VOL. XXX.] PHILOSOPHICAL TRANSACTIONS. 375 



draw NM parallel to the tangent kl, touching the circle bemg in m, and meet- 

 ing CD in N. Lastly, take the sector rcb to the area nmblkn, as the number 

 2 to the number n. Then the right line rc will cut the circle pa in the point 

 Q, which will be in the curve eqa of quickest descent. 



And if the sector bce be taken to the area bdg, in the said ratio of 2 to n, 

 that is, the points l, d, and m, g coinciding, because of a" = h", the point 

 E will be that from whence the body should begin to fall, to arrive at a in the 

 shortest time, and which in its descent describes the curve eqa, which the 

 right line ce touches in e, and which cb cuts at right angles in a. 



The demonstrations of these constructions, which are derived from Newton's 

 Quadratures, and from his Principles of Natural Philosophy, p. 39, &c. shall 

 be given on some other occasion. But it is a problem of another kind, to de- 

 scribe curves through which bodies would move from the highest point e, or 

 the beginning of the fall, with the swiftest descent to lower given points q, 

 when urged by any centripetal force ; the solution of which problem is in my 

 power. For the present it may suffice to have given a general idea of such 

 curves, and to show their relation to the quadratures of the circle and hyperbola, 

 without which it will not be very easy to construct them geometrically. 



De Potentid Cordis. Dissertatio Autore Jac. Jurin, M.D. R.S.S. N° 358, p. 863. 

 [An attempt to estimate the muscular power of the heart upon mathematical 

 principles. Such calculations display great ingenuity, but they are necessarily 

 involved in much uncertainty, being founded on data taken from inanimate 

 matter, the laws of which are not applicable to organs endowed with the prin- 

 ciple of vitality. In this paper Dr. Jurin rates the propulsive force of the heart 

 much higher than Dr. Keill had done in his Tentamina Medico-Physica, and 

 represents Dr. Keill to have misunderstood and misapplied the Newtonian law 

 or corollary on which his (Dr. K.'s) calculations are founded.- To this Dr. Keill 

 replied in a Latin paper inserted in this same vol. of the Phil. IVans. and this 

 reply was followed by a rejoinder from Dr. Jurin ; which two controversial papers, 

 together with the present, it is deemed unnecessary to translate for the reason 

 above stated. The subject, not being reducible to mathematical demonstration.] 



An Account of a Contagious Distemper which raged among the Cows near Lon- 

 don, 17 \ 4. By Thomas Bates, Esq. F, R. S. N° 538, p. 8/2. 

 About the middle of July, J 7 14, the distemper appeared at Islington, and 



were one in vol, 37, on a Distempered Skinj and another in vol. 40, being a solution of Kepler's 

 problem. By an approximation of Dr. Halley's, Mr. Machin computed the circumference of the 

 circle to 100 places of figures. And an ingenious approximation of his own is printed in Mr. 

 Jones's Synopsis Palmariorum Mathexios, tlie investigation of which is given in Dr. Button's large 

 book on Mensuration, p. 89, 90, ed. 3d. 



