UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

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

                                  SCHEDULE 13G
                                 (Rule 13d-102)

 INFORMATION TO BE INCLUDED IN STATEMENTS FILED PURSUANT TO RULES 13D-1(b), (c)
                      and (d) AND AMENDMENTS THERETO FILED
                              PURSUANT TO 13D-2(b)

                              (Amendment No. 4)(1)

                            Apex Silver Mines Limited
--------------------------------------------------------------------------------
                                (Name of Issuer)

                        Ordinary Shares, $0.01 Par Value
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    G04074103
--------------------------------------------------------------------------------
                                 (CUSIP Number)

                                December 31, 2004
--------------------------------------------------------------------------------
             (Date of Event Which Requires Filing of this Statement)

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

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

      |_|   Rule 13d-1 (b)
      |_|   Rule 13d-1 (c)
      |X|   Rule 13d-1 (d)

      (1) 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 the 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 or otherwise subject to the liabilites of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).



CUSIP NO. G04074103                   13G                      Page 2 of 5 Pages
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1.    NAME OF REPORTING PERSONS
      I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)

      Thomas S. Kaplan
--------------------------------------------------------------------------------
2.    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*                  (a) [_]
                                                                         (b) [_]

--------------------------------------------------------------------------------
3.    SEC USE ONLY


--------------------------------------------------------------------------------
4.    CITIZENSHIP OR PLACE OF ORGANIZATION

      United States
--------------------------------------------------------------------------------
               5.    SOLE VOTING POWER

                     2,720,913
               -----------------------------------------------------------------
  NUMBER OF    6.    SHARED VOTING POWER
   SHARES
 BENEFICIALLY        0
  OWNED BY     -----------------------------------------------------------------
    EACH       7.    SOLE DISPOSITIVE POWER
  REPORTING
   PERSON            2,720,913
    WITH       -----------------------------------------------------------------
               8.    SHARED DISPOSITIVE POWER

                     0
--------------------------------------------------------------------------------
9.    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

      2,720,913
--------------------------------------------------------------------------------
10.   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                                                          [_]

--------------------------------------------------------------------------------
11.   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

      5.63%
--------------------------------------------------------------------------------
12.   TYPE OF REPORTING PERSON*

      Individual (IN)
--------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!



CUSIP NO. G04074103                   13G                      Page 3 of 5 Pages

      Item 1(a). Name of Issuer:

      Apex Silver Mines Limited
      --------------------------------------------------------------------------

      Item 1(b). Address of Issuer's Principal Executive Offices:

      Walker House, Mary Street, George Town, Grand Cayman, Cayman Islands,
      British West Indies
      --------------------------------------------------------------------------

      Item 2(a). Name of Person Filing:

      Thomas Scott Kaplan
      --------------------------------------------------------------------------

      Item 2(b). Address of Principal Business Office, or, if None, Residence:

      154 West 18th Street, New York, New York 10011
      --------------------------------------------------------------------------

      Item 2(c). Citizenship:

      United States
      --------------------------------------------------------------------------

      Item 2(d). Title of Class of Securities:

      Ordinary Shares, $0.01 Par Value
      --------------------------------------------------------------------------

      Item 2(e). CUSIP NUMBER:

      G04074103
      --------------------------------------------------------------------------

      Item 3. If this statement is filed pursuant to Rule 13d-1(b), or 13d-2(b),
      check whether the person Filing is a:

(a)   |_|   Broker or dealer registered under Section 15 of the Act.

(b)   |_|   Bank as defined in Section 3(a)(6) of the Act.

(c)   |_|   Insurance Company as defined in Section 3(a)(19) of the Act.

(d)   |_|   Investment Company registered under Section 8 of the Investment
            Company Act.

(e)   |_|   Investment Adviser registered under Section 203 of the Investment
            Advisers Act of 1940.

(f)   |_|   Employee Benefit Plan, Pension Fund which is subject to the
            provisions of the Employee Retirement Income Security Act of 1974 or
            Endowment Fund; see 13d-1(b)(1)(ii)(F).

(g)   |_|   Parent Holding Company, in accordance with Rule 13d-1(b)(ii)(G); see
            Item 7.

(h)   |_|   Group, in accordance with Rule 13d-1(b)(1)(ii)(H).



CUSIP NO. G04074103                   13G                      Page 4 of 5 Pages

Item 4. Ownership.

      Provide the following information regarding the aggregate number and
percentage of the class of securities of the issuer identified in Item 1.

      (a)   Amount beneficially owned:

            2,720,913 (see Exhibit A)
            --------------------------------------------------------------------

      (b)   Percent of class:

            5.63%
            --------------------------------------------------------------------

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

            (i)   Sole power to vote or to direct the vote             2,720,913
                                                                       ---------

            (ii)  Shared power to vote or to direct the vote                   0
                                                                       ---------

            (iii) Sole power to dispose or to direct the disposition of
                                                                       2,720,913
                                                                       ---------

            (iv)  Shared power to dispose or to direct the disposition of
                                                                               0
                                                                       ---------

Item 5. Ownership of Five Percent or Less of a Class.

      If this statement is being filed to report the fact that as of the date
hereof the reporting person has ceased to be the Beneficial owner of more than
five percent of the class of securities, check the following |_|.

Item 6. Ownership of More than Five Percent on Behalf of Another Person.

      See Exhibit A.

Item 7. Identification and Classification of the Subsidiary Which Acquired the
        Security 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.



CUSIP NO. G04074103                   13G                      Page 5 of 5 Pages

Item 10. Certification.

      Not applicable.

                                    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 and correct.

                                                        January 3, 2005
                                                 -------------------------------
                                                             (Date)


                                                    /s/ Thomas Scott Kaplan
                                                 -------------------------------
                                                          (Signature)

                                                      Thomas Scott Kaplan
                                                 -------------------------------
                                                          (Name/Title)



                                    Exhibit A
                                 to Schedule 13G

      As of December 31, 2004, the Reporting Person beneficially owned 2,720,913
Ordinary Shares (the "Shares") of the Issuer, which includes 1,734,121 Shares of
the Issuer owned by Consolidated Commodities, Ltd., a company organized under
the laws of Bermuda, over which Shares the Reporting Person has voting and
dispositive control pursuant to a Voting Trust Agreement; 189,449 Shares owned
directly by the Reporting Person and 797,343 Shares that the Reporting Person
has the right to acquire upon the exercise of options within 60 days of the date
hereof. Based upon 47,500,547 Shares of the Issuer outstanding as of November 3,
2004, as reported in the Company's Form 10-Q filed with the Securities and
Exchange Commission on November 15, 2004, the Shares beneficially owned by the
Reporting Person constitute approximately 5.63% of the total Shares outstanding.