one is to find the maximum or minimum of a fresh definite integral, and so is a problem of exactly the same class as the original problem. The fact that integrals so obtained generally lead to differential equations of difficulty, prevents us from illustrating this statement. We have tried the plan with Todhunter's Researches, Art. 20, and in other cases, with success.

Want of space obliges us to defer the consideration of the many historical problems of great interest discussed in these Researches.

TRANSACTIONS OF SOCIETIES.

London Mathematical Society.

Thursday, Feb. 12th. Dr. Hirst, F.R.S., President, in the chair. Messrs. R. W. Genese, R. Rawson, and the Rev. M. M. U. Wilkinson, were admitted into the Society; the Revs. Dr. Booth, F.R.S, and W. H. Laverty, were elected Members; and Col. A. R. Clarke, R.E., C.B., F.R S., Mr. W. R. Browne, and Mr. Ernest Carpmael, Fellow of St. John's College, Cambridge, were proposed for election.

Professor Clifford gave an account of the views advanced in his paper "On the Foundations of Dynamics." A discussion ensued, in which Messrs. Perigal, Wilkinson, Moulton, Cayley, and Roberts, took part. Mr. Clifford having replied, proceeded to give an account of his paper "On the Free Motion of a Solid in Elliptic Space." A paper by Mr. C. J. Monro, entitled, "Note on the Inversion of Bernouilli's Theorem in Probabilities," was taken as read. The object of the paper was to shew, first, that there is an oversight in Laplace's statement of inversion, the correction of which removes the inconsistency of the results; and secondly, that upon the hypothesis of equally probable values within equal ranges, the inversion is so far legitimate, that either theorem may be inferred from the other with little calculation, and in particular without the approximate evaluation of a general integral, and accordingly that the two solutions are identical in principle (Todhunter's Hist., p. 555, §999; De Morgan's Treatise on Encyc. Metrop., §77).

Thursday, March 12th. Dr. Hirst, F.R.S., President, in the chair. Col. A. R. Clarke, R.E., C.B., F.R.S., and Messrs. W. R. Browne and Ernest Carpmael, were elected Members of the Society; and Prof. Charles Niven, M.A., Queen's College, Cork, and Thomas Muir, M.A., Assistant Professor of Natural Philosophy, Glasgow University, were proposed for election.

The following papers were read: "On certain constructions for bicircular quartics," and "On a Geometrical interpretation of the equations obtained by equating to zero the resultant and the discriminants of two binary quartics," Prof. Cayley, V.-P.; "On the Cartesian equation of the circle which cuts three given circles at given angles," Mr. J. Griffiths, M.A.; "On another system of poristic equations," Prof. Wolstenholme. The last two papers were read by the Secretary. The Chairman made some observations on the papers.

R. TUCKER, M.A., Hon. Sec.

THE END OF VOL. III.

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