SECURITIES AND EXCHANGE COMMISSION
                           Washington, D.C. 20549

                               Schedule 13D**

                  Under the Securities Exchange Act of 1934
                             (Amendment No. 3)*

                              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)

                              January 18, 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 2,187,100 shares, which
constitutes approximately 8.3% of the total number of shares outstanding.  All
ownership percentages set forth herein assume that there are 26,384,566 shares
outstanding.





        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 (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.

        No material change.

Item 4.  PURPOSE OF TRANSACTION.

        Item 4 is hereby amended by adding at the end thereof the following:

        The Reporting Persons are filing today a Notification and Report Form
pursuant to the Hart-Scott-Rodino Antitrust Improvements Act of 1976, as
amended, with the Federal Trade Commission and the United States Department of
Justice in which they have indicated their intention to acquire more than 15%
of the Issuer's Common Stock.

        Except as set forth in this Item 4, the Reporting Persons have no
present plans or proposals that relate to or that would result in any of the
actions specified in clauses (a) through (j) of Item 4 of Schedule 13D of the
Act.

Item 5.  INTEREST IN SECURITIES OF THE ISSUER.

        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:     January 18, 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