SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                  Schedule 13D

                    Under the Securities Exchange Act of 1934
                               (Amendment No. 19)*

                               TREMONT CORPORATION
                                (Name of Issuer)

                          Common Stock, $1.00 par value
                         (Title of Class of Securities)

                                   894745 20 7
                                 (CUSIP Number)

                                STEVEN L. WATSON
                              THREE LINCOLN CENTRE
                                   SUITE 1700
                                5430 LBJ FREEWAY
                            DALLAS, TEXAS 75240-2694
                                 (972) 233-1700
                  (Name, Address and Telephone Number of Person
                Authorized to Receive Notices and Communications)

                               September 27, 2001
                      (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  that is the subject of this Schedule 13D, and is filing
this schedule  because of sections  240.13d-1(e),  240.13d-1(f) or 240.13d-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).

                         (Continued on following pages)






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Tremont Group, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      OO

     5       CHECK 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

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,141,421
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,141,421

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,141,421

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.0%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO







CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Tremont Holdings, LLC

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      WC

     5       CHECK 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

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,149,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,149,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,149,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      OO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      NL Industries, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      WC

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      New Jersey

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,149,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,149,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,149,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Valhi, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      WC and BK

     5       CHECK 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

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Valhi Group, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Nevada

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      National City Lines, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK 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

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      NOA, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK 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
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Dixie Holding Company

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK 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

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Dixie Rice Agricultural Corporation, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Louisiana

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Southwest Louisiana Land Company, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED
             PURSUANT TO ITEMS 2(d) OR 2(e)  [  ]


     6       CITIZENSHIP OR PLACE OF ORGANIZATION

                      Louisiana

                               7      SOLE VOTING POWER

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Contran Corporation

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK 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

                                                            -0-
        NUMBER OF
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Harold Simmons Foundation, Inc.

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [   ]

             (b)  [   ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK 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
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      CO






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      The Combined Master Retirement Trust

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

             (a)  [   ]

             (b)  [   ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not Applicable

     5       CHECK 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
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                                      5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      5,154,588

    12       CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [  ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      80.2%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      EP






CUSIP No.  894745 20 7

     1       NAME OF REPORTING PERSON
             S.S. OR I.R.S. IDENTIFICATION NO.  OF ABOVE PERSON

                      Harold C. Simmons

     2       CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP(SEE INSTRUCTIONS)

             (a)  [  ]

             (b)  [  ]

     3       SEC USE ONLY



     4       SOURCE OF FUNDS (SEE INSTRUCTIONS)

                      Not applicable

     5       CHECK 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
          SHARES               8      SHARED VOTING POWER
       BENEFICIALLY
         OWNED BY                                     5,154,588
           EACH
        REPORTING              9      SOLE DISPOSITIVE POWER
          PERSON
           WITH                                             -0-

                               10     SHARED DISPOSITIVE POWER

                                               5,154,588

    11       AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

                      -0-

    12       CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES
             CERTAIN SHARES (SEE INSTRUCTIONS)  [ X ]

    13       PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

                      0.0%

    14       TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                      IN






                                AMENDMENT NO. 19
                                 TO SCHEDULE 13D

     This amended  statement on Schedule 13D (this  "Statement")  relates to the
common stock, par value $1.00 per share (the "Shares"),  of Tremont Corporation,
a Delaware  corporation  (the  "Company").  Items 4 and 7 of this  Statement are
hereby amended as set forth below.

Item 4.  Purpose of Transaction.

     Item 4 is amended as follows.

     On September 19, 2001,  Valhi,  Inc., a Delaware  corporation  of which the
Company is a majority owned subsidiary  ("Valhi"),  sent a letter to the Company
and Titanium  Metals  Corporation,  a Delaware  corporation  that is a 39% owned
subsidiary of the Company ("TIMET"),  proposing (the "Proposal") to sell each of
Valhi's and the Company's  shares of common stock of NL Industries,  Inc., a New
Jersey  corporation  that is a majority owned  subsidiary of Valhi, to TIMET for
shares  of  TIMET  common  stock  and  TIMET  debt  securities  on  terms  to be
appropriately  determined.  A copy of the  September 19, 2001 letter is attached
hereto as Exhibit 10 and  incorporated  herein by  reference.  On September  21,
2001,  Valhi  issued a press  release  stating  that Valhi would not approve any
transaction  that may be  negotiated  with an  independent  committee of TIMET's
board of directors and its advisors  without the affirmative  vote of a majority
of the TIMET  shares  voting  that are held by  persons  other than  Valhi,  the
Company and their affiliates.  On September 27, 2001, Valhi sent a letter to the
Company and TIMET  withdrawing  the  Proposal.  A copy of the September 27, 2001
letter is attached hereto as Exhibit 11 and incorporated herein by reference.

     Depending  upon their  evaluation of the Company's  business and prospects,
and upon future developments (including, but not limited to,
performance of the Shares in the market, availability of funds, alternative uses
of funds, the Reporting Persons' tax planning objectives and money, stock market
and general economic conditions), any of the Reporting Persons or other entities
that may be deemed to be affiliated with Contran may from time to time purchase
Shares, and any of the Reporting Persons or other entities that may be deemed to
be affiliated with Contran may from time to time dispose of all or a portion of
the Shares held by such person, or cease buying or selling Shares. Any such
additional purchases or sales of the Shares may be in open market or privately
negotiated transactions or otherwise.

Item 7.  Material to be Filed as Exhibits.

         Item 7 is amended and restated as follows.

Exhibit 1      Credit Agreement dated as of November 6, 1998 among Valhi,  Inc.,
               the  financial  institutions  from  time to time that are a party
               thereto  and  Societe   Generale,   Southwest   Agency,   as  the
               administrative agent, issuing bank and arranger  (incorporated by
               reference  to Exhibit 1 to  Amendment  No. 59 to the Schedule 13D
               filed on  November  23,  1999 with the  Securities  and  Exchange
               Commission by Tremont  Corporation,  Valmont  Insurance  Company,
               Valhi, Inc., Valhi Group,  Inc.,  National City Lines, Inc., NOA,
               Inc., Dixie Holding Company, Dixie Rice Agricultural Corporation,
               Inc.,   Southwest   Louisiana   Land   Company,   Inc.,   Contran
               Corporation,  The Combined Master  Retirement  Trust,  the Harold
               Simmons  Foundation,  Inc.  and Harold C. Simmons with respect to
               the common stock,  par value $0.125 per share,  of NL Industries,
               Inc.).

Exhibit 2      FirstAmendment  Agreement  dated as of  November  5,  1999  among
               Valhi,  Inc., the financial  institutions  from time to time that
               are a party thereto and Societe  Generale,  Southwest  Agency, as
               the administrative agent, issuing bank and arranger (incorporated
               by reference to Exhibit 2 to Amendment No. 60 to the Schedule 13D
               filed on  December  14,  1999 with the  Securities  and  Exchange
               Commission by Tremont  Corporation,  Valmont  Insurance  Company,
               Valhi, Inc., Valhi Group,  Inc.,  National City Lines, Inc., NOA,
               Inc., Dixie Holding Company, Dixie Rice Agricultural Corporation,
               Inc.,   Southwest   Louisiana   Land   Company,   Inc.,   Contran
               Corporation,  The Combined Master  Retirement  Trust,  the Harold
               Simmons  Foundation,  Inc.  and Harold C. Simmons with respect to
               the common stock,  par value $0.125 per share,  of NL Industries,
               Inc.).

Exhibit 3      Second  Amendment  Agreement  dated as of  November 3, 2000 among
               Valhi,  Inc., the financial  institutions  from time to time that
               are a party  thereto and U.S. Bank  National  Association  as the
               administrative agent, issuing bank and arranger  (incorporated by
               reference to Exhibit 3 to Amendment No. 15 to this Statement).

Exhibit 4      Form of  Accession  Agreement  dated as of December 1, 2000 among
               Valhi, Inc., the Banks and U.S. Bank National Association, as the
               administrative  agent of the banks,  and the  related  promissory
               note in the original  principal amount of $5.0 million payable to
               the order of Texas  Capital  Bank  (incorporated  by reference to
               Exhibit  4 to  Amendment  No.  63 to the  Schedule  13D  filed on
               September 25, 2001 with the Securities and Exchange Commission by
               Tremont Corporation,  Tremont Group, Inc., Tremont Holdings, LLC,
               Valhi, Inc., Valhi Group,  Inc.,  National City Lines, Inc., NOA,
               Inc., Dixie Holding Company, Dixie Rice Agricultural Corporation,
               Inc.,   Southwest   Louisiana   Land   Company,   Inc.,   Contran
               Corporation,  The Combined Master  Retirement  Trust,  the Harold
               Simmons  Foundation,  Inc.  and Harold C. Simmons with respect to
               the common stock,  par value $0.125 per share,  of NL Industries,
               Inc.).

Exhibit 5      StockPurchase  Agreement  dated as of  November  7, 2000  between
               Valhi,  Inc. and J. Landis Martin  (incorporated  by reference to
               Exhibit 4 to Amendment No. 16 to this Statement).

Exhibit 6      Certificate of Incorporation of Tremont Group, Inc. (incorporated
               by reference to Exhibit 5 to Amendment No. 17 to this Statement).

Exhibit 7      Voting  Agreement  dated as of December 31, 2000  between  Valhi,
               Inc.  and Tremont  Holdings,  LLC  (incorporated  by reference to
               Exhibit 6 to Amendment No. 17 to this Statement).

Exhibit 8      Tax Sharing  Agreement  dated as of January 1, 2001 among  Valhi,
               Inc., Contran Corporation and NL Industries,  Inc.  (incorporated
               by reference to Exhibit 7 to Amendment No. 17 to this Statement).

Exhibit 9      Tax Sharing  Agreement  dated as of January 1, 2001 among  Valhi,
               Inc., Contran Corporation and Tremont  Corporation  (incorporated
               by reference to Exhibit 8 to Amendment No. 17 to this Statement).

Exhibit 10     Letter dated September 19, 2001 from Valhi,  Inc. to the board of
               directors of Titanium Metals Corporation and Tremont  Corporation
               (incorporated  by reference to Exhibit 10 to Amendment  No. 18 to
               this Statement).

Exhibit 11*    Letter dated September 27, 2001 from Valhi,  Inc. to the board of
               directors of Titanium Metals Corporation and Tremont Corporation.

----------

*        Filed herewith.





                                    Signature

     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.

Date:  October 3, 2001




                                                          /s/ Harold C. Simmons
                                                          ----------------------
                                                          Harold C. Simmons
                                                          Signing in the
                                                          capacities listed on
                                                          Schedule "A" attached
                                                          hereto and
                                                          incorporated herein by
                                                          reference.





                                    Signature

     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.

Date:  October 3, 2001




                                                          /s/ J. Landis Martin
                                                          ----------------------
                                                          J. Landis Martin
                                                          Signing in the
                                                          capacity listed on
                                                          Schedule "A" attached
                                                          hereto and
                                                          incorporated herein by
                                                          reference.





                                    Signature

     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.

Date:  October 3, 2001





                                                          /s/ Steven L. Watson
                                                          ----------------------
                                                          Steven L. Watson
                                                          Signing in the
                                                          capacities listed on
                                                          Schedule "A" attached
                                                          hereto and
                                                          incorporated herein by
                                                          reference.





                                   SCHEDULE A


HAROLD C. SIMMONS, in his individual capacity and as trustee for THE COMBINED
MASTER RETIREMENT TRUST.


J. LANDIS MARTIN, as president of each of:

NL INDUSTRIES, INC.
TREMONT HOLDINGS, LLC

STEVEN L. WATSON, as president or vice president of each of:

CONTRAN CORPORATION
DIXIE HOLDING COMPANY
DIXIE RICE AGRICULTURAL CORPORATION, INC.
HAROLD SIMMONS FOUNDATION, INC.
NATIONAL CITY LINES, INC.
NOA, INC.
SOUTHWEST LOUISIANA LAND COMPANY, INC.
TREMONT GROUP, INC.
VALHI GROUP, INC.
VALHI, INC.





                                  Exhibit Index

Exhibit 1      Credit Agreement dated as of November 6, 1998 among Valhi,  Inc.,
               the  financial  institutions  from  time to time that are a party
               thereto  and  Societe   Generale,   Southwest   Agency,   as  the
               administrative agent, issuing bank and arranger  (incorporated by
               reference  to Exhibit 1 to  Amendment  No. 59 to the Schedule 13D
               filed on  November  23,  1999 with the  Securities  and  Exchange
               Commission by Tremont  Corporation,  Valmont  Insurance  Company,
               Valhi, Inc., Valhi Group,  Inc.,  National City Lines, Inc., NOA,
               Inc., Dixie Holding Company, Dixie Rice Agricultural Corporation,
               Inc.,   Southwest   Louisiana   Land   Company,   Inc.,   Contran
               Corporation,  The Combined Master  Retirement  Trust,  the Harold
               Simmons  Foundation,  Inc.  and Harold C. Simmons with respect to
               the common stock,  par value $0.125 per share,  of NL Industries,
               Inc.).

Exhibit 2      FirstAmendment  Agreement  dated as of  November  5,  1999  among
               Valhi,  Inc., the financial  institutions  from time to time that
               are a party thereto and Societe  Generale,  Southwest  Agency, as
               the administrative agent, issuing bank and arranger (incorporated
               by reference to Exhibit 2 to Amendment No. 60 to the Schedule 13D
               filed on  December  14,  1999 with the  Securities  and  Exchange
               Commission by Tremont  Corporation,  Valmont  Insurance  Company,
               Valhi, Inc., Valhi Group,  Inc.,  National City Lines, Inc., NOA,
               Inc., Dixie Holding Company, Dixie Rice Agricultural Corporation,
               Inc.,   Southwest   Louisiana   Land   Company,   Inc.,   Contran
               Corporation,  The Combined Master  Retirement  Trust,  the Harold
               Simmons  Foundation,  Inc.  and Harold C. Simmons with respect to
               the common stock,  par value $0.125 per share,  of NL Industries,
               Inc.).

Exhibit 3      Second  Amendment  Agreement  dated as of  November 3, 2000 among
               Valhi,  Inc., the financial  institutions  from time to time that
               are a party  thereto and U.S. Bank  National  Association  as the
               administrative agent, issuing bank and arranger  (incorporated by
               reference to Exhibit 3 to Amendment No. 15 to this Statement).

Exhibit 4      Form of  Accession  Agreement  dated as of December 1, 2000 among
               Valhi, Inc., the Banks and U.S. Bank National Association, as the
               administrative  agent of the banks,  and the  related  promissory
               note in the original  principal amount of $5.0 million payable to
               the order of Texas  Capital  Bank  (incorporated  by reference to
               Exhibit  4 to  Amendment  No.  63 to the  Schedule  13D  filed on
               September 25, 2001 with the Securities and Exchange Commission by
               Tremont Corporation,  Tremont Group, Inc., Tremont Holdings, LLC,
               Valhi, Inc., Valhi Group,  Inc.,  National City Lines, Inc., NOA,
               Inc., Dixie Holding Company, Dixie Rice Agricultural Corporation,
               Inc.,   Southwest   Louisiana   Land   Company,   Inc.,   Contran
               Corporation,  The Combined Master  Retirement  Trust,  the Harold
               Simmons  Foundation,  Inc.  and Harold C. Simmons with respect to
               the common stock,  par value $0.125 per share,  of NL Industries,
               Inc.).

Exhibit 5      StockPurchase  Agreement  dated as of  November  7, 2000  between
               Valhi,  Inc. and J. Landis Martin  (incorporated  by reference to
               Exhibit 4 to Amendment No. 16 to this Statement).

Exhibit 6      Certificate of Incorporation of Tremont Group, Inc. (incorporated
               by reference to Exhibit 5 to Amendment No. 17 to this Statement).

Exhibit 7      Voting  Agreement  dated as of December 31, 2000  between  Valhi,
               Inc.  and Tremont  Holdings,  LLC  (incorporated  by reference to
               Exhibit 6 to Amendment No. 17 to this Statement).

Exhibit 8      Tax Sharing  Agreement  dated as of January 1, 2001 among  Valhi,
               Inc., Contran Corporation and NL Industries,  Inc.  (incorporated
               by reference to Exhibit 7 to Amendment No. 17 to this Statement).

Exhibit 9      Tax Sharing  Agreement  dated as of January 1, 2001 among  Valhi,
               Inc., Contran Corporation and Tremont  Corporation  (incorporated
               by reference to Exhibit 8 to Amendment No. 17 to this Statement).

Exhibit 10     Letter dated September 19, 2001 from Valhi,  Inc. to the board of
               directors of Titanium Metals Corporation and Tremont  Corporation
               (incorporated  by reference to Exhibit 10 to Amendment  No. 18 to
               this Statement).

Exhibit 11*    Letter dated September 27, 2001 from Valhi,  Inc. to the board of
               directors of Titanium Metals Corporation and Tremont Corporation.

----------

*        Filed herewith.