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The Master's Lodge, St. John's College, Cambridge. - Will be very glad to have the letters from Sylvester to Cayley. When Sylvester died MacMahon handed over a bundle of letters to Sylvester which Scott now has in his keeping; these letters would be an 'interesting addition to the collection'.

Trinity College, Cambridge. - Has been through Cayley's father's papers gathers that 'everything of value in the MS memoirs and papers has already been printed. All appear to have been carefully examined by Forsyth many years ago, and nothing more can be picked out for publication'. The largest part of the papers 'consist of notes for and incomplete drafts of memoirs included in his published works. All these rough and incomplete notes I propose to destroy'.

Lists proposed recipients of materials. Has no letters himself from Arthur Cayley. Thinks letters from living writers should be either returned to them or destroyed; is therefore returning MacMahon's letters, and destroying those from Glaisher and Forsyth. Of letters from people now dead he proposes to send those from Sylvester to the Master of St John's [R. F. Scott]; thinks most of the rest should be destroyed, though he mentions a few people to whom he would like to send 'a certain number' which he feels would be unproblematic to send. Encloses a few letters and papers 'of a personal character' for Cayley to take care of.

(Paris.)—Welcomes him back to England. Is about to go to Dublin for the British Association meeting, and is sorry Clifford will not be there. C. S. Pierce is expected to attend. Thanks him for some manuscripts, which he presumes are for the American Journal of Mathematics. Discusses points relating to the application of chemistry to algebra (sic).

(Letter-head of the Athenaeum Club.)

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Transcript

Athenæum Club
9th August 1878

My dear Clifford,

Welcome back to England! This is written from Paris which I leave on Sunday night next for London whence on Tuesday evening I purpose to proceed to the B.A. at Dublin where I grieve to infer from yr letter you do not intend to be present. Peerce† (C. S. I suppose you mean) I am informed will also attend the meeting of the British Association.

Many thanks for the precious Mss which I presume you intend for the American Journal. Have you seen the second number of it? I think that I have gone one step beyond you in interpreting multiplication of graphs.

Überschiebung we have in common. I now see that in applying Chemistry to Algebra we must always begin with supposing an indefinite number of Quartics of each given species: we may thus ex-gr à priori determine that there are only 5 irreducible combinations of hydrogen and oxygen atoms

viz Oxygen. Hydrogen. Hydroxyl. Water and Ozone.

Jordan has taught me something about indefinite systems which I only suspected before but now know to be true and which are essential to the development of the chemical side of the subject.

Let me know if not too troublesome how you are getting on and what your intentions are for the future.

If you feel writing a fatigue ask your excellent wife to write for you.

With my kindest regards to her and yourself believe me

My dear Clifford
Yours very truly
J. J. Sylvester

It requires a somehat delicate handling to prove graphically that the covariant of the 2d order in the variables and of the 3d or higher degree in the coefficients of an infinite system of Quadrics is verifiable.

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† Sic.

'As Savilian Prof[esso]r of Geometry I think it desirable to appear from time to time as a worker on Geometry so as to make up for my deficiencies in the eyes of the University in other parts of my duties as Professor'; intends to write a short article for the Philosophical Magazine on Magnus' theorem and asks Cayley to refer him to Magnus' original paper; 'I can apply my equations to obtain the motion required to bring the two schemes onto perspective relation very simply - ie I can get what you call the kinetic matrix'. Further discussion of this, in relation to Cayley's work.

The Master's Lodge, St. John's College, Cambridge. - Thanks Rouse Ball for sending him the letters from Sylvester to Cayley; has 'only as yet just opened the parcel but it is clear that there is a good deal of matter in them'.

Athenaeum Club, Pall Mall.—Encloses a cheque for the Clifford fund.

(With an envelope.)

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Transcript

Athenæum Club, Pall Mall
7th April 1876

Dear Mr Pollock—I enclose cheque (£5) for the Conspiracy Fund. I would do the same over again if a fresh application is found necessary. I am very glad that the thing has been undertaken and think that nothing too much can be done that may tend to the preservation of so valuable a life.

Believe me,
Yours very truly
J. J. Sylvester

[Direction on envelope:] F. Pollock Esqr | 12 Bryanston St | Portman Square | W

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The envelope was postmarked at London, S.W., and London, W., on 7 April 1876, and is marked ‘Sylvester’ in a later hand.