The want of a central Scientific Library in the New Museums, for the use of the Professors, Lecturers, and students, has long been felt, and recognized in various ways by the University. If such a Library were founded and placed in a suitable room, the Council of the Philosophical Society would be prepared to recommend to the Society that their Library should be deposited in it, under regulations to be approved by the Society. It would thus form a nucleus for such a collection of books as is required, which, there is reason to believe, would before long be largely increased by donations. I remain, dear Mr Vice-Chancellor, ALFRED NEWTON (President of the Cambridge Philosophical Society). At the meeting of the Council, held 8 November, the following Minutes were made: 'A letter was read from the Vice-Chancellor, acknowledging the receipt of the President's letter, and stating that he had forwarded it to the Museums and Lecture Rooms Syndicate. 'A letter was also read from Mr J. W. Clark, the Secretary of the Museums and Lecture Rooms Syndicate, containing the following Minute of the Syndicate: "A Sub-Syndicate was appointed to confer with the Philosophical Society, and to prepare a draft report on the subject for the use of the Syndicate. A Committee was then appointed to confer with the SubSyndicate above mentioned, and to report to the Council. They reported as follows: 'At a Conference of the Members of the Sub-Syndicate appointed by the Museums and Lecture Rooms Syndicate, and of the Members of the Committee appointed by the Council of the Cambridge Philosophical Society, held 10 December, 1880, it was agreed that: 1. The Library of the Philosophical Society, consisting of about 5000 volumes, has become too large to be conveniently accommodated in the room in the New Museums where it is at present placed. 2. This Library, consisting chiefly of scientific periodicals and the publications of learned Societies (British and foreign), which last are received by the Society in exchange for its own publications, would, if rendered more accessible to the Professors, officers and students engaged at the New Museums and Lecture Rooms, be a most valuable assistance to them in the execution of their duties and prosecution of their studies. '3. The recent alteration in the central block of buildings of the New Museums has given a large room at present unappropriated, which from its size and convenient situation seems admirably fitted, among other purposes, for a library. '4. If the books of the Philosophical Society could be removed to this large room, and be placed under proper custody and regulations so that they could be used by those who work in the New Museums and Lecture Rooms, the advantages above indicated (2) would, it is believed, be attained. 5. In this case the services of a fit librarian would be required for the proper custody of the books and the keeping of the catalogue, but the funds of the Philosophical Society are not, nor are they likely to be, sufficient to pay the salary of such an officer; all its income being required for the expenses attending its own publications in exchange for which so many valuable works are received, subscription to scientific periodicals, and purchase of other additions to the Library. '6. It would therefore be necessary that the librarian should be paid by the University, and presuming that his services would be required for six hours daily during full Term and certain portions of the Vacations-especially in the months of July and August -his salary might be estimated at not less than £70 per annum, but it is possible that this sum might be somewhat reduced, if any arrangement could be made with the University Library Syndicate for partly employing one of the Library-Assistants, and thus ensuring the services of one properly trained in library work. 7. The management of the Philosophical Society's Library might be entrusted to a Committee of (say) six persons, one half to be appointed by the Museums and Lecture Rooms Syndicate, and the other half by the Council of the Society, but it would be expedient that a few definite conditions should at the outset be agreed upon by the University and the Society, which should not be altered except with the express leave of both. '8. These conditions should among other things define the position of the Fellows of the Philosophical Society as regards the privilege of removing books from the Library, especially in view of access to the roon being forbidden when required for examinations; and should also pledge the Society as a body to such outlay in the purchase of new works and the continuance of its subscription to scientific periodicals as its income will admit-due allowance being made for its other necessary expenses. 9. It seems inexpedient at present to enter into further details--but if the considerations urged above find favour with the University and the Society-it is hoped that the details required to give effect to them may without much difficulty be arranged in a manner satisfactory to both parties.' This Report was adopted by the Council, and the Committee was requested to continue its services, and to make suggestions with regard to the proposed arrangement. After further preliminary negotiations between the Council and the Syndicate, a draft of the Conditions referred to in § 7 and § 8 of the Report so far as they relate to the privilege of removing books from the Library, was adopted in the following form by the Council of the Philosophical Society, and the Syndicate have since expressed their general approval of them and of the whole scheme. 'I. That no book be taken out of the buildings of the New Museums, except by Fellows of the Cambridge Philosophical Society; and by them only for a limited time, not exceeding in any case seven days. 'II. That every book removed from the Library be entered in a register to be kept for the purpose. 'III. That in addition to the Fellows of the Society all Professors, Demonstrators, Teachers recognized by the University, and Curators, together with such persons as the Committee of Management may from time to time decide, be permitted to use the books of the Library within the buildings of the New Museums. 'IV. That certain books be marked "Not to be taken out;" provided that books so marked may be taken out by Fellows of the Society during the last hour in any day on which the Library is open; and further, provided that they be brought back during the first two hours that the Library is next open. 'V. That it be the duty of the Committee of Management specified in the Report already referred to, § 7, to decide from time to time which books shall be marked "Not to be taken out;" and to enforce the payment of fines imposed for the breach of any of these rules. 'VI. That subject to conditions necessary for the safety of the Library the Fellows of the Philosophical Society have access, so far as is practicable, to the Library, at hours other than those during which it is generally open. 'VII. That these rules shall apply of necessity only to the books which are or shall become the property of the Philosophical Society.' The Council think that the time is now come to lay before the Society a statement of these preliminary negotiations. The Council recommend: I. That they be authorized by the Society to offer the use of the Library to the University on the following conditions, and to take the necessary steps for that purpose. 1. That the books be deposited in the large room on the ground floor of the central block of the New Museums. 2. That the University undertake to make provision for the necessary fittings in the New Library, and for the services of a fit Librarian for the proper custody of the books and the keeping of a catalogue. 3. That the Society undertake to expend yearly, as heretofore, such sums in the purchase of new works and subscriptions to scientific periodicals, and in binding, as its income will admit— due allowance being made for its other necessary expenses. 4. That the management of the Library be entrusted to a Committee of six persons, one half to be appointed by the Museums and Lecture Rooms Syndicate and one half by the Council of the Philosophical Society. Provided that the fundamental regulations for the Library, marked I. VII. in the foregoing Report, be not altered except with the consent both of the Society and of the University. II. That on the acceptance by the University of the foregoing conditions and on the removal of the Society's Library into the new room, Chapter XIII. of the Bye Laws of the Society be repealed. April 25, 1881. Signed on behalf of the Council, ALFRED NEWTON, President. It was moved by Mr E. Hill and seconded by the Master of Gonville and Caius College, that this Report be confirmed. The motion was carried unanimously. May 23, 1881. PROFESSOR NEWTON, PRESIDENT, IN THE CHAIR. The following communications were made to the Society: (1) On the elliptic-function solution of the equation a3 +y3−1=0. By Professor CAYLEY. I had occasion to find elliptic-function expressions for the coordinates (x, y) of a point on the cubic curve x+y=1. These are derivable from the formulæ given, Legendre, Fonctions Elliptiques, t. I. pp. 185, 186, for the reduction to elliptic integrals of dr the integral R = viz. Legendre writing (1-2) and then writing r = √3, x=tan 16, and c2 = † (2 — r3), finds and we thence obtain an expression for z in terms of the elliptic functions sn u, cn u, dn u. Writing a instead of z, and k for c, then m= √2, r= And working out the substitutions, the resulting formulæ are where the modulus is k as above; and these values give The verification is interesting enough; starting from the expression for a, and for shortness representing it by |