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                                                                     Exhibit 4.5

                              Schlumberger Limited

             1.500% Series A Convertible Debentures due June 1, 2023
             2.125% Series B Convertible Debentures due June 1, 2023

                          Registration Rights Agreement

                                                                    June 9, 2003

Citigroup Global Markets Inc.
Goldman, Sachs & Co.,
  As representatives of the several Purchasers
  named in Schedule I hereto
c/o Goldman, Sachs & Co.
85 Broad Street
New York, New York 10004

Ladies and Gentlemen:

       Schlumberger Limited (Schlumberger N.V.), a Netherlands Antilles
corporation established in Curacao (the "Company"), proposes to issue and sell
to the several parties named in Schedule I to the Purchase Agreement (the
"Purchasers") for whom you are acting as representatives, upon the terms set
forth in the purchase agreement dated June 4, 2003 (the "Purchase Agreement"),
its 1.500% Series A Convertible Debentures due June 1, 2023 and its 2.125%
Series B Convertible Debentures due June 1, 2023 (collectively, the
"Securities"). As an inducement to the Purchasers to enter into the Purchase
Agreement and in satisfaction of a condition to the obligations of the
Purchasers thereunder, the Company agrees with the several Purchasers for the
benefit of Holders (as defined herein) from time to time of the Registrable
Securities (as defined herein) as follows:

       1.  Definitions.

       (a) Capitalized terms used herein without definition shall have the
meanings ascribed to them in the Purchase Agreement. As used in this Agreement,
the following defined terms shall have the following meanings:

       "Act" or "Securities Act" means the United States Securities Act of 1933,
as amended.

       "Affiliate" of any specified person means any other person which,
directly or indirectly, is in control of, is controlled by, or is under common
control with such specified person. For purposes of this definition, control of
a person means the power, direct or indirect, to direct or cause the direction
of the management and policies of such person whether by contract or otherwise;
and the terms "controlling" and "controlled" have meanings correlative to the
foregoing.

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       "Applicable Amount" means, (i) with respect to the Securities, the
principal amount of the Securities and, (ii) with respect to shares of Common
Stock issued upon conversion of the Securities pursuant to the Indenture, the
principal amount of Securities that would then be convertible into such shares.

       "Business Day" means each Monday, Tuesday, Wednesday, Thursday and Friday
which is not a day on which banking institutions in New York are generally
authorized or obligated by law or executive order to close.

       "Closing Date" means the First Time of Delivery as defined in the
Purchase Agreement.

       "Commission" means the United States Securities and Exchange Commission,
or any other federal agency at the time administering the Exchange Act, the
Securities Act or the Trust Indenture Act, whichever is the relevant statute for
the particular purpose.

       "Common Stock" means the Company's common stock, par value $.01 per
share.

       "DTC" means The Depository Trust Company.

       "Effectiveness Period" has the meaning assigned thereto in Section
2(b)(i) hereof.

       "Effective Time" means the time at which the Commission declares the
Shelf Registration Statement effective or at which the Shelf Registration
Statement otherwise becomes effective.

       "Electing Holder" has the meaning assigned thereto in Section 3(a)(iii)
hereof.

       "Exchange Act" means the United States Securities Exchange Act of 1934,
as amended.

       "Holder" means, any person that is the record owner of Registrable
Securities (and includes any person that has a beneficial interest in any
Registrable Security in book-entry form).

       "Indenture" means the Indenture, dated as of June 9, 2003, between the
Company and Citibank, N.A., as supplemented by the first supplemental indenture
thereto dated as of the same date, and as further amended and supplemented from
time to time in accordance with its terms.

       "Liquidated Damages" has the meaning assigned thereto in Section 7(a)
hereof.

       "Managing Underwriters" means the investment banker or investment bankers
and manager or managers that shall administer an underwritten offering, if any,
conducted pursuant to Section 6 hereof.

       "NASD Rules" means the Rules of the National Association of Securities
Dealers, Inc., as amended from time to time.

       "Notice and Questionnaire" means a Notice of Registration Statement and
Selling Securityholder Questionnaire substantially in the form of Appendix A
hereto.

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       The term "person" means an individual, partnership, corporation, trust or
unincorporated organization, or a government or agency or political subdivision
thereof.

       "Prospectus" means the prospectus (including, without limitation, any
preliminary prospectus, any final prospectus and any prospectus that discloses
information previously omitted from a prospectus filed as part of an effective
registration statement in reliance upon Rule 430A under the Act) included in the
Shelf Registration Statement, as amended or supplemented by any prospectus
supplement with respect to the terms of the offering of any portion of the
Registrable Securities covered by the Shelf Registration Statement and by all
other amendments and supplements to such prospectus, including all material
incorporated by reference in such prospectus and all documents filed after the
date of such prospectus by the Company under the Exchange Act and incorporated
by reference therein.

       "Registrable Securities" means all or any portion of the Securities
issued from time to time under the Indenture in registered form and the shares
of Common Stock issuable upon conversion of such Securities; provided, however,
that a security ceases to be a Registrable Security when it is no longer a
Restricted Security.

       "Registration Default" has the meaning assigned thereto in Section 7(a)
hereof.

       "Restricted Security" means any Security or share of Common Stock
issuable upon conversion thereof except any such Security or share of Common
Stock that (i) has been effectively registered under the Securities Act and sold
in a manner contemplated by the Shelf Registration Statement, (ii) has been
transferred in compliance with Rule 144 under the Securities Act (or any
successor provision thereto) or is transferable pursuant to paragraph (k) of
such Rule 144 (or any successor provision thereto) (assuming that the Holder
thereto is not an Affiliate of the Company) or (iii) has otherwise been
transferred and a new Security or share of Common Stock not subject to transfer
restrictions under the Securities Act has been delivered by or on behalf of the
Company in accordance with the Indenture.

       "Rules and Regulations" means the published rules and regulations of the
Commission promulgated under the Securities Act or the Exchange Act, as in
effect at any relevant time.

       "Shelf Registration" means a registration effected pursuant to Section 2
hereof.

       "Shelf Registration Statement" means a "shelf" registration statement
filed under the Securities Act providing for the registration of, and the sale
on a continuous or delayed basis by the Holders of, all of the Registrable
Securities pursuant to Rule 415 under the Securities Act and/or any similar rule
that may be adopted by the Commission, filed by the Company pursuant to the
provisions of Section 2 of this Agreement, including the Prospectus contained
therein, any amendments and supplements to such registration statement,
including post-effective amendments, and all exhibits and all material
incorporated by reference in such registration statement.

       "Suspension Period" has the meaning assigned thereto in Section 2(c)
hereof.

       "Trust Indenture Act" means the Trust Indenture Act of 1939, or any
successor thereto, and the rules, regulations and forms promulgated thereunder,
as the same shall be amended from time to time.

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       The term "underwriter" means any underwriter of Registrable Securities in
connection with an offering thereof under a Shelf Registration Statement.

       (b) Wherever there is a reference in this Agreement to a percentage of
the "principal amount" of Registrable Securities or to a percentage of
Registrable Securities, Common Stock shall be treated as representing the
Applicable Amount with respect thereto.

       2.  Shelf Registration.

       (a) The Company shall, no later than 120 calendar days following the
Closing Date, file with the Commission a Shelf Registration Statement relating
to the offer and sale of the Registrable Securities by the Holders from time to
time in accordance with the methods of distribution elected by such Holders and,
thereafter, shall use its best efforts to cause such Shelf Registration
Statement to be declared effective under the Act no later than 180 calendar days
following the Closing Date; provided, however, that the Company may, upon
written notice to all Electing Holders, postpone having the Shelf Registration
Statement declared effective for a reasonable period not to exceed 90 days if
the Company possesses material non-public information, the disclosure of which
would have a material adverse effect on the Company and its subsidiaries taken
as a whole; provided, further, however, that no Holder shall be entitled to be
named as a selling securityholder in the Shelf Registration Statement or to use
the Prospectus forming a part thereof for resales of Registrable Securities
unless such Holder is an Electing Holder.

       (b) The Company shall use its reasonable best efforts:

           (i)   to keep the Shelf Registration Statement continuously
       effective, supplemented and amended as required by the provisions of
       Section 3(j) hereto, in order to permit the Prospectus forming a part
       thereof to be usable by Holders until the earliest of (1) the sale of all
       Registrable Securities registered under the Shelf Registration Statement;
       (2) the expiration of the period referred to in Rule 144(k) of the Act
       with respect to all Registrable Securities held by Persons that are not
       Affiliates of the Company; (3) two years from the last date of original
       issuance of any Registrable Securities; and (4) the date when there are
       no Registrable Securities outstanding (such period being referred to
       herein as the "Effectiveness Period").

           (ii)  after the Effective Time of the Shelf Registration Statement,
       promptly upon the request of any Holder of Registrable Securities that is
       not then an Electing Holder, to take any action reasonably necessary to
       enable such Holder to use the Prospectus forming a part thereof for
       resales of Registrable Securities, including, without limitation, any
       action necessary to identify such Holder as a selling securityholder in
       the Shelf Registration Statement; provided, however, that nothing in this
       subparagraph shall relieve such Holder of the obligation to return a
       completed and signed Notice and Questionnaire to the Company in
       accordance with Section 3(a)(ii) hereof; and

           (iii) if at any time the Securities, pursuant to the Indenture, are
       convertible into securities other than Common Stock, to cause, or to
       cause any successor under the Indenture to cause, such securities to be
       included in the Shelf Registration Statement no later than the date on
       which the Securities may then be convertible into such securities.

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The Company shall be deemed not to have used its reasonable best efforts to keep
the Shelf Registration Statement effective during the Effectiveness Period if
the Company voluntarily takes any action that would result in Holders of
Registrable Securities covered thereby not being able to offer and sell any of
such Registrable Securities during that period, unless such action is (A)
required by applicable law and the Company thereafter promptly complies with the
requirements of paragraph 3(j) below or (B) permitted pursuant to Section 2(c)
below.

       (c)     The Company may suspend the use of the Prospectus for a period
not to exceed 45 days in any 90-day period or an aggregate of 120 days in any
360-day period, during the period beginning on the issue date and ending on or
prior to the second anniversary of the last issue date of any Debentures (each,
a "Suspension Period") if the Company shall have determined in good faith that
because of valid business reasons (not including avoidance of the Company's
obligations hereunder), including the acquisition or divestiture of assets,
pending corporate developments and similar events, it is in the best interests
of the Company to suspend such use, and prior to suspending such use the Company
provides the Holders with written notice of such suspension, which notice need
not specify the nature of the event giving rise to such suspension. Each Holder,
by its acceptance of the Securities, agrees to hold any such communication by
the Company in confidence.

       3.      Registration Procedures. In connection with the Shelf
Registration Statement, the following provisions shall apply:

       (a) (i) Not less than 30 calendar days prior to the Effective Time of the
Shelf Registration Statement, the Company shall mail the Notice and
Questionnaire to the Holders of Registrable Securities. Holders of Registrable
Securities shall have at least 20 calendar days from the date on which the
Notice and Questionnaire is first mailed to such Holders to return a completed
and signed Notice and Questionnaire to the Company. The Company shall take
action to name each Holder that is an Electing Holder as of the date that is 5
business days prior to the effectiveness of the Shelf Registration Statement as
a selling securityholder in the Shelf Registration Statement at the time of its
effectiveness so that such Holder is permitted to deliver the Prospectus forming
a part thereof as of such time to purchasers of such Holder's Registrable
Securities in accordance with applicable law. The Company shall not be required
to take any action to name any Holder as a selling securityholder in the Shelf
Registration Statement or to enable any Holder to use the Prospectus forming a
part thereof for resales of Registrable Securities until such Holder has
returned a completed and signed Notice and Questionnaire to the Company.

               (ii) After the Effective Time of the Shelf Registration
       Statement, the Company shall, upon the request of any Holder of
       Registrable Securities that is not then an Electing Holder, promptly send
       a Notice and Questionnaire to such Holder. From and after the Effective
       Time of the Shelf Registration Statement, the Company shall (A) as
       promptly as is practicable after the date a completed and signed Notice
       and Questionnaire is delivered to the Company, and in any event within
       ten Business Days after such date, prepare and file with the Commission
       (x) a supplement to the Prospectus or, if required by applicable law, a
       post-effective amendment to the Shelf Registration Statement and (y) any
       other document required by applicable law, so that the Holder delivering
       such Notice and Questionnaire is named as a selling securityholder in the
       Shelf Registration Statement and is permitted to deliver the Prospectus
       to purchasers of such Holder's Registrable Securities in accordance with
       applicable law, and (B) if the Company shall file a post-effective
       amendment to the Shelf

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       Registration Statement, use its reasonable best efforts to cause such
       post-effective amendment to become effective under the Securities Act as
       promptly as is practicable; provided, however, that if a Notice and
       Questionnaire is delivered to the Company during a Suspension Period, the
       Company shall not be obligated to take the actions set forth in this
       clause (ii) until the termination of such Suspension Period.

           (iii) The term "Electing Holder" shall mean any Holder of Registrable
       Securities that has returned a completed and signed Notice and
       Questionnaire to the Company in accordance with Section 3(a)(i) or
       3(a)(ii) hereof.

       (b) The Company shall furnish to one counsel for the Electing Holders,
prior to the Effective Time, a copy of the Shelf Registration Statement
initially filed with the Commission, and shall furnish to such counsel, prior to
the filing thereof with the Commission, copies of each amendment thereto and
each amendment or supplement, if any, to the Prospectus included therein, and
shall use its best efforts to reflect in each such document, at the Effective
Time or when so filed with the Commission, as the case may be, such comments as
the Holders and their counsel reasonably may propose.

       (c) The Company shall promptly take such action as may be necessary so
that (i) each of the Shelf Registration Statement and any amendment thereto and
the Prospectus forming a part thereof and any amendment or supplement thereto
(and each report or other document incorporated therein by reference in each
case) complies in all material respects with the Securities Act and the Exchange
Act and the respective rules and regulations thereunder, (ii) each of the Shelf
Registration Statement and any amendment thereto does not, when it becomes
effective, contain an untrue statement of a material fact or omit to state a
material fact required to be stated therein or necessary to make the statements
therein not misleading and (iii) each of the Prospectus forming a part of the
Shelf Registration Statement, and any amendment or supplement to such
Prospectus, does not at any time during the Effectiveness Period include an
untrue statement of a material fact or omit to state a material fact necessary
in order to make the statements therein, in the light of the circumstances under
which they were made, not misleading.

       (d) The Company shall promptly advise each Electing Holder, and shall
confirm such advice in writing if so requested by any such Electing Holder:

           (i)   when a Shelf Registration Statement and any amendment thereto
       has been filed with the Commission and when a Shelf Registration
       Statement or any post-effective amendment thereto has become effective,
       in each case making a public announcement thereof on the Company's web
       site or by release made to Dow Jones & Company, Inc., Reuters Economic
       Services and Bloomberg Business News;

           (ii)  of any request by the Commission for amendments or supplements
       to the Shelf Registration Statement or the Prospectus included therein or
       for additional information;

           (iii) of the issuance by the Commission of any stop order suspending
       the effectiveness of the Shelf Registration Statement or the initiation
       of any proceedings for such purpose;

           (iv)  of the receipt by the Company of any notification with respect
       to the

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       suspension of the qualification of the securities included in the Shelf
       Registration Statement for sale in any jurisdiction or the initiation of
       any proceeding for such purpose; and

           (v) of the happening of any event or the existence of any state of
       facts that requires the making of any changes in the Shelf Registration
       Statement or the Prospectus included therein so that, as of such date,
       such Shelf Registration Statement and Prospectus do not contain an untrue
       statement of a material fact and do not omit to state a material fact
       required to be stated therein or necessary to make the statements therein
       (in the case of the Prospectus, in light of the circumstances under which
       they were made) not misleading (which advice shall be accompanied by an
       instruction to such Holders to suspend the use of the Prospectus until
       the requisite changes have been made which notice need not specify the
       nature of the event giving rise to such suspension).

       (e) The Company shall use its reasonable best efforts to prevent the
issuance, and if issued to obtain the withdrawal at the earliest possible time,
of any order suspending the effectiveness of the Shelf Registration Statement.

       (f) The Company shall furnish to each Electing Holder who so requests in
writing, without charge, at least one copy of the Shelf Registration Statement
and all post-effective amendments thereto, including financial statements and
schedules, and, if so requested, all reports, other documents and exhibits that
are filed with or incorporated by reference in the Shelf Registration Statement.

       (g) The Company shall, during the Effectiveness Period, deliver to each
Electing Holder, without charge, as many copies of the Prospectus (including
each preliminary Prospectus) included in the Shelf Registration Statement and
any amendment or supplement thereto as such Electing Holder may reasonably
request; and the Company consents (except during a Suspension Period or during
the continuance of any event described in Section 3(d)(v) above) to the use of
the Prospectus and any amendment or supplement thereto by each of the Electing
Holders in connection with the offering and sale of the Registrable Securities
covered by the Prospectus and any amendment or supplement thereto during the
Effectiveness Period.

       (h) Prior to any offering of Registrable Securities pursuant to the Shelf
Registration Statement, the Company shall (i) register or qualify or cooperate
with the Electing Holders and their respective counsel in connection with the
registration or qualification of such Registrable Securities for offer and sale
under the securities or "blue sky" laws of such jurisdictions within the United
States as any Electing Holder may reasonably request, (ii) keep such
registrations or qualifications in effect and comply with such laws so as to
permit the continuance of offers and sales in such jurisdictions for so long as
may be necessary to enable any Electing Holder or underwriter, if any, to
complete its distribution of Registrable Securities pursuant to the Shelf
Registration Statement, and (iii) take any and all other actions necessary or
advisable to enable the disposition in such jurisdictions of such Registrable
Securities; provided, however, that in no event shall the Company be obligated
to (A) qualify as a foreign corporation or as a dealer in securities in any
jurisdiction where it would not otherwise be required to so qualify but for this
Section 3(h) or (B) file any general consent to service of process in any
jurisdiction where it is not as of the date hereof so subject.

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       (i) Unless any Registrable Securities shall be in book-entry only form,
the Company shall cooperate with the Electing Holders to facilitate the timely
preparation and delivery of certificates representing Registrable Securities to
be sold pursuant to the Shelf Registration Statement, which certificates, if so
required by any securities exchange upon which any Registrable Securities are
listed, shall be penned, lithographed or engraved, or produced by any
combination of such methods, on steel engraved borders, and which certificates
shall be free of any restrictive legends and in such permitted denominations and
registered in such names as Electing Holders may request in connection with the
sale of Registrable Securities pursuant to the Shelf Registration Statement.

       (j) Upon the occurrence of any fact or event contemplated by paragraph
3(d)(v) above, subject to Section 2(c) hereof, the Company shall promptly, but
in any event within 5 Business Days following such occurrence, prepare, file
(and have declared effective) a post-effective amendment to any Shelf
Registration Statement or an amendment or supplement to the related Prospectus
included therein or file any other document with the Commission so that, as
thereafter delivered to purchasers of the Registrable Securities, the Prospectus
will not include an untrue statement of a material fact or omit to state any
material fact necessary to make the statements therein, in the light of the
circumstances under which they were made, not misleading. If the Company
notifies the Electing Holders of the occurrence of any fact or event
contemplated by paragraph 3(d)(v) above, the Electing Holder shall suspend the
use of the Prospectus until the requisite changes to the Prospectus have been
made.

       (k) Not later than the Effective Time of the Shelf Registration
Statement, the Company shall provide a CUSIP number for the Registrable
Securities that are debt securities.

       (l) The Company shall use its reasonable best efforts to comply with all
applicable Rules and Regulations, and to make generally available to its
securityholders as soon as practicable, but in any event not later than eighteen
months after (i) the effective date (as defined in Rule 158(c) under the
Securities Act) of the Shelf Registration Statement, (ii) the effective date of
each post-effective amendment to the Shelf Registration Statement, and (iii) the
date of each filing by the Company with the Commission of an Annual Report on
Form 10-K that is incorporated by reference in the Shelf Registration Statement,
an earning statement of the Company and its subsidiaries complying with Section
11(a) of the Securities Act and the rules and regulations of the Commission
thereunder (including, at the option of the Company, Rule 158).

       (m) Not later than the Effective Time of the Shelf Registration
Statement, the Company shall cause the Indenture to be qualified under the Trust
Indenture Act; in connection with such qualification, the Company shall
cooperate with the Trustee under the Indenture and the Holders (as defined in
the Indenture) to effect such changes to the Indenture as may be required for
such Indenture to be so qualified in accordance with the terms of the Trust
Indenture Act; and the Company shall execute, and shall use all reasonable
efforts to cause the Trustee to execute, all documents that may be required to
effect such changes and all other forms and documents required to be filed with
the Commission to enable such Indenture to be so qualified in a timely manner.
In the event that any such amendment or modification referred to in this Section
3(m) involves the appointment of a new trustee under the Indenture, the Company
shall appoint a new trustee thereunder pursuant to the applicable provisions of
the Indenture.

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       (n) In the event of an underwritten offering conducted pursuant to
Section 6 hereof, the Company shall, if requested, promptly include or
incorporate in a Prospectus supplement or post-effective amendment to the Shelf
Registration Statement such information as the Managing Underwriters reasonably
agree should be included therein and to which the Company does not reasonably
object and shall make all required filings of such Prospectus supplement or
post-effective amendment as soon as practicable after it is notified of the
matters to be included or incorporated in such Prospectus supplement or
post-effective amendment.

       (o) The Company shall enter into such customary agreements (including an
underwriting agreement in customary form in the event of an underwritten
offering conducted pursuant to Section 6 hereof) and take all other appropriate
action in order to expedite and facilitate the registration and disposition of
the Registrable Securities, and in connection therewith, if an underwriting
agreement is entered into, cause the same to contain indemnification provisions
and procedures substantially identical to those set forth in Section 5 hereof
with respect to all parties to be indemnified pursuant to Section 5 hereof.

       (p) The Company shall:

           (i) (A) make reasonably available for inspection by the Electing
       Holders, any underwriter participating in any disposition pursuant to the
       Shelf Registration Statement, and any attorney, accountant or other agent
       retained by such Electing Holders or any such underwriter all relevant
       financial and other records, pertinent corporate documents and properties
       of the Company and its subsidiaries, and (B) cause the Company's
       officers, directors and employees to supply all information reasonably
       requested by such Electing Holders or any such underwriter, attorney,
       accountant or agent in connection with the Shelf Registration Statement,
       in each case, as is customary for similar due diligence examinations;
       provided, however, that all records, information and documents that are
       designated in writing by the Company, in good faith, as confidential
       shall be kept confidential by such Electing Holders and any such
       underwriter, attorney, accountant or agent, unless such disclosure is
       made in connection with a court proceeding or required by law, or such
       records, information or documents become available to the public
       generally or through a third party without an accompanying obligation of
       confidentiality; and provided further that, if the foregoing inspection
       and information gathering would otherwise disrupt the Company's conduct
       of its business, such inspection and information gathering shall, to the
       greatest extent possible, be coordinated on behalf of the Electing
       Holders and the other parties entitled thereto by one counsel designated
       by and on behalf of the Electing Holders and other parties;

           (ii)    in connection with any underwritten offering conducted
       pursuant to Section 6 hereof, make such representations and warranties to
       the Managing Underwriters, in form, substance and scope as are
       customarily made by the Company to underwriters in primary underwritten
       offerings of equity and convertible debt securities and covering matters
       including, but not limited to, those set forth in the Purchase Agreement;

           (iii)   in connection with any underwritten offering conducted
       pursuant to Section 6 hereof, use reasonable best efforts to obtain
       opinions of counsel to the Company (which counsel and opinions (in form,
       scope and substance) shall generally be consistent with the opinions of
       counsel of the Company under the Purchase Agreement and be reasonably
       satisfactory to the Managing Underwriters) addressed to the

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       underwriters, covering such matters as are customarily covered in
       opinions requested in primary underwritten offerings of equity and
       convertible debt securities and such other matters as may be reasonably
       requested by such Electing Holders and underwriters (it being agreed that
       the matters to be covered by such opinions shall include, without
       limitation, as of the date of the opinion and as of the Effective Time of
       the Shelf Registration Statement or most recent post-effective amendment
       thereto, as the case may be, the absence from the Shelf Registration
       Statement and the Prospectus, including the documents incorporated by
       reference therein, of an untrue statement of a material fact or the
       omission of a material fact required to be stated therein or necessary to
       make the statements therein (in the case of the Prospectus, in the light
       of the circumstances under which they were made) not misleading;

              (iv)   in connection with any underwritten offering conducted
       pursuant to Section 6 hereof, use reasonable best efforts to obtain "cold
       comfort" letters and updates thereof from the independent public
       accountants of the Company (and, if necessary, from the independent
       public accountants of any subsidiary of the Company or of any business
       acquired by the Company for which financial statements and financial data
       are, or are required to be, included in the Shelf Registration
       Statement), addressed to each Electing Holder participating in such
       underwritten offering (if such Electing Holder has provided such letter,
       representations or documentation, if any, required for such cold comfort
       letter to be so addressed) and the underwriters, in customary form and
       covering matters of the type customarily covered in "cold comfort"
       letters in connection with primary underwritten offerings;

              (v)    in connection with any underwritten offering conducted
       pursuant to Section 6 hereof, deliver such documents and certificates as
       may be reasonably requested by any Electing Holders participating in such
       underwritten offering and the Managing Underwriters, if any, including,
       without limitation, certificates to evidence compliance with Section 3(j)
       hereof and with any conditions contained in the underwriting agreement or
       other agreements entered into by the Company.

       (q)    The Company will use its best efforts to cause the Common Stock
issuable upon conversion of the Securities to be listed on the New York Stock
Exchange or other stock exchange or trading system on which the Common Stock
primarily trades on or prior to the Effective Time of the Shelf Registration
Statement hereunder.

       (r)    The Company shall use its reasonable best efforts to take all
other steps necessary to effect the registration, offering and sale of the
Registrable Securities covered by the Shelf Registration Statement contemplated
hereby.

       4.     Registration Expenses. Except as otherwise provided in Section 3,
the Company shall bear all fees and expenses incurred in connection with the
performance of its obligations under Sections 2, 3 and 6 hereof and shall bear
or reimburse the Electing Holders for the reasonable fees and disbursements of a
single counsel selected by a plurality of all Electing Holders who own an
aggregate of not less than 25% of the principal amount of the Registrable
Securities covered by the Shelf Registration Statement, or designated by the
Purchasers if Electing Holders have not so designated, to act as counsel
therefore in connection therewith. Each Electing Holder shall pay all
underwriting discounts and commissions and transfer taxes, if any, relating to
the sale or disposition of such Electing Holder's Registrable Securities
pursuant to the Shelf Registration Statement.

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       5.     Indemnification and Contribution.

       (a)    Indemnification by the Company. Upon the registration of the
Registrable Securities pursuant to Section 2 hereof, the Company shall indemnify
and hold harmless each Electing Holder and each underwriter, selling agent or
other securities professional, if any, which facilitates the disposition of
Registrable Securities, and each of their respective officers and directors and
each person who controls such Electing Holder, underwriter, selling agent or
other securities professional within the meaning of Section 15 of the Securities
Act or Section 20 of the Exchange Act (each such person being sometimes referred
to as an "Indemnified Person") against any losses, claims, damages or
liabilities, joint or several, to which such Indemnified Person may become
subject under the Securities Act or otherwise, insofar as such losses, claims,
damages or liabilities (or actions in respect thereof) arise out of or are based
upon an untrue statement or alleged untrue statement of a material fact
contained in any Shelf Registration Statement under which such Registrable
Securities are to be registered under the Securities Act, or any Prospectus
contained therein or furnished by the Company to any Indemnified Person, or any
amendment or supplement thereto, or arise out of or are based upon the omission
or alleged omission to state therein a material fact required to be stated
therein or necessary to make the statements therein not misleading, and the
Company hereby agrees to reimburse such Indemnified Person for any legal or
other expenses reasonably incurred by them in connection with investigating or
defending any such action or claim as such expenses are incurred; provided,
however, that the Company shall not be liable to any such Indemnified Person in
any such case to the extent that any such loss, claim, damage or liability
arises out of or is based upon an untrue statement or alleged untrue statement
or omission or alleged omission made in such Shelf Registration Statement or
Prospectus, or amendment or supplement, in reliance upon and in conformity with
written information furnished to the Company by such Indemnified Person
expressly for use therein.

       (b)    Indemnification by the Electing Holders and any Agents and
Underwriters. Each Electing Holder agrees, as a consequence of the inclusion of
any of such Electing Holder's Registrable Securities in such Shelf Registration
Statement, and each underwriter, selling agent or other securities professional,
if any, which facilitates the disposition of Registrable Securities shall agree,
as a consequence of facilitating such disposition of Registrable Securities,
severally and not jointly, to (i) indemnify and hold harmless the Company, its
directors, officers who sign any Shelf Registration Statement and each person,
if any, who controls the Company within the meaning of either Section 15 of the
Securities Act or Section 20 of the Exchange Act, against any losses, claims,
damages or liabilities to which the Company or such other persons may become
subject, under the Securities Act or otherwise, insofar as such losses, claims,
damages or liabilities (or actions in respect thereof) arise out of or are based
upon an untrue statement or alleged untrue statement of a material fact
contained in such Shelf Registration Statement or Prospectus, or any amendment
or supplement, or arise out of or are based upon the omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein not misleading, in each case to the
extent, but only to the extent, that such untrue statement or alleged untrue
statement or omission or alleged omission was made in reliance upon and in
conformity with written information furnished to the Company by such Electing
Holder, underwriter, selling agent or other securities professional expressly
for use therein, and (ii) reimburse the Company for any legal or other expenses
reasonably incurred by the Company in connection with investigating or defending
any such action or claim as such expenses are incurred.

                                       11

<PAGE>

       (c)    Notices of Claims, Etc. Promptly after receipt by an indemnified
party under subsection (a) or (b) above of notice of the commencement of any
action, such indemnified party shall, if a claim in respect thereof is to be
made against an indemnifying party under this Section 5, notify such
indemnifying party in writing of the commencement thereof; but the omission so
to notify the indemnifying party shall not relieve it from any liability which
it may have to any indemnified party otherwise than under the indemnification
provisions of or contemplated by subsection (a) or (b) above. In case any such
action shall be brought against any indemnified party and it shall notify an
indemnifying party of the commencement thereof, such indemnifying party shall be
entitled to participate therein and, to the extent that it shall wish, jointly
with any other indemnifying party similarly notified, to assume the defense
thereof, with counsel satisfactory to such indemnified party (who shall not,
except with the consent of the indemnified party, be counsel to the indemnifying
party), and, after notice from the indemnifying party to such indemnified party
of its election so to assume the defense thereof, such indemnifying party shall
not be liable to such indemnified party under this Section 5 for any legal
expenses of other counsel or any other expenses, in each case subsequently
incurred by such indemnified party, in connection with the defense thereof other
than reasonable costs of investigation. No indemnifying party shall, without the
written consent of the indemnified party, effect the settlement or compromise
of, or consent to the entry of any judgment with respect to, any pending or
threatened action or claim in respect of which indemnification or contribution
may be sought hereunder (whether or not the indemnified party is an actual or
potential party to such action or claim) unless such settlement, compromise or
judgment (i) includes an unconditional release of the indemnified party from all
liability arising out of such action or claim and (ii) does not include a
statement as to, or an admission of, fault, culpability or a failure to act, by
or on behalf of any indemnified party.

       (d)    Contribution. If the indemnification provided for in this Section
5 is unavailable to or insufficient to hold harmless an indemnified party under
subsection (a) or (b) above in respect of any losses, claims, damages or
liabilities (or actions in respect thereof) referred to therein, then each
indemnifying party shall contribute to the amount paid or payable by such
indemnified party as a result of such losses, claims, damages or liabilities (or
actions in respect thereof) in such proportion as is appropriate to reflect the
relative fault of the indemnifying party and the indemnified party in connection
with the statements or omissions which resulted in such losses, claims, damages
or liabilities (or actions in respect thereof), as well as any other relevant
equitable considerations. The relative fault of such indemnifying party and
indemnified party shall be determined by reference to, among other things,
whether the untrue or alleged untrue statement of a material fact or omission or
alleged omission to state a material fact relates to information supplied by
such indemnifying party or by such indemnified party, and the parties' relative
intent, knowledge, access to information and opportunity to correct or prevent
such statement or omission. The parties hereto agree that it would not be just
and equitable if contribution pursuant to this Section 5(d) were determined by
pro rata allocation (even if the Electing Holders or any underwriters, selling
agents or other securities professionals or all of them were treated as one
entity for such purpose) or by any other method of allocation which does not
take account of the equitable considerations referred to in this Section 5(d).
The amount paid or payable by an indemnified party as a result of the losses,
claims, damages or liabilities (or actions in respect thereof) referred to above
shall be deemed to include any legal or other fees or expenses reasonably
incurred by such indemnified party in connection with investigating or defending
any such action or claim. No person guilty of fraudulent misrepresentation
(within the meaning of Section 11(f) of the Securities Act) shall be entitled to
contribution from any person who was not guilty of such fraudulent
misrepresentation. The

                                       12

<PAGE>

obligations of the Electing Holders and any underwriters, selling agents or
other securities professionals in this Section 5(d) to contribute shall be
several in proportion to the percentage of principal amount of Registrable
Securities registered or underwritten, as the case may be, by them and not
joint.

       (e)    Notwithstanding any other provision of this Section 5, in no event
will any (i) Electing Holder be required to undertake liability to any person
under this Section 5 for any amounts in excess of the dollar amount of the
proceeds to be received by such Holder from the sale of such Holder's
Registrable Securities (after deducting any fees, discounts and commissions
applicable thereto) pursuant to any Shelf Registration Statement under which
such Registrable Securities are to be registered under the Securities Act and
(ii) underwriter, selling agent or other securities professional be required to
undertake liability to any person hereunder for any amounts in excess of the
discount, commission or other compensation payable to such underwriter, selling
agent or other securities professional with respect to the Registrable
Securities underwritten by it and distributed to the public.

       (f)    The obligations of the Company under this Section 5 shall be in
addition to any liability which the Company may otherwise have to any
Indemnified Person and the obligations of any Indemnified Person under this
Section 5 shall be in addition to any liability which such Indemnified Person
may otherwise have to the Company. The remedies provided in this Section 5 are
not exclusive and shall not limit any rights or remedies which may otherwise be
available to an indemnified party at law or in equity.

       6.     Underwritten Offering. Any Holder of Registrable Securities who
desires to do so may sell Registrable Securities (in whole or in part) in an
underwritten offering; provided that (i) the Electing Holders of at least 50% in
aggregate principal amount of the Registrable Securities initially covered by
the Shelf Registration Statement shall request such an offering and (ii) at
least such aggregate principal amount of such Registrable Securities shall be
included in such offering. Upon receipt of such a request, the Company shall
provide all Holders of Registrable Securities written notice of the request,
which notice shall inform such Holders that they have the opportunity to
participate in the offering. In any such underwritten offering, the investment
banker or bankers and manager or managers that will administer the offering will
be selected by, and the underwriting arrangements with respect thereto
(including the size of the offering) will be approved by, the holders of a
majority of the Registrable Securities to be included in such offering;
provided, however, that such investment bankers and managers and underwriting
arrangements must be reasonably satisfactory to the Company. No Holder may
participate in any underwritten offering contemplated hereby unless (a) such
Holder agrees to sell such Holder's Registrable Securities to be included in the
underwritten offering in accordance with any approved underwriting arrangements,
(b) such Holder completes and executes all reasonable questionnaires, powers of
attorney, indemnities, underwriting agreements, lock-up letters and other
documents required under the terms of such approved underwriting arrangements,
and (c) if such Holder is not then an Electing Holder, such Holder returns a
completed and signed Notice and Questionnaire to the Company in accordance with
Section 3(a)(ii) hereof within a reasonable amount of time before such
underwritten offering. The Holders participating in any underwritten offering
shall be responsible for any underwriting discounts and commissions and fees
and, subject to Section 4 hereof, expenses of their own counsel. The Company
shall pay all expenses customarily borne by issuers in an underwritten offering,
including but not limited to filing fees, the fees and disbursements of its
counsel and independent public accountants and any printing expenses incurred in
connection with such

                                       13

<PAGE>

underwritten offering. Notwithstanding the foregoing or the provisions of
Section 3(n) hereof, upon receipt of a request from the Managing Underwriter or
a representative of holders of a majority of the Registrable Securities to be
included in an underwritten offering to prepare and file an amendment or
supplement to the Shelf Registration Statement and Prospectus in connection with
an underwritten offering, the Company may delay the filing of any such amendment
or supplement for up to 90 days if the Board of Directors of the Company shall
have determined in good faith that the Company has a bona fide business reason
for such delay.

       7.     Liquidated Damages.

       (a)    Notwithstanding any postponement of the effectiveness pursuant to
Section 2(a) hereof, if (i) on or prior to the 120th day following the Closing
Date, a Shelf Registration Statement has not been filed with the Commission,
(ii) on or prior to the 180th day following the Closing Date, such Shelf
Registration Statement is not declared effective by the Commission or (iii) if,
after the effectiveness date of the Shelf Registration Statement, (x) the Shelf
Registration Statement ceases to be effective or usable for the offer and sale
of Registrable Securities (other than due to a Suspension Period), and the
Company fails to file (and have declared effective), within 5 Business Days, a
post-effective amendment to the Shelf Registration Statement or amendment or
supplement to the Prospectus contained therein or such other document with the
SEC to make the Shelf Registration Statement effective or such Prospectus
usable, or (y) Suspension Periods exceed 45 days, whether or not consecutive, in
any 90-day period, or more than 120 days, whether or not consecutive, during any
360-day period during the Effectiveness Period (each, a "Registration Default"),
the Company shall be required to pay liquidated damages ("Liquidated Damages"),
from and including the day following such Registration Default until such
Registration Default is cured, at a rate per annum equal to one-quarter of one
percent (0.25%) of the Applicable Amount, to and including the 90th day
following such Registration Default and one-half of one percent (0.5%) thereof
from and after the 91st day following such Registration Default.

       (b)    A Holder will not be entitled to Liquidated Damages unless it has
complied with such Holder's obligations under this Agreement.

       (c)    Any amounts to be paid as Liquidated Damages pursuant to
paragraphs (a) of this Section 7 shall be paid in cash semi-annually in arrears,
with the first semi-annual payment due on the first June 1 or December 1, as
applicable, following the date on which such Liquidated Damages begin to accrue,
to Holders of record on the preceding May 15 or November 15, as the case may be.

       (d)    Except as provided in Section 8(b) hereof, the Liquidated Damages
as set forth in this Section 7 shall be the exclusive monetary remedy available
to the Holders of Registrable Securities for such Registration Default. In no
event shall the Company be required to pay Liquidated Damages in excess of the
applicable maximum amount of one-half of one percent (0.5%) set forth above,
regardless of whether one or multiple Registration Defaults exist.

       7.     Miscellaneous.

       (a)    Other Registration Rights. The Company may grant registration
rights that would permit any person that is a third party the right to
piggy-back on any shelf registration statement, provided that if the Managing
Underwriter of any underwritten offering conducted pursuant to Section 6 hereof
notifies the Company and the Electing Holders that the total

                                       14

<PAGE>

amount of securities which the Electing Holders and the holders of such
piggy-back rights intend to include in any Shelf Registration Statement is so
large as to materially threaten the success of such offering (including the
price at which such securities can be sold), then the amount, number or kind of
securities to be offered for the account of holders of such piggy-back rights
will be reduced to the extent necessary to reduce the total amount of securities
to be included in such offering to the amount, number and kind recommended by
the Managing Underwriter prior to any reduction in the amount of Registrable
Securities to be included in such Shelf Registration Statement.

       (b)    Specific Performance. The parties hereto acknowledge that there
would be no adequate remedy at law if the Company fails to perform any of its
obligations hereunder and that the Purchasers and the Holders from time to time
may be irreparably harmed by any such failure, and accordingly agree that the
Purchasers and such Holders, in addition to any other remedy to which they may
be entitled at law or in equity and without limiting the remedies available to
the Electing Holders under Section 7 hereof, shall be entitled to compel
specific performance of the obligations of the Company under this Registration
Rights Agreement in accordance with the terms and conditions of this
Registration Rights Agreement, in any court of the United States or any State
thereof having jurisdiction.

       (c)    Amendments and Waivers. This Agreement, including this Section
8(c), may be amended, and waivers or consents to departures from the provisions
hereof may be given, only by a written instrument duly executed by the Company
and the holders of a majority in Applicable Amount of Registrable Securities
then outstanding. Each Holder of Registrable Securities outstanding at the time
of any such amendment, waiver or consent or thereafter shall be bound by any
amendment, waiver or consent effected pursuant to this Section 8(c), whether or
not any notice, writing or marking indicating such amendment, waiver or consent
appears on the Registrable Securities or is delivered to such Holder.

       (d)    Notices. All notices and other communications provided for or
permitted hereunder shall be given as provided in the Indenture.

       (e)    Parties in Interest. The parties to this Agreement intend that all
Holders of Registrable Securities shall be entitled to receive the benefits of
this Agreement and that any Electing Holder shall be bound by the terms and
provisions of this Agreement by reason of such election with respect to the
Registrable Securities which are included in a Shelf Registration Statement. All
the terms and provisions of this Agreement shall be binding upon, shall inure to
the benefit of and shall be enforceable by the respective successors and assigns
of the parties hereto and any Holder from time to time of the Registrable
Securities to the aforesaid extent. In the event that any transferee of any
Holder of Registrable Securities shall acquire Registrable Securities, in any
manner, whether by gift, bequest, purchase, operation of law or otherwise, such
transferee shall, without any further writing or action of any kind, be entitled
to receive the benefits of and, if an Electing Holder, be conclusively deemed to
have agreed to be bound by and to perform all of the terms and provisions of
this Agreement to the aforesaid extent.

       (f)    Counterparts. This Agreement may be executed in any number of
counterparts and by the parties hereto in separate counterparts, each of which
when so executed shall be deemed to be an original and all of which taken
together shall constitute one and the same agreement.

                                       15

<PAGE>

       (g)    Headings. The headings in this Agreement are for convenience of
reference only and shall not limit or otherwise affect the meaning hereof.

       (h)    Governing Law. This Agreement shall be governed by and construed
in accordance with the laws of the State of New York.

       (i)    Severability. In the event that any one or more of the provisions
contained herein, or the application thereof in any circumstances, is held
invalid, illegal or unenforceable in any respect for any reason, the validity,
legality and enforceability of any such provision in every other respect and of
the remaining provisions hereof shall not be in any way impaired or affected
thereby, it being intended that all of the rights and privileges of the parties
hereto shall be enforceable to the fullest extent permitted by law.

       (j)    Survival. The respective indemnities, agreements, representations,
warranties and other provisions set forth in this Agreement or made pursuant
hereto shall remain in full force and effect, regardless of any investigation
(or any statement as to the results thereof) made by or on behalf of any
Electing Holder, any director, officer or partner of such Holder, any agent or
underwriter, any director, officer or partner of such agent or underwriter, or
any controlling person of any of the foregoing, and shall survive the transfer
and registration of the Registrable Securities of such Holder.

       9.     Submission to Jurisdiction; Appointment of Agent for Service

       The Company agrees that any suit, action or proceeding against the
Company arising out of or based upon this Agreement or the transactions
contemplated hereby may be instituted in any State or Federal court in The City
of New York, New York, and waives any objection which it may now or hereafter
have to the laying of venue of any such proceeding, and irrevocably submits to
the non-exclusive jurisdiction of such courts in any suit, action or proceeding.
The Company has appointed National Registered Agents, Inc. as its authorized
agent (the "Authorized Agent") upon whom process may be served in any suit,
action or proceeding arising out of or based upon this Agreement or the
transactions contemplated herein which may be instituted in any State or Federal
court in The City of New York, New York, and expressly accepts the non-exclusive
jurisdiction of any such court in respect of any such suit, action or
proceeding. The Company hereby represents and warrants that the Authorized Agent
has accepted such appointment and has agreed to act as said agent for service of
process, and the Company and agrees to take any and all action, including the
filing of any and all documents that may be necessary to continue such
appointment in full force and effect as aforesaid.

                                       16

<PAGE>

       Please confirm that the foregoing correctly sets forth the agreement
between the Company and you.

                                                   Very truly yours,

                                                   Schlumberger Limited


                                                   By: /s/ Michel Soublin
                                                       -------------------------
                                                       Name:  Michel Soublin
                                                       Title: Treasurer

Accepted as of the date hereof:

       Citigroup Global Markets Inc.


       By: /s/ Jean-Pierre Buyze
           -----------------------------
           Name:  Jean-Pierre Buyze
           Title: Vice President



       Goldman, Sachs & Co.


       /s/ Goldman, Sachs & Co.
           -----------------------------
               (Goldman, Sachs & Co.)

                                       17

<PAGE>

                                                                      Appendix A

                              Schlumberger Limited

                         INSTRUCTION TO DTC PARTICIPANTS

                                (Date of Mailing)

                     URGENT - IMMEDIATE ATTENTION REQUESTED

                          DEADLINE FOR RESPONSE: [DATE]

          The Depository Trust Company ("DTC") has identified you as a DTC
Participant through which beneficial interests in either the 1.500% Series A
Convertible Debentures due June 1, 2023 or the 2.125% Series B Convertible
Debentures due June 1, 2023 (collectively, the "Securities") of Schlumberger
Limited (the "Company") are held.

          The Company is in the process of registering the Securities under the
Securities Act of 1933 for resale by the beneficial owners thereof. In order to
have their Securities included in the registration statement, beneficial owners
must complete and return the enclosed Notice of Registration Statement and
Selling Securityholder Questionnaire.

          It is important that beneficial owners of the Securities receive a
copy of the enclosed materials as soon as possible as their rights to have the
Securities included in the registration statement depend upon their returning
the Notice and Questionnaire by [Deadline for response]. Please forward a copy
of the enclosed documents to each beneficial owner that holds interests in the
Securities through you. If you require more copies of the enclosed materials or
have any questions pertaining to this matter, please contact [Name, address and
telephone number of contact at the Issuer].

                                      A-1

<PAGE>

                              Schlumberger Limited

                        Notice of Registration Statement
                                       and
                      Selling Securityholder Questionnaire

                                     [Date]

          Schlumberger Limited (the "Company") has filed with the United States
Securities and Exchange Commission (the "Commission") a registration statement
on Form S-3 (the "Shelf Registration Statement") for the registration and resale
under Rule 415 of the United States Securities Act of 1933, as amended (the
"Securities Act"), of the Company's 1.500% Series A Convertible Debentures due
June 1, 2023 (the "Series A Debentures") and 2.125% Series B Convertible
Debentures due June 1, 2023 (the "Series B Debentures" and, together with the
Series A Debentures, the "Securities") and the shares of common stock, par value
$.01 per share (the "Common Stock"), issuable upon conversion thereof, in
accordance with the Registration Rights Agreement, dated as of June 9, 2003 (the
"Registration Rights Agreement"), between the Company and the purchasers named
therein. A copy of the Registration Rights Agreement is attached hereto. All
capitalized terms not otherwise defined herein shall have the meanings ascribed
thereto in the Registration Rights Agreement.

          In order to have Registrable Securities included in the Shelf
Registration Statement (or a supplement or amendment thereto), this Notice of
Registration Statement and Selling Securityholder Questionnaire ("Notice and
Questionnaire") must be completed, executed and delivered to the Company at the
address set forth herein for receipt ON OR BEFORE [DEADLINE FOR RESPONSE].
Beneficial owners of Registrable Securities who do not complete, execute and
return this Notice and Questionnaire by such date (i) will not be named as
selling securityholders in the Shelf Registration Statement and (ii) may not use
the Prospectus forming a part thereof for resales of Registrable Securities.

          Certain legal consequences arise from being named as a selling
securityholder in the Shelf Registration Statement and related Prospectus.
Accordingly, holders and beneficial owners of Registrable Securities are advised
to consult their own securities law counsel regarding the consequences of being
named or not being named as a selling securityholder in the Shelf Registration
Statement and related Prospectus.

                                      A-2

<PAGE>

          The term "Registrable Securities" is defined in the Registration
Rights Agreement to mean all or any portion of the Securities issued from time
to time under the Indenture in registered form and the shares of Common Stock
issuable upon conversion of such Securities; provided, however, that a security
ceases to be a Registrable Security when it is no longer a Restricted Security.

          The term "Restricted Security" is defined in the Registration Rights
Agreement to mean any Security or share of Common Stock issuable upon conversion
thereof except any such Security or share of Common Stock that (i) has been
effectively registered under the Securities Act and sold in a manner
contemplated by the Shelf Registration Statement, or (ii) has been transferred
in compliance with Rule 144 under the Securities Act (or any successor provision
thereto) or is transferable pursuant to paragraph (k) of such Rule 144 (or any
successor provision thereto), or (iii) has otherwise been transferred and a new
Security or share of Common Stock not subject to transfer restrictions under the
Securities Act has been delivered by or on behalf of the Company in accordance
with the Indenture.

                                    ELECTION

          The undersigned holder (the "Selling Securityholder") of Registrable
Securities hereby elects to include in the Shelf Registration Statement the
Registrable Securities beneficially owned by it and listed below in Item (3).
The undersigned, by signing and returning this Notice and Questionnaire, agrees
to be bound with respect to such Registrable Securities by the terms and
conditions of this Notice and Questionnaire and the Registration Rights
Agreement, including, without limitation, Section 5 of the Registration Rights
Agreement, as if the undersigned Selling Securityholder were an original party
thereto.

          Upon any sale of Registrable Securities pursuant to the Shelf
Registration Statement, the Selling Securityholder will be required to deliver
to the Company and the Trustee the Notice of Transfer (completed and signed) set
forth in Exhibit 1 to this Notice and Questionnaire.

          The Selling Securityholder hereby provides the following information
to the Company and represents and warrants that such information is accurate and
complete:

                                      A-3

<PAGE>

                                  QUESTIONNAIRE

(1) (a) Full Legal Name of Selling Securityholder:

        ________________________________________________________________________

    (b) Full Legal Name of Registered Holder (if not the same as in (a) above)
        of Registrable Securities Listed in Item (3) Below:

        ________________________________________________________________________

    (c) Full Legal Name of DTC Participant (if applicable and if not the same as
        (b) above) Through Which Registrable Securities Listed in Item (3) Below
        are Held:

(2)     Address for Notices to Selling Securityholder:

                        ________________________
                        ________________________
                        ________________________
        Telephone:      ________________________
        Fax:            ________________________
        Contact Person: ________________________


(3)     Beneficial Ownership of Securities:

        Except as set forth below in this Item (3), the undersigned Selling
        Securityholder does not beneficially own any Securities or shares of
        Common Stock issued upon conversion, repurchase or redemption of any
        Securities.

    (a) Principal amount of Registrable Securities (as defined in the
        Registration Rights Agreement) beneficially owned:

        Series A Debentures ____________________________________________________

        Series B Debentures ____________________________________________________


        CUSIP No(s). of such Registrable Securities:

        Series A Debentures ____________________________________________________

        Series B  Debentures ___________________________________________________

        Number of shares of Common Stock (if any) issued upon conversion,
        repurchase or redemption of Registrable Securities: ____________________

    (b) Principal amount of Securities other than Registrable Securities
        beneficially owned:
        ________________________________________________________________________

        CUSIP No(s). of such other Securities: _________________________________

                                      A-4

<PAGE>

      Number of shares of Common Stock (if any) issued upon conversion of such
      other Securities: ________________________________________________________

  (c) Principal amount of Registrable Securities which the undersigned wishes to
      be included in the Shelf Registration Statement:

      Series A Debentures ______________________________________________________

      Series B Debentures ______________________________________________________

      CUSIP No(s). of such Registrable Securities to be included in the Shelf
      Registration Statement:

      Series A Debentures ______________________________________________________

      Series B Debentures ______________________________________________________

      Number of shares of Common Stock (if any) issued upon conversion of
      Registrable Securities which are to be included in the Shelf Registration
      Statement:

      __________________________________________________________________________


(4)   Beneficial Ownership of Other Securities of the Company:

      Except as set forth below in this Item (4), the undersigned Selling
      Securityholder is not the beneficial or registered owner of any shares of
      Common Stock or any other securities of the Company, other than the
      Securities and shares of Common Stock listed above in Item (3).

      State any exceptions here:



(5)   Relationships with the Company:

      Except as set forth below, neither the Selling Securityholder nor any of
      its affiliates, officers, directors or principal equity holders (5% or
      more) has held any position or office or has had any other material
      relationship with the Company (or its predecessors or affiliates) during
      the past three years.

      State any exceptions here:



(6)   Nature of the Selling Securityholder:

  (a) Is the selling Securityholder a reporting company under the Securities
      Exchange Act, a majority owned subsidiary of a reporting company under the
      Securities Exchange Act or a registered investment company under the
      Investment Company Act? If so, please state which one.

                                      A-5

<PAGE>

     If the entity is a majority owned subsidiary of a reporting company,
     identify the majority stockholder that is a reporting company.

     If the entity is not any of the above, identify the natural person or
     persons having voting and investment control over the Company's securities
     that the entity owns.


(b)  Is the Selling Securityholder a registered broker-dealer? Yes ____ No ____


     State whether the Selling Securityholder received the Registrable
     Securities as compensation for underwriting activities and, if so, provide
     a brief description of the transaction(s) involved.





     State whether the Selling Securityholder is an affiliate of a broker-dealer
     and if so, list the name(s) of the broker-dealer affiliate(s).

          Yes ____    No ____



          If the answer is "Yes," you must answer the following:

     If the Selling Securityholder is an affiliate of a registered
     broker-dealer, the Selling Securityholder purchased, the Registrable
     Securities (i) in the ordinary course of business and (ii) at the time of
     the purchase of the Registrable Securities, had no agreements or
     understandings, directly or indirectly, with any person to distribute the
     Registrable Securities.

          Yes ____    No ____

          If the answer is "No", state any exceptions here:




          If the answer is "No," this may affect your ability to be included in
          the registration statement.

                                      A-6

<PAGE>

(7)  Plan of Distribution:

     Except as set forth below, the undersigned Selling Securityholder intends
     to distribute the Registrable Securities listed above in Item (3) only as
     follows (if at all): Such Registrable Securities may be sold from time to
     time directly by the undersigned Selling Securityholder or, alternatively,
     through underwriters, broker-dealers or agents. Such Registrable Securities
     may be sold in one or more transactions at fixed prices, at prevailing
     market prices at the time of sale, at varying prices determined at the time
     of sale or at negotiated prices. Such sales may be effected in transactions
     (which may involve crosses or block transactions) (i) on any national
     securities exchange or quotation service on which the Registrable
     Securities may be listed or quoted at the time of sale, (ii) in the
     over-the-counter market, (iii) in transactions otherwise than on such
     exchanges or services or in the over-the-counter market or (iv) through the
     writing of options. In connection with sales of the Registrable Securities
     or otherwise, the Selling Securityholder may enter into transactions with
     broker-dealers, which may in turn engage in short sales of the Registrable
     Securities in the course of hedging the positions they assume. The Selling
     Securityholder may also sell Registrable Securities short and deliver
     Registrable Securities to close out such short positions, or loan or pledge
     Registrable Securities to broker-dealers that in turn may sell such
     securities.

     State any exceptions here:



         Note: In no event may such method(s) of distribution take the form of
an underwritten offering of the Registrable Securities except pursuant to
Section 6 of the Registration Rights Agreement.

         By signing below, the Selling Securityholder acknowledges that it
understands its obligation to comply, and agrees that it will comply, with the
prospectus delivery and other provisions of the Securities Act and the Exchange
Act and the rules and regulations thereunder, particularly Regulation M.

         In the event that the Selling Securityholder transfers all or any
portion of the Registrable Securities listed in Item (3) above after the date on
which such information is provided to the Company, the Selling Securityholder
agrees to notify the transferee(s) at the time of the transfer of its rights and
obligations under this Notice and Questionnaire and the Registration Rights
Agreement.

         By signing below, the Selling Securityholder consents to the disclosure
of the information contained herein in its answers to Items (1) through (6)
above and the inclusion of such information in the Shelf Registration Statement
and related Prospectus. The Selling Securityholder understands that such
information will be relied upon by the Company in connection with the
preparation of the Shelf Registration Statement and related Prospectus.

         In accordance with the Selling Securityholder's obligation under
Section 3(a) of the Registration Rights Agreement to provide such information as
may be required by law for inclusion in the Shelf Registration Statement, the
Selling Securityholder agrees to promptly notify the Company of any inaccuracies
or changes in the information provided herein which

                                      A-7

<PAGE>

may occur subsequent to the date hereof at any time while the Shelf
Registration Statement remains in effect. All notices hereunder and pursuant to
the Registration Rights Agreement shall be made in writing, by hand-delivery,
first-class mail or air courier guaranteeing overnight delivery as follows:

      (i) To the Company:

                                          _________________________

                                          _________________________

                                          _________________________

                                          _________________________

                                          _________________________


      (ii) With a copy to:

                                          _________________________

                                          _________________________

                                          _________________________

                                          _________________________

                                          _________________________


     Once this Notice and Questionnaire is executed by the Selling
Securityholder and received by the Company, the terms of this Notice and
Questionnaire, and the representations and warranties contained herein, shall be
binding on, shall inure to the benefit of and shall be enforceable by the
respective successors, heirs, personal representatives, and assigns of the
Company and the Selling Securityholder (with respect to the Registrable
Securities beneficially owned by such Selling Securityholder and listed in Item
(3) above). This Agreement shall be governed in all respects by the laws of the
State of New York.

                                      A-8

<PAGE>

     IN WITNESS WHEREOF, the undersigned, by authority duly given, has caused
this Notice and Questionnaire to be executed and delivered either in person or
by its duly authorized agent.

Dated: ____________________________



          ______________________________________________________________________
          Selling Securityholder
          (Print/type full legal name of beneficial owner of Registrable
          Securities)



          By: __________________________________________________________________
          Name:
          Title:



PLEASE RETURN THE COMPLETED AND EXECUTED NOTICE AND QUESTIONNAIRE FOR RECEIPT ON
OR BEFORE [DEADLINE FOR RESPONSE] TO THE COMPANY AT:

                                    _________________________

                                    _________________________

                                    _________________________

                                    _________________________

                                    _________________________

                                      A-9

<PAGE>

                                                                       Exhibit 1
                                                                   to Appendix A

              NOTICE OF TRANSFER PURSUANT TO REGISTRATION STATEMENT

Schlumberger Limited
153 East 53/rd/ Street, 57/th/ Floor
New York, New York 10022

Attention: General Counsel

Citibank, N.A.
111 Wall Street
14/th/ Floor, Zone 3
New York, New York 10005

Attention: Nancy Forte

     Re:   Schlumberger Limited (the "Company")
           1.500% Convertible Debentures due June 1, 2023 (the"Series A
           Debentures") and 2.125% Convertible Debentures due June 1, 2023 (the
           "Series B Debentures")

Dear Sirs:

     Please be advised that _____________________ has transferred $____________
aggregate principal amount of the Series A Debentures and/or $_____________
aggregate principal amount of the Series B Debentures, or shares of the
Company's common stock, issued upon conversion of Securities, pursuant to an
effective Registration Statement on Form S-3 (File No. 333-____) filed by the
Company.

     We hereby certify that the prospectus delivery requirements, if any, of the
Securities Act of 1933, as amended, have been satisfied with respect to the
transfer described above and that the above-named beneficial owner of the
Securities or common stock is named as a selling securityholder in the
Prospectus dated [date], or in amendments or supplements thereto, and that the
aggregate principal amount of the Securities or number of shares of common stock
transferred are a portion of the Securities or shares of common stock listed in
such Prospectus as amended or supplemented opposite such owner's name.

Dated:

                                                 Very truly yours,

                                                 _________________________
                                                 (Name)

                                           By:   _________________________
                                                 (Authorized Signature)