SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


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


                    Under the Securities Exchange Act of 1934

                                  SCHEDULE 13G

             INFORMATION STATEMENT PURSUANT TO RULES 13d-1 AND 13d-2
                    UNDER THE SECURITIES EXCHANGE ACT OF 1934



                           DAWSON GEOPHYSICAL COMPANY
                           --------------------------
                                (Name of Issuer)



                                  Common Stock
                                  ------------
                         (Title of Class of Securities)



                                    239359102
                                    ---------
                                 (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:

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


                                   -----------


                                Page 1 of 6 Pages






                                  SCHEDULE 13G

CUSIP No. 239359102                                           Page 2 of 6 Pages
-------------------------------------------------------------------------------

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

       Gilder, Gagnon, Howe & Co. LLC
       13-3174112
-------------------------------------------------------------------------------
2)     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP          (a) |_|

                                                                 (b) |_|
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3)     SEC USE ONLY


-------------------------------------------------------------------------------
4)     CITIZENSHIP OR PLACE OF ORGANIZATION

       New York
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                         5)     SOLE VOTING POWER

       NUMBER                   6,895
       OF                ------------------------------------------------------
       SHARES            6)     SHARED VOTING POWER
       BENEFICIALLY
       OWNED BY                 None
       EACH              ------------------------------------------------------
       REPORTING         7)     SOLE DISPOSITIVE POWER
       PERSON
       WITH                     None
                         ------------------------------------------------------
                         8)     SHARED DISPOSITIVE POWER

                                285,900
-------------------------------------------------------------------------------
9)     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       285,900
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10)    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES

                                                                   |_|
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11)    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

       5.1%
-------------------------------------------------------------------------------
12)    TYPE OF REPORTING PERSON

       BD
-------------------------------------------------------------------------------







                                  Schedule 13G
                                  ------------

Item 1(a).  Name of Issuer:

DAWSON GEOPHYSICAL COMPANY

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

508 West Wall - Suite 800
Midland, TX  79701

Item 2(a).  Name of Person Filing:

Gilder, Gagnon, Howe & Co. LLC

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

1775 Broadway, 26th Floor
New York, NY  10019

Item 2(c).  Citizenship:

New York

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

Common Stock

Item 2(e).  CUSIP Number:

239359102

Item 3.     If this statement is filed pursuant to ss.ss. 240.13d-1(b), or
240.13d-2(b) or (c), check whether the person filing is a:

            (a)   [x] Broker or Dealer Registered Under Section 15 of the Act
                      (15 U.S.C. 78o)

            (b)   |_| Bank as defined in section 3(a)(6) of the Act (15 U.S.C.
                      78c)

            (c)   |_| Insurance Company as defined in section 3(a)(19) of the
                      Act (15 U.S.C. 78c)

            (d)   |_| Investment Company registered under section 8 of the
                      Investment Company Act of 1940 (15 U.S.C. 80a-8)

            (e)   |_| Investment Adviser in accordance with ss.
                      240.13d-1(b)(1)(ii)(E)

            (f)   |_| Employee benefit plan or endowment fund in accordance with
                      ss. 240.13d-1(b)(1)(ii)(F)

            (g)   |_| Parent Holding Company or control person in accordance
                      with ss.240.13d-1(b)(ii)(G)




            (h)   |_| Savings Association as defined in ss.3(b) of the Federal
                      Deposit Insurance Act (12 U.S.C. 1813)

            (i)   |_| Church plan that is excluded from the definition of an
                      investment company under ss.3(c)(15) of the Investment
                      Company Act of 1940 (15 U.S.C. 80a-3)

            (j)   |_| Group, in accordance with ss.240.13d-1(b)(ii)(J)

Item 4.     Ownership.

            (a)   Amount beneficially owned: 285,900

            (b)   Percent of class: 5.1%

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

                  (i)   Sole power to vote or to direct the vote: 6,895

                  (ii)  Shared power to vote or to direct the vote: None

                  (iii) Sole power to dispose or to direct the disposition of:
                        None

                  (iv)  Shared power to dispose or to direct the disposition of:
                        285,900

            The shares reported include 266,140 shares held in customer accounts
            over which partners and/or employees of the Reporting Person have
            discretionary authority to dispose of or direct the disposition of
            the shares, 12,865 shares held in accounts owned by the partners of
            the Reporting Person and their families, and 6,895 shares held in
            the account of the profit-sharing plan of the Reporting Person ("the
            Profit-Sharing Plan").

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

Not applicable

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

The owners of the accounts (including the Profit-Sharing Plan) in which the
shares reported on this Schedule are held have the right to receive or the power
to direct the receipt of dividends from, or the proceeds from the sale of, such
securities.

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

Item 10.    Certification.

            By signing below I certify that, to the best of my knowledge and
belief, the securities referred to above were acquired in the ordinary course of
business and were not acquired for the purpose of and do not have the effect of
changing or influencing the control of the issuer of such securities and were
not acquired in connection with or as a participant in any transaction having
such purposes or effect.





                                    SIGNATURE
                                    ---------


         After reasonable inquiry and to the best knowledge and belief of the
undersigned, the undersigned certifies that the information set forth in this
Statement is true, complete and correct.


                                      February 14, 2005
                                      -------------------------------
                                        Date


                                      /s/  Walter Weadock
                                      -------------------------------
                                        Signature


                                      Walter Weadock, Member
                                      -------------------------------
                                        Name/Title