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                                 UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION

                            WASHINGTON, D.C. 20549

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

                                 SCHEDULE 13D

                   UNDER THE SECURITIES EXCHANGE ACT OF 1934

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

                               NUMAR CORPORATION
                               (Name of Issuer)

                    Common Stock, par value $.01 per share
                        (Title of Class of Securities)

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

                                   67052E105
                                (CUSIP Number)

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

                               Lester L. Coleman
                 Executive Vice President and General Counsel
                              Halliburton Company
                              3600 Lincoln Plaza
                            500 North Akard Street
                           Dallas, Texas 75201-3391
                                (214) 978-2600
                (Name, Address and Telephone Number of Persons
               Authorized to Receive Notices and Communications)

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

                                 June 9, 1997
            (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 this statement: [X]

        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, as amended (the "Act"), or otherwise subject to the liabilities of
that Section of the Act but shall be subject to all other provisions of the Act.

        Beneficial ownership percentages set forth herein assume that at June 9,
1996, there were 8,640,742 shares outstanding, consisting of 8,412,891 shares
issued and outstanding and an estimated 227,851 unissued shares beneficially
owned by the Affiliates (as herein defined).

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      NAME OF REPORTING PERSON                             HALLIBURTON COMPANY
 1    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON             75-0271280
                          


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      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
 2                                                              (a) [_]
                                                                (b) [_]
                                                 
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      SEC USE ONLY
 3
 

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      SOURCE OF FUNDS
 4
      Not Applicable

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


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      CITIZENSHIP OR PLACE OF ORGANIZATION
 6    

      Delaware
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                          SOLE VOTING POWER
                     7     
     NUMBER OF            0          
                          
      SHARES       -----------------------------------------------------------
                          SHARED VOTING POWER
   BENEFICIALLY      8    
                          2,177,492
     OWNED BY             
                   -----------------------------------------------------------
       EACH               SOLE DISPOSITIVE POWER
                     9     
    REPORTING             0
                          
      PERSON       -----------------------------------------------------------
                          SHARED DISPOSITIVE POWER
       WITH         10    
                          0
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      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
11    
      2,145,492
      
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      CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES
12                  
      [_]
 
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      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) EXCLUDES CERTAIN
13    SHARES
      
      25.2% (approximate)
- ------------------------------------------------------------------------------
      TYPE OF REPORTING PERSON
14
      co
      
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ITEM 1.    SECURITY AND ISSUER.
           
           This Schedule 13D relates to the common stock, par value $.01 per 
share ("NUMAR Common Stock"), of NUMAR Corporation, a corporation organized 
under the laws of the Commonwealth of Pennsylvania ("NUMAR"). The principal 
executive offices of NUMAR are located at 508 Lapp Road, Malvern, Pennsylvania 
19355.

ITEM 2.    IDENTITY AND BACKGROUND

           This Schedule 13D is being filed by Halliburton Company, a
corporation organized under the laws of the State of Delaware ("Halliburton").
Halliburton is one of the world's largest diversified energy services and
engineering and construction services companies. The principal executive offices
of Halliburton are located at 3600 Lincoln Plaza, 500 North Akard Street,
Dallas, Texas, 75201-3391.

           Other than executive officers and directors, there are no persons or 
corporations controlling or ultimately in control of Halliburton.

           During the last five years, to the best of Halliburton's knowledge, 
neither Halliburton nor any of its executive officers or directors has been 
convicted in a criminal proceeding (excluding traffic violations or similar 
misdemeanors) or has been a party to a civil proceeding of a judicial or 
administrative body of competent jurisdiction as a result of which Halliburton
or such person was or is subject to a judgment, decree or final order enjoining
future violations of, or prohibiting or mandating activities subject to, federal
or state securities laws, or finding any violation with respect to such laws.

           With the exception of Lord Clitheroe who is a citizen of the United
Kingdom, each executive officer and director of Halliburton is a citizen of the
United States. The name, business address and present principal occupation of
each executive officer and director of Halliburton are set forth in Exhibit 99.1
to this Schedule 13D and are specifically incorporated herein by reference.

ITEM 3.    SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.

           Not applicable.

ITEM 4.    PURPOSE OF TRANSACTION.

           Halliburton, Halliburton M.S. Corp., a Delaware corporation and 
wholly owned subsidiary of Halliburton ("Merger Sub"), and NUMAR entered into an
Agreement and Plan of Merger, dated as of June 9, 1997 (the "Merger Agreement") 
pursuant to which Merger Sub will be merged with and into NUMAR (the "Merger"). 
Pursuant to the Merger Agreement, each share of NUMAR Common Stock issued and 
outstanding immediately prior to the effective time of the Merger (the 
"Effective Time") will be converted into 0.9664 of one share (the "Exchange 
Ratio") of common stock, par value $2.50 per share, of Halliburton ("Halliburton
Common Stock"). Halliburton has declared a two-for-one stock split to be
effected in the form of a 100% stock dividend payable in July 1997 to holders of
Halliburton Common Stock of record on June 26, 1997 (the "Stock Split"). All
information relating to Halliburton Common Stock set forth herein, including the
Exchange Ratio and all per share information, gives effect to the two-for-one
Stock Split. Notwithstanding the foregoing, if between June 9, 1997 and the
Effective Time the outstanding shares of Halliburton Common Stock or NUMAR
Common Stock are again changed into a different number of shares or a different
class by reason of any stock dividend, subdivision, combination or exchange of
shares or any reclassification or recapitalization, the Exchange Ratio will
again be correspondingly adjusted to reflect such stock dividend, subdivision,
combination or exchange of shares or any reclassification or recapitalization. A
copy of the Merger Agreement is

                                       2

 
included as Exhibit 99.2 to this Schedule 13D, and the Merger Agreement is
specifically incorporated by reference herein.

        Consummation of the transactions contemplated by the Merger Agreement is
subject to the terms and conditions contained in the Merger Agreement, including
the receipt of approval of the Merger by the shareholders of NUMAR, the receipt
of certain regulatory approvals, the receipt of legal opinions that the Merger
will be tax-free and the receipt of an opinion from Halliburton's independent
public accountants that the Merger will be accounted for as a pooling of
interests. The Merger Agreement will be submitted for approval at a special
meeting of shareholders of NUMAR (the "Special Meeting") that is expected to
take place during the latter part of the third calendar quarter of 1997.

        In order to induce Halliburton to enter into the Merger Agreement, four
directors of NUMAR and two other related parties (together, the "Affiliates")
have entered into Voting Agreements with Halliburton pursuant to which the
Affiliates have agreed to vote all shares of NUMAR Common Stock owned by them in
favor of the Merger Agreement (the "Voting Agreements"). The Affiliates who are
directors are Melvin N. Miller, the Chairman of the Board, President and Chief
Executive Officer of NUMAR, Barry M. Davis, Seymour G. Mandell and James H.
Simons. The other Affiliates are Davis Venture Partners, L.P., an affiliate of
Mr. Davis, and the Bermuda Trust Company Limited, as trustee of the Lord Jim
Trust, of which Mr. Simons is a principal beneficiary. An aggregate of 2,177,492
shares of NUMAR Common Stock, owned beneficially by the Affiliates, are subject
to the Voting Agreements. Such shares, as of the date hereof, represented
approximately 25.2% of the then outstanding shares of NUMAR Common Stock.

        Pursuant to the Voting Agreements, the Affiliates have, among other 
things, agreed to vote all shares of NUMAR Common Stock beneficially owned by 
them in favor of the Merger and against any business combination proposal or 
other matter that may interfere or be inconsistent with the Merger (including a 
Competing Transaction, as such term is defined in the Merger Agreement). They 
have also agreed, if reasonably requested by Halliburton in order to facilitate 
the Merger, not to attend and not to vote any shares of NUMAR Common Stock 
beneficially owned by them at any annual or special meeting of shareholders and 
not to execute any written consent of shareholders.

        Each of the Affiliates has also agreed that neither such Affiliate nor 
any corporation or other person or entity controlled by such affiliate, other 
than NUMAR and its subsidiaries (an "Affiliate Group"), will, directly or 
indirectly, sell, transfer, pledge or otherwise dispose of, or grant a proxy 
with respect to, any shares of NUMAR Common Stock beneficially owned by any
member of such Affiliate Group to any person or entity (other than to any member
of such Affiliate Group or its designee), or grant an option with respect to any
of the foregoing, or enter into any other agreement or arrangement with respect
to any of the foregoing.

        The Voting Agreements will terminate on the earlier of February 28, 1998
or the termination of the Merger Agreement. A copy of one of the Voting
Agreements, all of which are substantially identical, is included as Exhibit
99.3 to this Schedule 13D, and such Voting Agreement is specifically
incorporated by reference herein.

        Except as set forth herein, Halliburton presently does not have any 
plans or proposals that relate to or would result in any of the actions
specified in clauses (a) through (j) of Item 4 of Schedule 13D.

                                       3

 
ITEM 5.    INTEREST IN SECURITIES OF ISSUER.

           Pursuant to the Voting Agreements, each Affiliate, as described above
in Item 4, has agreed to vote, and to cause each member of his or its Affiliate 
Group to vote, all shares of NUMAR Common Stock beneficially owned by them in 
favor of the Merger and against any business combination proposal or other 
matter that may interfere or be inconsistent with the Merger (including a 
Competing Transaction). Each Affiliate also has agreed, if reasonably requested 
by Halliburton in order to facilitate the Merger, that he or it will not, and 
will cause each member of his or its Affiliate Group not to, attend or vote any 
shares of NUMAR Common Stock beneficially owned by them at any annual or special
meeting of shareholders or execute any written consent of shareholders. 
Consequently, Halliburton shares voting, but no dispositive, power as to such 
2,145,492 shares of NUMAR Common Stock.

           Each Affiliate also has agreed that neither he or it nor any member 
of his or its Affiliate Group will, directly or indirectly, sell, transfer, 
pledge or otherwise dispose of, or grant a proxy with respect to, any shares of 
NUMAR Common Stock beneficially owned by any member of such Affiliate Group to 
any person or entity (other than to any member of such Affiliate Group or its 
designee), or grant an option with respect to any of the foregoing, or enter 
into any other agreement or arrangement with respect to any of the foregoing.

           Pursuant to a Stock Option Agreement, dated as of June 9, 1997 (the
"Stock Option Agreement"), by and between Halliburton and NUMAR, NUMAR has
granted to Halliburton an irrevocable option (the "Stock Option") to purchase a
number of shares equal to up to 15% of the shares of NUMAR Common Stock
outstanding as of June 9, 1997 (as adjusted) for an exercise price of $36.00 per
share. The Stock Option is exercisable only after the occurrence of certain
specific events, to wit: either (i) the commencement by any person (other than
Halliburton or any of its affiliates) of a tender or exchange offer to purchase
35% or more of the outstanding shares of NUMAR Common Stock and the failure of
the NUMAR Board of Directors, within ten business days thereafter, to recommend
against acceptance of such tender or exchange offer by the NUMAR shareholders or
its election to take no position with respect thereto; or (ii) the acquisition
by any person (other than Halliburton or any of its subsidiaries) or group,
subsequent to the date of the Merger Agreement, of beneficial ownership or the
right to acquire beneficial ownership of (A) 35% or more of the then outstanding
shares of NUMAR Common Stock and the Merger Agreement has failed to receive the
requisite vote for adoption thereof at the Special Meeting or (B) 45% or more of
the then outstanding shares of NUMAR Common Stock.

           The Stock Option was granted by NUMAR to Halliburton in connection
with, and as an inducement for, Halliburton's entering into the Merger
Agreement. A copy of the stock Option Agreement is included as Exhibit 99.4 to
this Schedule 13D, and the Stock Option Agreement is specifically incorporated
by reference herein.

           No transactions in NUMAR Common Stock were effected during the past 
sixty days by Halliburton or, to the best of Halliburton's knowledge, by any 
executive officer or director of Halliburton. In addition, no other person is 
known by Halliburton to have the right to receive or the power to direct the 
receipt of dividends from, or the proceeds from the sale of, the securities 
covered by this Schedule 13D.

                                       4

 
ITEM 6.    CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT
           TO SECURITIES OF THE ISSUER.

           Contracts, arrangements, understandings or relationships with respect
to securities of NUMAR consist of the Merger Agreement, the Voting Agreements,
the Stock Option Agreement and certain affiliate's agreements, by and between
Halliburton, on the one hand, and the affiliates of NUMAR or the affiliates of
Halliburton, on the other (collectively, the "Affiliate's Agreements"). Copies
of each form of the Affiliate's Agreements are attached hereto as Exhibits 99.5
and 99.6, and are specifically incorporated herein by reference. See also
description of certain of aforementioned documents in Items 4 and 5 above.

ITEM 7.    MATERIAL TO BE FILED AS EXHIBITS.

           The following Exhibits are filed as part of this Schedule 13D:

Exhibit 99.1  --  Name, Business Address, and Present Principal Occupation of
                  Each Executive Officer and Director of Halliburton.

Exhibit 99.2  --  Agreement and Plan of Merger, dated as of June 9, 1997, by and
                  among Halliburton, Merger Sub and NUMAR (incorporated by
                  reference to Exhibit 2(a) to Halliburton's Current Report on
                  Form 8-K dated June 13, 1997).

Exhibit 99.3  --  Voting Agreement dated as of June 9, 1997 by and between
                  Halliburton and Dr. Melvin N. Miller (incorporated by
                  reference to Exhibit 2(c) to Halliburton's Current Report on
                  Form 8-K dated June 13, 1997). Each of the other Voting
                  Agreements is substantially identical thereto.

Exhibit 99.4  --  Stock Option Agreement dated as of June 9, 1997, by and
                  between Halliburton and NUMAR (incorporated by reference to
                  Exhibit 2(b) to Halliburton's Current Report on Form 8-K dated
                  June 13, 1997).

Exhibit 99.5  --  Form of Affiliate's Agreement by and between Halliburton and
                  certain affiliates of NUMAR.

Exhibit 99.6  --  Form of Affiliate's Agreement by and between Halliburton and
                  certain affiliates of Halliburton.


                                   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: June 16, 1997                             HALLIBURTON COMPANY

                                            By: /s/ SUSAN S. KEITH
                                                ____________________________
                                                Susan S. Keith
                                                Vice President and Secretary

 

                                                                    EXHIBIT 99.1

          NAME, BUSINESS ADDRESS AND PRESENT PRINCIPAL OCCUPATION OF
              EACH EXECUTIVE OFFICER AND DIRECTOR OF HALLIBURTON

I.   Executive Officers of Halliburton

NAME BUSINESS ADDRESS PRESENT PRINCIPAL OCCUPATION - ----------------- ------------------------- -------------------------------- Richard B. Cheney 3600 Lincoln Plaza, Chairman of the Board and Chief 500 North Akard Street Executive Officer and Director Dallas, Texas 75201-3391 David J. Lesar 3600 Lincoln Plaza, President and Chief Operating 500 North Akard Street Officer Dallas, Texas 75201-3391 Lester L. Coleman 3600 Lincoln Plaza Executive Vice President and 500 North Akard Street General Counsel Dallas, Texas 75201-3391 Dale P. Jones 3600 Lincoln Plaza, Vice Chairman and Director 500 North Akard Street Dallas, Texas 75201-3391 Kenneth R. LeSuer 5151 San Felipe Vice Chairman Houston, Texas 77056 Gary V. Morris 4100 Clinton Drive Executive Vice President and Houston, Texas 77020 Chief Financial Officer Lewis W. Powers 4100 Clinton Drive Senior Vice President Houston, Texas 77020 Jerry H. Blurton 4100 Clinton Drive Vice President and Treasurer Houston, Texas 77020 Robert Charles Muchmore, Jr. 4100 Clinton Drive Vice President and Controller Houston, Texas 77020 II. Directors of Halliburton NAME BUSINESS ADDRESS PRESENT PRINCIPAL OCCUPATION - ----------------- ------------------------- -------------------------------- Anne L. Armstrong Kleberg National Bank Building Chairman of the Board of 6th and Kleberg Streets Trustees, Center for Strategic and Kingsville, Texas 78363 International Studies, Washington, DC Richard B. Cheney 3600 Lincoln Plaza, Chairman of the Board and Chief 500 North Akard Street Executive Officer of Halliburton Dallas, Texas 75201-3391 Company Lord Clitheroe Downham Hall, Clitheroe Chairman, The Yorkshire Bank, Lancashire, BB7 4DN PLC
NAME BUSINESS ADDRESS PRESENT PRINCIPAL OCCUPATION - ----------------- ------------------------- -------------------------------- Robert L. Crandall AMR Corporation Chairman, President and Chief 4333 Amon Carter Boulevard Executive Officer, 6 North AMR Corporation; and Chairman Ft. Worth, Texas 76155 and Chief Executive Officer, American Airlines, Inc. W.R. Howell 6501 Legacy Drive, Building A Chairman Emeritus, J.C. Penney 1st Floor Company, Inc. Plano, Texas 75024 Delano E. Lewis 635 Massachusetts Avenue, N.W. President and Chief Executive Washington, DC 20001-3753 Officer, National Public Radio Dale P. Jones 3600 Lincoln Plaza, Vice Chairman, Halliburton 500 North Akard Street Company Dallas, Texas 75201-3391 C.J. Silas P.O Box 2127 Retired Chairman of the Board 408 Professional Building and Chief Executive Officer, 4th & Keeler Streets Phillips Petroleum Company Bartlesville, Oklahoma 74003 Roger T. Staubach 6750 LBJ Freeway, Suite 1100 Chairman and Chief Executive Dallas, Texas 75240 Officer, The Staubach Company Richard J. Stegemeier 376 South Valencia Avenue Chairman Emeritus, Unocal Brea, California 92621 Corporation