement dated June 25,  1993,
as  amended  by Amendment No. 1 dated February 24, 1994, Amendment No.  2  dated
August  30, 1994, Amendment No. 3 dated August 10, 1995, Amendment No.  4  dated
November  10,  1995, Amendment No. 5 dated December 15, 1995,  Amendment  No.  6
dated January 8, 1996, Amendment No. 7 dated February 22, 1996, Amendment No.  8
dated  May 15, 1996, Amendment No. 9 dated July 19, 1996 Amendment No. 10  dated
October 22, 1998, Amendment No. 11 dated November 9, 1998 and Amendment  No.  12
dated March 22, 1999 (as amended, the "Schedule 13D"), relating to the Units  of
Beneficial Interest of Mesa Royalty Trust.

Item 1.   SECURITY AND ISSUER.

     No material change.

Item 2.   IDENTITY AND BACKGROUND.

     No material change.

Item 3.   SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.

Item 3 is hereby amended in its entirety as follows:

     The  source  and  amount  of  the funds used by the  Reporting  Persons  to
purchase Units are as follows:

REPORTING PERSON     SOURCE OF FUNDS        AMOUNT OF FUNDS

     Alpine          Working Capital(1)     $29,564,080.06

     Bruce           Not Applicable         Not Applicable

     Algenpar        Not Applicable         Not Applicable

     Crandall        Not Applicable         Not Applicable

     Foundation      Working Capital(1)     $ 1,942,776.54

     A. Bass         Not Applicable         Not Applicable

     R. Bass         Not Applicable         Not Applicable

     (1)   As  used herein, the term "Working Capital" includes income from  the
business  operations of the entity plus sums borrowed from banks  and  brokerage
firm  margin  accounts to operate such business in general.  None of  the  funds
reported herein as "Working Capital" were borrowed or otherwise obtained for the
specific purpose of acquiring, handling, trading or voting the Stock.

Item 4.   PURPOSE OF TRANSACTION.

     No material change.

Item 5.   INTEREST IN SECURITIES OF THE ISSUER.

     Item 5 is hereby amended and restated in its entirety as follows:

     (a)
     ALPINE

     The  aggregate number of Units that Alpine owns beneficially,  pursuant  to
Rule  13d-3(d)(1)(i)  of  the Act, is 740,216, which  constitutes  approximately
39.7% of the outstanding Units.

     BRUCE

     Because  of  his position as one of two general partners of Alpine  and  as
principal of Bruce Management (which has shared investment discretion  over  the
Units owned by the Foundation), Bruce may, pursuant to Rule 13d-3 of the Act, be
deemed   to  be  the  beneficial  owner  of  790,000  Units,  which  constitutes
approximately 42.4% of the outstanding Units.

     ALGENPAR

     Because  of its position as one of two general partners of Alpine, Algenpar
may, pursuant to Rule 13d-3 of the Act, be deemed to be the beneficial owner  of
740,216 Units, which constitutes approximately 39.7% of the outstanding Units.

     CRANDALL

     Because of his positions as President and sole stockholder of Algenpar, one
of  two general partners of Alpine, and a director of Foundation, Crandall  may,
pursuant  to  Rule  13d-3 of the Act, be deemed to be the  beneficial  owner  of
790,000 Units, which constitutes approximately 42.4% of the outstanding Units.

     FOUNDATION

     The  aggregate number of Units that Foundation owns beneficially,  pursuant
to  Rule  13d-3(d)(1)(i) of the Act, is 49,784, which constitutes  approximately
2.7% of the outstanding Units.

     A. BASS

     Because  of her position as a director of Foundation, A. Bass may, pursuant
to  Rule 13d-3 of the Act, be deemed to be the beneficial owner of 49,784 Units,
which constitutes approximately 2.7% of the outstanding Units.

     R. BASS

     Because  of his position as a director of Foundation, R. Bass may, pursuant
to  Rule 13d-3 of the Act, be deemed to be the beneficial owner of 49,784 Units,
which constitutes approximately 2.7% of the outstanding Units.

     To  the best of the knowledge of each of the Reporting Persons, other  than
as set forth above, none of the persons named in Item 2 herein is the beneficial
owner of any Units.

     (b)

     ALPINE

     Acting through its two general partners, Alpine has the sole power to  vote
or  to  direct the vote and to dispose or to direct the disposition  of  740,216
Units.

     BRUCE
     As one of two general partners of Alpine, Bruce has shared power to vote or
to direct the vote and to dispose or to direct the disposition of 740,216 Units.
As  principal of Bruce Management (which exercises shared investment  discretion
over  the Units owned by the Foundation), Bruce has shared power to vote  or  to
direct the vote and to dispose or to direct the disposition of 49,784 Units.

     ALGENPAR

     As one of two general partners of Alpine, Algenpar has shared power to vote
or  to  direct the vote and to dispose or to direct the disposition  of  740,216
Units.

     CRANDALL

     As  the  President and sole stockholder of Algenpar, which is  one  of  two
general  partners of Alpine, Crandall has shared power to vote or to direct  the
vote  and to dispose or to direct the disposition of 740,216 Units.  As  one  of
three  directors of Foundation, Crandall has shared power to vote or  to  direct
the vote and to dispose or to direct the disposition of 49,784 Units.

     FOUNDATION

     Acting  through  its  three  directors and Bruce  (as  principal  of  Bruce
Management which exercises shared investment discretion over the Units owned  by
the Foundation), Foundation has the sole power to vote or to direct the vote and
to dispose or to direct the disposition of 49,784 Units.

     A. BASS

     As  one of three directors of Foundation, A. Bass has shared power to  vote
or  to  direct  the vote and to dispose or to direct the disposition  of  49,784
Units.

     R. BASS

     As  one of three directors of Foundation, R. Bass has shared power to  vote
or  to  direct  the vote and to dispose or to direct the disposition  of  49,784
Units.

     (c)   In  the  last  60  days, Alpine has purchased Units  in  open  market
transactions on the New York Stock Exchange as follows:

                   NO. OF SHARES   PRICE PER
       DATE         PURCHASED           SHARE

     04/26/99         1,000         $44.03
     04/27/99         2,000          44.43
     05/14/99         1,000          44.16
     05/17/99         2,000          44.53
     06/02/99         1,500          45.03
     06/07/99         1,400          45.37
     06/09/99         4,000          45.54
     06/10/99           400          45.31
     06/11/99         1,100          45.55
     06/15/99         1,200          45.78
     06/16/99         1,400          46.03

     Except as set forth in this paragraph (c), to the best of the knowledge  of
each  of  the  Reporting  Persons, none of the  persons  named  in  response  to
paragraph (a) has effected any transactions in the Units in the last 60 days.

     (d)- (e)

     No material change.

Item 6.   CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH  RESPECT
          TO SECURITIES OF THE ISSUER.

     No material change.

Item 7.   MATERIAL TO BE FILED AS EXHIBITS.

     Exhibit  99.1  --  Agreement  pursuant  to  Rule  13d-1(k)(1)(iii),   filed
herewith.

<PAGE>
     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 17, 1999

                                  ALPINE CAPITAL, L.P.

                                  By: /s/ Robert W. Bruce III
                                      Robert W. Bruce III,
                                      Manager

                                  /s/ Robert W. Bruce
                                  ROBERT W. BRUCE III

                                  ALGENPAR, INC.

                                  By: /s/ J. Taylor Crandall
                                      J. Taylor Crandall,
                                      President


                                  /s/ J. Taylor Crandall
                                  J. TAYLOR CRANDALL

                                  /s/ W. R. Cotham
                                   W. R. Cotham,
                                  Attorney-in-Fact for:

                                  THE ANNE T. AND ROBERT M.
                                    BASS FOUNDATION (1)
                                  ANNE T. BASS (2)
                                  ROBERT M. BASS (3)

(1)  A  Power of Attorney authorizing W. R. Cotham, et al., to act on behalf  of
     The  Anne  T. and Robert M. Bass Foundation previously has been filed  with
     the Securities and Exchange Commission.

(2)  A  Power of Attorney authorizing W. R. Cotham, et al., to act on behalf  of
     Anne  T.  Bass  previously has been filed with the Securities and  Exchange
     Commission.

(3)  A  Power of Attorney authorizing W. R. Cotham, et al., to act on behalf  of
     Robert  M. Bass previously has been filed with the Securities and  Exchange
     Commission.



                                  Exhibit 99.1

      Pursuant to Rule 13d-1(k)(1)(iii) of Regulation 13D-G of the General Rules
and  Regulations of the Securities and Exchange Commission under the  Securities
Exchange  Act of 1934, as amended, the undersigned agrees that the statement  to
which  this  Exhibit  is attached is filed on behalf of  each  of  them  in  the
capacities set forth below.

                                  ALPINE CAPITAL, L.P.

                                  By: /s/ Robert W. Bruce III
                                      Robert W. Bruce III,
                                      Manager

                                  /s/ Robert W. Bruce III
                                  ROBERT W. BRUCE III

                                  ALGENPAR, INC.

                                  By: /s/ J. Taylor Crandall
                                      J. Taylor Crandall,
                                      President

                                  /s/ J. Taylor Crandall
                                  J. TAYLOR CRANDALL

                                   /s/ W. R. Cotham
                                   W. R. Cotham,
                                  Attorney-in-Fact for:

                                  THE ANNE T. AND ROBERT M.
                                    BASS FOUNDATION (1)
                                  ANNE T. BASS (2)
                                  ROBERT M. BASS (3)

(1)  A  Power of Attorney authorizing W. R. Cotham, et al., to act on behalf  of
     The  Anne  T. and Robert M. Bass Foundation previously has been filed  with
     the Securities and Exchange Commission.

(2)  A  Power of Attorney authorizing W. R. Cotham, et al., to act on behalf  of
     Anne  T.  Bass  previously has been filed with the Securities and  Exchange
     Commission.

(3)  A  Power of Attorney authorizing W. R. Cotham, et al., to act on behalf  of
     Robert  M. Bass previously has been filed with the Securities and  Exchange
     Commission.



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