SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                 Schedule 13D**

                    Under the Securities Exchange Act of 1934
                               (Amendment No. 4)*

                                Kirby Corporation
                                (Name of Issuer)

                    Common Stock, Par Value $0.10 Per Share        
                         (Title of Class of Securities)

                                    497266106
                                 (Cusip Number)

                                W. Robert Cotham
                           201 Main Street, Suite 2600
                             Fort Worth, Texas 76102
                                 (817) 390-8400                        
                  (Name, Address and Telephone Number of Person
                Authorized to Receive Notices and Communications)

                                 August 14, 1996
             (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 [ ].

Check the following box if a fee is being paid with the statement [ ].

*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 shares reported herein is 2,489,000 shares, which
constitutes approximately 10.1% of the 24,719,986 shares deemed outstanding
pursuant to Rule 13d-3(d)(1)(i) under the Act.  All other ownership
percentages set forth herein assume that there are 24,714,986 shares
outstanding unless otherwise stated.



1.   Name of Reporting Person:

     Trinity I Fund, 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: Delaware


               7.   Sole Voting Power: 2,484,000 (1) (2)
Number of
Shares
Beneficially   8.   Shared Voting Power: -0-
Owned By
Each
Reporting      9.   Sole Dispositive Power: 2,484,000 (1) (2)
Person
With
               10.  Shared Dispositive Power: -0-

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     2,484,000 (2)

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

                                                       /   /


13.  Percent of Class Represented by Amount in Row (11): 10.1% 


14.  Type of Reporting Person: PN

- ----------
(1)  Power is exercised through its sole general partner, TF Investors, L.P.

(2)  Solely in its capacity as the sole stockholder of Portfolio Associates,
     Inc., which is the sole general partner of Portfolio A Investors, L.P.


1.   Name of Reporting Person:

     TF Investors, 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: Delaware


               7.   Sole Voting Power: 2,484,000 (1) (2)
Number of
Shares
Beneficially   8.   Shared Voting Power: -0-
Owned By
Each
Reporting      9.   Sole Dispositive Power: 2,484,000 (1) (2)
Person
With
               10.  Shared Dispositive Power: -0-

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     2,484,000 (2)

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

                                                       /   /


13.  Percent of Class Represented by Amount in Row (11): 10.1% 


14.  Type of Reporting Person: PN

- ----------
(1)  Power is exercised through its sole general partner, Trinity Capital
     Management, Inc.

(2)  Solely in its capacity as the sole general partner of Trinity I Fund,
     L.P., which is the sole stockholder of Portfolio Associates, Inc., which
     is the sole general partner of Portfolio A Investors, L.P.


1.   Name of Reporting Person:

     Trinity Capital Management, 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: Delaware


               7.   Sole Voting Power: 2,484,000 (1) (2)
Number of
Shares
Beneficially   8.   Shared Voting Power: -0-
Owned By
Each
Reporting      9.   Sole Dispositive Power: 2,484,000 (1) (2)
Person
With
               10.  Shared Dispositive Power: -0-

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     2,484,000 (2)

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

                                                       /   /


13.  Percent of Class Represented by Amount in Row (11): 10.1% 


14.  Type of Reporting Person: CO

- ----------
(1)  Power is exercised through its President, Thomas M. Taylor.

(2)  Solely in its capacity as the sole general partner of TF  Investors,
     L.P., which is the sole general partner of Trinity I Fund, L.P., which is
     the sole stockholder of Portfolio Associates, Inc., which is the sole
     general partner of Portfolio A Investors, L.P.


1.   Name of Reporting Person:

     Thomas M. Taylor

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: 2,484,000 (1)
Number of
Shares
Beneficially   8.   Shared Voting Power: -0-
Owned By
Each
Reporting      9.   Sole Dispositive Power: 2,484,000 (1)
Person
With
               10.  Shared Dispositive Power: -0-

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     2,489,000 (1) (2)

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

                                                       /   /


13.  Percent of Class Represented by Amount in Row (11): 10.1% (3)


14.  Type of Reporting Person: IN

- ----------
(1)  Solely in his capacity as President and sole stockholder of Trinity
     Capital Management, Inc., which is the sole general partner of TF
     Investors, L.P., which is the sole general partner of Trinity I Fund,
     L.P., which is the sole stockholder of Portfolio Associates, Inc., which
     is the sole general partner of Portfolio A Investors, L.P.
(2)  Assumes the exercise of director options held by Mr. Taylor to purchase
     5,000 shares of Common Stock.
(4)  Assumes, pursuant to Rule 13d-3(d)(1)(i) under the Act, that there are
     24,719,986 shares of Common stock outstanding, which  number includes
     options to purchase 5,000 shares of Common Stock held by Mr. Taylor.


1.   Name of Reporting Person:

     Portfolio A Investors, L.P.

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

                                                       (b) / X /

3.   SEC Use Only


4.   Source of Funds: 00 - Partnership Contributions

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


6.   Citizenship or Place of Organization: Delaware


               7.   Sole Voting Power: 2,484,000 (1)
Number of
Shares
Beneficially   8.   Shared Voting Power: -0-
Owned By
Each
Reporting      9.   Sole Dispositive Power: 2,484,000 (1)
Person
With
               10.  Shared Dispositive Power: -0-

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     2,484,000

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

                                                       /   /


13.  Percent of Class Represented by Amount in Row (11): 10.1%


14.  Type of Reporting Person: PN

- ----------
(1)  Power is exercised through its sole general partner, Portfolio
     Associates, Inc.



1.   Name of Reporting Person:

     Portfolio Associates, 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: Delaware


               7.   Sole Voting Power: 2,484,000 (1)
Number of
Shares
Beneficially   8.   Shared Voting Power: -0-
Owned By
Each
Reporting      9.   Sole Dispositive Power: 2,484,000 (1)
Person
With
               10.  Shared Dispositive Power: -0-

11.  Aggregate Amount Beneficially Owned by Each Reporting Person:

     2,484,000 (1)

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

                                                       /   /


13.  Percent of Class Represented by Amount in Row (11): 10.1% 


14.  Type of Reporting Person: CO

- ----------
(1)  Solely in its capacity as the sole general partner of Portfolio A
     Investors, L.P.





       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 October 27,
1995, as amended by Amendment No. 1 dated November 29, 1995, Amendment No. 2
dated January 17, 1996 and Amendment No. 3 dated January 18, 1996 (the
"Schedule 13D"), relating to the Common Stock, par value $.10 per share, of
Kirby Corporation.  Unless otherwise indicated, all defined terms used herein
shall have the same meanings respectively ascribed to them in the Schedule
13D.

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 and restated in its entirety as follows:

       The source and amount of the funds used or to be used by the Reporting
Persons to purchase shares of the Stock are as follows:

REPORTING PERSON       SOURCE OF FUNDS        AMOUNT OF FUNDS
       
       TIF             Not Applicable         Not Applicable

       TFI             Not Applicable         Not Applicable

       TCM             Not Applicable         Not Applicable

       TMT             Not Applicable         Not Applicable

       PAI             Other (1)              $39,025,931.03

       PA              Not Applicable         Not Applicable

       (1)  Contributions from partners.      

Item 4.  PURPOSE OF TRANSACTION.

       No material change.

Item 5.  INTEREST IN SECURITIES OF THE ISSUER.

       Paragraphs (a)-(c) of Item 5 are hereby amended and restated in their
entireties as follows:

       (a)

       TIF

       Because of its position as the sole stockholder of PA, which is the
sole general partner of PAI, TIF may, pursuant to Rule 13d-3 of the Act, be
deemed to be the beneficial owner of 2,484,000 shares of the Stock, which
constitutes approximately 10.1% of the outstanding shares of the Stock.

       TFI   

       Because of its position as the sole general partner of TIF, which is
the sole stockholder of PA, which is the sole general partner of PAI, TFI may,
pursuant to Rule 13d-3 of the Act, be deemed to be the beneficial owner of
2,484,000 shares of the Stock, which constitutes approximately 10.1% of the
outstanding shares of the Stock.

       TCM

       Because of its position as the sole general partner of TFI, which is
the sole general partner of TIF, which is the sole stockholder of PA, which is
the sole general partner of PAI, TCM may, pursuant to Rule 13d-3 of the Act,
be deemed to be the beneficial owner of 2,484,000 shares of the Stock, which
constitutes approximately 10.1% of the outstanding shares of the Stock.

       TMT

       Because of his position as the President and sole stockholder of TCM,
which is the sole general partner of TFI, which is the sole general partner of
TIF, which is the sole stockholder of PA, which is the sole general partner of
PAI, and because he holds director stock options to purchase 5,000 shares of
the Stock, TMT may, pursuant to Rule 13d-3, be deemed to be the beneficial
owner of 2,489,000 shares of the Stock in the aggregate, which constitutes
approximately 10.1% of the 24,719,986 shares of the Stock deemed outstanding
pursuant to Rule 13d-3(d)(1)(i).

       PAI

       The aggregate number of shares of the Stock that PAI owns
beneficially, pursuant to Rule 13d-3 of the Act, is 2,484,000, which
constitutes approximately 10.1% of the outstanding shares of the Stock.

       PA 

       Because of its position as the sole general partner of PAI, PA may,
pursuant to Rule 13d-3 of the Act, be deemed to be the beneficial owner of
2,484,000 shares of the Stock, which constitutes approximately 10.1% of the
outstanding shares of the Stock.

       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 shares of the Stock.

       (b)

       TIF

       As the sole stockholder of PA, which is the sole general partner of
PAI, TIF has the sole power to vote or to direct the vote and to dispose or to
direct the disposition of 2,484,000 shares of the Stock.

       TFI   

       As the sole general partner of TIF, which is the sole stockholder of
PA, which is the sole general partner of PAI, TFI has the sole power to vote
or to direct the vote and to dispose or to direct the disposition of 2,484,000
shares of the Stock.


       TCM

       As the sole general partner of TFI, which is the sole general partner
of TIF, which is the sole stockholder of PA, which is the sole general partner
of PAI, TCM has the sole power to vote or to direct the vote and to dispose or
to direct the disposition of 2,484,000 shares of the Stock.

       TMT

       As the President and sole stockholder of TCM, which is the sole
general partner of TFI, which is the sole general partner of TIF, which is the
sole stockholder of PA, which is the sole general partner of PAI, TMT has the
sole power to vote or to direct the vote and to dispose or to direct the
disposition of 2,484,000 shares of the Stock.

       PAI

       Acting through its sole general partner, PAI has the sole power to
vote or to direct the vote and to dispose or to direct the disposition of
2,484,000 shares of the Stock.

       PA 

       As the sole general partner of PAI, PA has the sole power to vote or
to direct the vote and to dispose or to direct the disposition of 2,484,000
shares of the Stock.

       (c)  During the past 60 days, PAI has purchased shares of the Stock in
transactions on the American Stock Exchange, as follows:

                            NO. OF SHARES        PRICE PER
             DATE             PURCHASED            SHARE  

            07-31-96          10,000              $16.06
            08-01-96          30,500               16.19
            08-02-96           6,000               16.31
            08-14-96         250,400               15.93

      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 shares of the Stock since the
most recent filing on Schedule 13D.

      (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 and Power of Attorney pursuant to Rule
13d-1(f)(1)(iii) previously filed herewith.


       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:     August 15, 1996


      
                                    TRINITY I FUND, L.P.,
                                    a Delaware limited partnership

                                    By:   TF INVESTORS, L.P.,
                                          a Delaware limited partnership,
                                          General Partner

                                    By:   TRINITY CAPITAL MANAGEMENT, INC.,
                                          a Delaware corporation,
                                          General Partner

                                    By:/s/ W. R. Cotham
                                          W. R. Cotham,
                                          Vice President


                                    TF INVESTORS, L.P.,
                                    a Delaware limited partnership

                                    By:   TRINITY CAPITAL MANAGEMENT, INC.,
                                          a Delaware corporation,
                                          General Partner

                                    By:/s/ W. R. Cotham
                                          W. R. Cotham,
                                          Vice President



                                    TRINITY CAPITAL MANAGEMENT, INC.,
                                    a Delaware corporation

                                    By:/s/ W. R. Cotham
                                          W. R. Cotham,
                                          Vice President


                                    PORTFOLIO A INVESTORS, L.P.,
                                    a Delaware limited partnership

                                    By: PORTFOLIO ASSOCIATES, INC.,
                                          a Delaware corporation,
                                          General Partner

                                    By:/s/ W. R. Cotham
                                          W. R. Cotham,
                                          Vice President


                                    PORTFOLIO ASSOCIATES, INC.,
                                    a Delaware corporation

                                    By:/s/ W. R. Cotham
                                          W. R. Cotham,
                                          Vice President


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

                                          THOMAS M. TAYLOR (1)

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

      


                          EXHIBIT INDEX

EXHIBIT                 DESCRIPTION              

  99.1               Agreement and Power of Attorney pursuant to Rule
                     13d-1(f)(1)(iii), previously filed with the Securities
                     and Exchange Commission