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                                                       Page 1 of 4

SCHEDULE 13G
 (12/31/98)

DAWSON GEOPHYSICAL C
Cusip # 239359102
NEW FILING

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Cusip # 239359102

Item  1:    REPORTING PERSONS
            Dimensional Fund Advisors Inc. (Tax ID: 22-2370029)

Item  4:    CITIZENSHIP
            Delaware Corporation

Item  5:    SOLE VOTING POWER
            281,800           ** see Note 1 **

Item  6:    SHARED VOTING POWER --
            None

Item  7:    SOLE DISPOSITIVE POWER --
            281,800           ** see Note 1 **

Item  8:    SHARED DISPOSITIVE POWER --
            0

Item  9:    AGGREGATE AMOUNT BENEFICIALLY OWNED --
            281,800           ** see Note 1 **

Item 11:    PERCENT OF CLASS REPRESENTED BY LINE 9 --
            5.26

Item 12:    TYPE OF REPORTING PERSON --
            IA

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ITEM 1(A).  NAME OF ISSUER

            DAWSON GEOPHYSICAL C

ITEM 1(B).  ADDRESS OF ISSUER

            208 South Marienfeld
            Midland, TX  79701


ITEM 2(A).  NAME OF PERSON FILING

            Dimensional Fund Advisors

ITEM 2(B).  ADDRESS OF PRINCIPAL BUSINESS OFFICE

            1299 Ocean Avenue, 11th Floor, Santa Monica, CA  90401

ITEM 2(C).  CITIZENSHIP

            A Delaware Corporation

ITEM 2(D).  TITLE OF CLASS OF SECURITIES

            Common Stock

ITEM 2(E).  CUSIP NUMBER

            239359102

ITEM 3.     This statement is filed pursuant to Rule 13d-1 (b), or
            13d-2 (b) and the person filing is an investment advisor
            registered under section 203 of the Investment Advisors
            Act of 1940.

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ITEM 4.     OWNERSHIP
ITEM 4(a).  AMOUNT BENEFICIALLY OWNED
              281,800            ** see Note 1 **
ITEM 4(b).  PERCENT OF CLASS
             5.26
ITEM 4(c).  NUMBER OF SHARE AS TO WHICH SUCH PERSON HAS:
      (i).  SOLE POWER TO VOTE OR DIRECT THE VOTE --
              281,800            ** see Note 1 **
     (ii).  SHARED POWER TO VOTE OR TO DIRECT THE VOTE --
            None
    (iii).  SOLE POWER TO DISPOSE OR TO DIRECT DISPOSITION OF --
              281,800            ** see Note 1 **
     (iv).  SHARE POWER TO DISPOSE OR TO DIRECT DISPOSISTION OF --
            None

    ** Note 1 **
    Dimensional Fund Advisors Inc. ("Dimensional"), an investment
    advisor registered under the Investment Advisors Act of 1940,
    furnishes investment advice to four investment companies
    registered under Investment Company Act of 1940, and serves as
    investment manager to certain other investment vehicles, including
    commingled group trusts.  (These investment companies and
    investment vehicles are the "Portfolios"). In its role as
    investment advisor and investment manager, Dimensional possesses
    both voting and investment power over the securities of the Issuer
    described in this schedule that are owned by the Portfolios.  All
    securities reported in this schedule are owned by the Portfolios,
    and Dimensional disclaims beneficial ownership of such securities.

ITEM 5.     OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS
            If this statement is being filed to report the fact that
            as of 12/31/98 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
            All Securities reported in this schedule are onwed by
            advisory clients of Dimensional Fund Advisors Inc., no one
            of which to the knowledge of Dimensional Fund Advisors Inc.
            owns more than 5% of the class.  Dimensional Fund Advisors
            Inc disclaims beneficial ownership of all 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.

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 are correct.

Signature

   Friday, February 12, 1999

   Michael T. Scardina
   Vice President and Chief Finacial Officer