Exhibit 5.1

[BAKER BOTTS LLP LOGO] ONE SHELL PLAZA 910 LOUISIANA HOUSTON, TEXAS 77002-4995 713.229.1234 FAX 713.229.1522 AUSTIN BAKU DALLAS HOUSTON LONDON MOSCOW NEW YORK RIYADH WASHINGTON

October 31, 2003

Schlumberger Limited

153 East 53rd Street, 57th Floor

New York, New York 10022-4624

Ladies and Gentlemen:

As set forth in the Registration Statement on Form S-3 (Registration No. 333-108730) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Act”), relating to the registration by the Company of the resale of $975,000,000 aggregate principal amount of 1.500% Series A Convertible Debentures due June 1, 2023 (the “Series A Debentures”), $450,000,000 aggregate principal amount of 2.125% Series B Convertible Debentures due June 1, 2023 (the “Series B Debentures” and, together with the Series A Debentures, the “Debentures”) and an indeterminate number of shares of common stock, par value $.01 per share, of the Company issuable upon conversion of the Debentures (the “Conversion Shares”), certain United States legal matters in connection with the Debentures and the Conversion Shares are being passed upon for you by us.

In our capacity as your counsel in the connection referred to above, we have examined (i) the Registration Statement, (ii) the Indenture dated as of June 9, 2003 between the Company and Citibank, N.A., as trustee (the “Trustee”), as supplemented by the First Supplemental Indenture thereto dated as of June 9, 2003 (such indenture, as so amended and supplemented, the “Indenture”) and (iii) the Series A Debentures and the Series B Debentures. As a basis for the opinions hereinafter expressed, we have also examined originals, or copies certified or otherwise identified, of corporate records or other organizational records and documents of the Company and its subsidiaries, certificates of public officials and of officers or other representatives of the Company, and statutes and other instruments and documents. We have assumed that all signatures on documents examined by us are genuine, all documents submitted to us as originals are authentic and complete and all documents submitted to us as certified or photostatic copies are true and correct copies of such documents. We have also assumed that the execution, delivery and performance by the Company of the Indenture and the Debentures have been duly authorized by all requisite corporate action of the Company, and that the Indenture and Debentures have been duly executed, authenticated, issued and delivered insofar as such matters are governed by the laws of the Netherlands Antilles.

Based on the foregoing, and subject to the limitations and qualifications set forth herein, we are of the opinion that the Debentures have been duly executed, authenticated, issued and delivered by the Company insofar as such matters are governed by the laws of the State of New York and constitute valid and legally binding obligations of the Company, enforceable in accordance with their terms, subject to applicable bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium or similar laws affecting creditors’ rights generally and general principles of equity (whether considered in a proceeding at law or in equity).

The opinions set forth above are limited in all respects to matters of federal law of the United States and the contract law of the State of New York, each as currently in effect. In particular, we are not passing on any matters governed by the laws of the Netherlands Antilles. We have, however, consulted with G.C.A. Smeets, counsel qualified to practice in the Netherlands Antilles. Insofar as the opinions expressed above involve conclusions as to matters governed by the laws of the Netherlands Antilles, we are relying on the opinion of such counsel.

[BAKER BOTTS LLP LOGO]

Schlumberger N.V. (Schlumberger Limited) 2 October 31, 2003

We hereby consent to the filing of this opinion of counsel as Exhibit 5.1 to the Registration Statement. We also consent to the reference to our Firm under the heading “Legal Matters” in the prospectus forming a part of the Registration Statement. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

Very truly yours,

/s/ Baker Botts L.L.P.