316 Royal Society .*— 



this truest and best, hie labor, hoc opus est. It will be delightful 



P 



to find, if it turn out to be true, that for the best form, -^ repre- 



*4 



sen ting \'X (P being a rational function of the «th degree, 

 and Q of the (i — l)th in x), the rational quantity 



XQf-^XP^(Q^X) 



must.be a perfect (2i — l)th power of a linear function of a?; but 

 in the present state of my ignorance I dare not do more than 

 affirm that there is a bare probability in favour of this being 

 true : whoever shall first succeed in discovering the true form of 

 the expression will have established a remarkable theorem. Here 

 for the moment I break off, contented with having pointed to a 

 theory as yet, if the expression may be allowed, sleeping in its 

 cradle, but destined, I am persuaded, at no distant day to set in 

 motion as large a mass of algebraical thought as has been set in 

 motion by the never-to-be-forgotten Hessian discussion of the 

 flexures of the cubic curve, — the turning-point between the old 

 algebra and the new. 



Henceforward Poncelet's theorem figures no longer as a de- 

 tached method, a mere stroke of art in aid of the computer, but 

 becomes integrally attached to the grand and progressive body 

 of doctrine of the modern algebra. 



XL. Proceedings of Learned Societies, 



ROYAL SOCIETY. 

 [Continued from p. 239.] 

 February 23, I860.— Sir Benjamin C. Brodie, Bart., President, 

 in the Chair. 

 H^HE following communication was read : — 

 -*- " Measurement of the Electromotive Force required to produce 

 a Spark in Air between parallel metal plates at different distances." 

 By Professor W. Thomson, F.R.S. 



The electrometers used in this investigation were the absolute 

 electrometer and the portable electrometer described in my last 

 communication to the Royal Society, and the operations were ex- 

 ecuted by the same gentlemen, Mr. Smith and Mr. Ferguson. The 

 conductors between which the sparks passed were two unvarnished 

 plates of a condenser, of which one was moved by a micrometer 

 screw, giving a motion of -^ of an inch per turn, and having its 

 head divided into 40 equal parts of circumference. The readings 

 on the screw-head could be readily taken to tenth parts of a division, 

 that is to say, to ^— of an inch on the distance to be measured. 

 The point from which the spark would pass in successive trials being 

 somewhat variable and often near the edges of the discs, a thin flat 

 piece of metal, made very slightly convex on its upper surface like an 

 extremely flat watch- glass, was laid on the lower plate. It was then 



