<PAGE>   1
                                                                 EXHIBIT 10.19




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                            SMITH INTERNATIONAL, INC.



                                 FIRST AMENDMENT


                             Dated as of May 5, 1997



                                       TO



                                 NOTE AGREEMENT


                            Dated as of May 21, 1996



                        RE: 7.24% SENIOR GUARANTEED NOTES
                                DUE APRIL 2, 2001
                                       AND
                          7.63% SENIOR GUARANTEED NOTES
                                DUE APRIL 2, 2006



===============================================================================



<PAGE>   2


         THIS FIRST AMENDMENT dated as of May 5, 1997 (the or this "First
Amendment") to the several Note Agreements, each dated as of May 21, 1996
between SMITH INTERNATIONAL, INC., a Delaware corporation (the "Company"), and
each of the institutions identified in Schedule 1 thereto (collectively, the
"Purchasers"), is between the Company and each of the institutions which is a
signatory to this First Amendment (the "Required Noteholders").

                                    RECITALS:

         A. The Company and each of the Purchasers have heretofore entered into
separate and several Note Agreements, each dated as of May 21, 1996 (the "Note
Agreements"). The Required Noteholders are the holders of at least 66-2/3% of
the Company's 7.24% Senior Guaranteed Notes due April 2, 2001 in the aggregate
principal amount of $30,000,000 and the Company's 7.63% Senior Guaranteed Notes
due April 2, 2006 in the aggregate principal amount of $20,000,000
(collectively, the "Notes") issued and sold under and pursuant to the Note
Agreements.

         B. The Company and the Required Noteholders now desire to amend the
Note Agreements effective as of even date herewith (the "First Amendment
Effective Date") in the respects, but only in the respects, hereinafter set
forth. Pursuant to Section 7.1 of the Note Agreements, the consent of the
Required Noteholders is required to amend the Note Agreements as contemplated
herein.

         C. Capitalized terms used herein but not otherwise defined shall have
the meanings assigned thereto in the Note Agreements.

         NOW, THEREFORE, the acceptance hereof by the Required Noteholders and
the full and complete satisfaction of the conditions precedent to the
effectiveness of this First Amendment set forth in Section 3.1 hereof, will
confirm the understanding of the Company and the Required Noteholders that the
Note Agreements shall be and are hereby amended in the following respects:

SECTION 1.  AMENDMENTS.

         SECTION 1.1. AMENDMENT TO SECTION 5.9(a)(5). Section 5.9(a)(5) of the
Note Agreements shall be and is hereby amended in its entirety so that the same
shall henceforth read as follows:

         "(5) Funded Debt or Current Debt of M-I Drilling and its Subsidiaries
not exceeding the sum of (i) $80,000,000 in the aggregate at any one time
outstanding under the M-I Drilling Loan Facility or any Qualified Replacement
Facility (including Guaranties thereof by the Company to the extent, and only to
the extent, of its ownership interest in M-I Drilling) plus (ii) $7,400,000 in
the aggregate; and"

<PAGE>   3

         SECTION 1.2 AMENDMENT OF DEFINITIONS. The following definitions shall
be and are hereby added to Section 8.1 of the Existing Note Agreements in their
alphabetical order:

         ""First Amendment" shall mean the First Amendment dated as of May 5,
1997 to the Note Agreement entered into by the Company and the Required
Noteholders."

         ""First Amendment Effective Date" shall mean May 5, 1997."

SECTION 2. REPRESENTATIONS AND WARRANTIES OF THE COMPANY.

         The Company hereby represents and warrants to each of you that all of
the representations and warranties set forth in Exhibit A attached hereto are
true and correct as of the date of acceptance set forth on the signature pages
to this First Amendment and are incorporated herein by reference with the same
force and effect as though herein set forth in full.

SECTION 3. MISCELLANEOUS.

         SECTION 3.1. This First Amendment shall become effective and binding
upon the Company and the holders of the Notes on the First Amendment Effective
Date upon the acceptance hereof by the Required Noteholders in the space below
and upon the satisfaction in full of the following conditions:

         (a) each of the holders of the Notes shall have received a certificate
dated the date of acceptance set forth on the signature pages to this First
Amendment, signed by the President or a Vice-President of the Company, the truth
and accuracy of which shall be a condition to their obligations under this First
Amendment to the effect that: (1) the representations and warranties of the
Company set forth in Exhibit A attached hereto are true and correct on and with
respect to the First Amendment Effective Date and (2) no Default or Event of
Default has occurred and is then continuing, after giving effect to the
amendments set forth herein;

         (b) the holders of the Notes shall have received, in form and substance
reasonably satisfactory to such holders and their special counsel, such
documents and evidence with respect to the Company as such holders may
reasonably request in order to establish the existence and good standing of the
Company and the authorization, execution and delivery of this First Amendment;

         (c) the holders of the Notes shall have received an opinion of counsel
from counsel to the Company covering the matters set forth in clause (b) of this
Section 3.1 and such other matters relating to the First Amendment as the
holders of the Notes may reasonably request;

         (d) ACQCO shall have consented to the execution and delivery of this
First Amendment and the holders of the Notes shall have received a true, correct
and complete originally executed copy thereof; and

<PAGE>   4
          (e) Any consents or approvals from any holder or holders of any
outstanding Security of the Company or ACQCO and any amendments of agreements
pursuant to which any Securities may have been issued which shall be necessary
to permit the consummation of the transactions contemplated hereby shall have
been obtained and all such consents or amendments shall be reasonably
satisfactory in form and substance to the holders of the Notes and their special
counsel and such holders and their special counsel shall have received true,
correct and complete copies of such executed consents and amendments.

         SECTION 3.2. The Company agrees to pay all reasonable fees and expenses
of the holders of the Notes and their special counsel in connection with the
preparation, execution and delivery of this First Amendment.

         SECTION 3.3. Whenever in any certificate, letter, notice or other
instrument reference is made to the Note Agreements, such reference without more
shall include reference to this First Amendment.

         SECTION 3.4. Except as modified and expressly amended by this First
Amendment, the Note Agreements and the Notes are in all respects ratified,
confirmed and approved and all of the terms, provisions and conditions thereof
shall be and remain in full force and effect, including (without limitation)
Sections 9.9, 9.10 and 9.12 of the Note Agreements. The descriptive headings of
the various Sections or parts of this First Amendment are for convenience only
and shall not affect the meaning or construction of any of the provisions
hereof.

         SECTION 3.5. This First Amendment may be executed and delivered in any
number of counterparts, each of such counterparts constituting an original, but
all together only one First Amendment.


<PAGE>   5

                                                     SMITH INTERNATIONAL, INC.



                                                     By  /s/ TRACY M. WELCH
                                                        ------------------------
                                                        Its Assistant Treasurer


                                                     By  /s/ JOHN J. KENNEDY
                                                        ------------------------
                                                        Its Sr. Vice President,
                                                            CFO & Treasurer 




SMITH INTERNATIONAL, INC. - FIRST AMENDMENT TO NOTE AGREEMENT

<PAGE>   6

                                                   PRINCIPAL MUTUAL LIFE
                                                   INSURANCE COMPANY



                                                   By  /s/
                                                      --------------------------
                                                      Its



                                                   By  /s/
                                                      --------------------------
                                                      Its Securities Investment



AGREED TO AND ACCEPTED
THIS 5TH DAY OF MAY, 1997



SMITH INTERNATIONAL, INC. - FIRST AMENDMENT TO NOTE AGREEMENT

<PAGE>   7




                                               JOHN HANCOCK MUTUAL
                                               INSURANCE COMPANY



                                               By /s/ EUGENE R. HODGE, JR.
                                                  ------------------------------
                                                  Its Senior Investment Officer






AGREED TO AND ACCEPTED
THIS 5TH DAY OF MAY, 1997



SMITH INTERNATIONAL, INC. - FIRST AMENDMENT TO NOTE AGREEMENT


<PAGE>   8




                                               JOHN HANCOCK VARIABLE
                                               LIFE INSURANCE COMPANY



                                               By /s/ EUGENE R. HODGE, JR.
                                                  ------------------------------
                                                  Its Senior Investment Officer






AGREED TO AND ACCEPTED
THIS 5TH DAY OF MAY, 1997



SMITH INTERNATIONAL, INC. - FIRST AMENDMENT TO NOTE AGREEMENT



<PAGE>   9




                                                      IDS CERTIFICATE COMPANY



                                                      By
                                                         ----------------------
                                                         Its






AGREED TO AND ACCEPTED
THIS 5TH DAY OF MAY, 1997



SMITH INTERNATIONAL, INC. - FIRST AMENDMENT TO NOTE AGREEMENT


<PAGE>   10



                                                      MELLON BANK, N.A., SOLELY
                                                      IN ITS CAPACITY AS TRUSTEE
                                                      FOR THE AT&T MASTER
                                                      PENSION TRUST (AS DIRECTED
                                                      BY JOHN HANCOCK MUTUAL
                                                      LIFE INSURANCE COMPANY),
                                                      AND NOT IN ITS INDIVIDUAL
                                                      CAPACITY



                                                      By  /s/ ROBERT SASS
                                                         ----------------------
                                                         Its Vice President






AGREED TO AND ACCEPTED
THIS 5TH DAY OF MAY, 1997



SMITH INTERNATIONAL, INC. - FIRST AMENDMENT TO NOTE AGREEMENT


<PAGE>   11




                                                      THE MARITIME LIFE
                                                      ASSURANCE COMPANY



                                                      By
                                                         ----------------------
                                                         Its



                                                      By
                                                         ----------------------
                                                         Its



AGREED TO AND ACCEPTED
THIS 5TH DAY OF MAY, 1997



SMITH INTERNATIONAL, INC. - FIRST AMENDMENT TO NOTE AGREEMENT

<PAGE>   12
                                                                     EXHIBIT A


                         REPRESENTATIONS AND WARRANTIES


The Company represents and warrants to you as follows:

1.       Corporate Organization and Authority.  The Company and each Subsidiary

         (a) is a corporation duly organized, validly existing and in good
standing under the laws of its jurisdiction of incorporation and has not
commenced any proceedings to dissolve;

         (b) has all requisite power and authority and all necessary licenses
and permits to own and operate its properties and to carry on its business as
now conducted and as presently proposed to be conducted; and

         (c) is duly licensed or qualified and is in good standing as a foreign
corporation in each jurisdiction wherein the nature of the business transacted
by it or the nature of the property owned or leased by it makes such licensing
or qualification necessary, except for such jurisdictions wherein the failure to
be so licensed or qualified would not have a Material Adverse Effect.

         2. Full Disclosure. Neither the First Amendment nor any other written
statement furnished by the Company to you in connection with the negotiation of
the First Amendment, contain any untrue statement of a material fact or omit a
material fact necessary to make the statements contained therein or herein not
misleading. There is no fact peculiar to the Company which the Company has not
disclosed to you in writing which materially affects adversely nor, so far as
the Company can now foresee, will materially affect adversely the properties,
business, prospects, profits or condition (financial or otherwise) of the
Company or the ability of the Company to enter into and perform the First
Amendment.

         3. Transactions Legal and Authorized. The execution and delivery of the
First Amendment

         (a) are within the corporate powers of the Company;

         (b) will not violate any material provisions of any law or any order of
any court or governmental authority or agency and will not conflict with or
result in any breach of any of the terms, conditions or provisions of, or
constitute a default under, the Certificate of Incorporation or By-laws of the
Company or any loan agreement, indenture or other agreement or instrument to
which the Company will be a party or by which it may be bound on the First
Amendment Effective Date or result in the imposition of any Lien on any property
of the Company; and


<PAGE>   13

         (c) have been duly authorized by proper corporate action on the part of
the Company (no action by the stockholders of the Company being required by law,
by the Certificate of Incorporation or the By-laws of the Company or otherwise),
executed and delivered by the Company and the First Amendment constitutes the
legal, valid and binding obligation, contract and agreement of the Company
enforceable in accordance with its terms.

         4. Pending Litigation. There are no proceedings pending or, to the
knowledge of the Company, threatened against or affecting the Company in any
court or before any governmental authority or arbitration board or tribunal
which, if adversely determined, could in the aggregate have a material adverse
effect on the properties, business, prospects, profits or condition (financial
or otherwise) of the Company and its Subsidiaries. The Company is not in default
with respect to any order of any court or governmental authority or arbitration
board or tribunal.

         5. No Defaults. Neither the Company nor any Subsidiary is in default
(a) in the payment of principal or interest on any Indebtedness for borrowed
money or (b) under any instrument or instruments or agreements under and subject
to which any Indebtedness for borrowed money has been issued, and no event has
occurred and is continuing under the provisions of any such instrument or
agreement which with the lapse of time or the giving of notice, or both, would
constitute an event of default thereunder. Neither the Company nor any
Subsidiary is in violation of any term of any agreement, charter instrument,
regulation or other instrument to which it is a party or by which it may be
bound which violation would in the aggregate have a material adverse effect on
the business or the financial condition of the Company.

         6. Consents. No approval, consent or withholding of objection on the
part of any regulatory body, state, Federal or local, is necessary in connection
with the execution and delivery by the Company of the First Amendment or
compliance by the Company with any of the provisions thereof. All approvals and
consents required from any other Person for the due execution and delivery by
the Company of the First Amendment and compliance by the Company with any of the
provisions thereof have been obtained and are in full force and effect.

         7. Compliance with Law. Neither the Company nor any Subsidiary (a) is
in violation of any law, ordinance, franchise, governmental rule or regulation
to which it is subject; or (b) has failed to obtain any license, permit,
franchise or other governmental authorization necessary to the ownership of its
property or to the conduct of its business, which violation or failure to obtain
would, individually or in the aggregate, materially adversely affect the
business, prospects, profits, properties or condition (financial or otherwise)
of the Company and its Subsidiaries, taken as a whole, or impair the ability of
the Company to perform its obligations contained in the First Amendment. Neither
the Company nor any Subsidiary is in default with respect to any order of any
court or governmental authority or arbitration board or tribunal.

<PAGE>   14

                       CONFIRMATION OF GUARANTY AGREEMENT



         Smith International Acquisition Corp. (the "GUARANTOR") pursuant to
that certain Guaranty Agreement dated as of May 26, 1996 (the "GUARANTY"), which
has been executed and delivered by the Guarantor to the Noteholders (as defined
in the Guaranty), hereby agrees that its liabilities thereunder are and shall
remain enforceable against such Guarantor in accordance with their terms, and
are, and shall continue to be, in full force and effect and shall not be
reduced, altered, limited, lessened or in any way affected by the execution and
delivery of the First Amendment to Note Agreement dated as of even date herewith
and to which this Confirmation of Guaranty Agreement is attached, executed by
the Company (as defined in the First Amendment) and the Required Noteholders (as
defined in the First Amendment), and are hereby confirmed and ratified in all
respects.

     WITNESS THE EXECUTION HEREOF, effective as of the 5th day of May, 1997.

                              SMITH INTERNATIONAL ACQUISITION CORP.



                              By:
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                                  Name: 
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                                  Title:
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