52 Mr. Chase on Numerical Relations of 



AM.OC ,-■-/'",, 



a q M q of the points A, M, 0, C is = \ ( V% — 1 ) ; hence the 



corresponding anharmonic ratio of the projections of the four 

 points is also =-|( V'Z — 1); and the projections of A, B, C, D, 

 and consequently those of A, C, 0, being known, the projection 

 of M is thus also known. 

 Cambridge, June 15, 1865. 



VIII. On Numerical Relations of Gravity and Magnetism. 

 By Pliny Earle Chase, M.A., S.P.A.S.* 



IN the fifth century before the Christian era, Leucippus and 

 his disciple Democritus taught that heat is the soul of the 

 world, the principle of life and intelligence, and that space is an 

 infinite plenum, pervaded by material atoms too minute to be 

 perceptible to the senses, which, by their constant motions, 

 unions, and separations, form the beginnings and ends of things. 

 In this theory, which is said to have been borrowed from the 

 priests of Isis and Osiris, we may trace the origin of the modern 

 belief in a universal kinetic sether, and of the attempts to resolve 

 all forces into " modes of motion," which were practically in- 

 augurated by our own countryman, Benjamin Thompson, Count 

 Bumford, and which have been so successfully prosecuted by 

 Carnot, Seguin, Mayer, Colding, Joule, Grove, and their col- 

 laborators. 



The mutual convertibility of Light, Heat, Electricity, Mag- 

 netism, Chemical Affinity, and Vital Energy, may be now re- 

 garded as one of the most probable physical hypotheses. Fara- 

 day has endeavoured also to connect gravitation and magnetism, 

 or electric action by experimental results, but in vain. Still 

 the conviction of such a connexion is almost irresistible, and 

 various physicists have given us incidental pointings in that 

 direction. Ampere discovered the magnetic effect of electric 

 currents circulating around iron bars; Arago, whose experi- 

 ments were repeated and extended by Babbage, Herschel, Bar- 

 low, Christie, and others, showed that simple rotation produces 

 magnetic disturbances which are governed by fixed laws; the 

 distribution of induced magnetism in masses of iron, as deter- 

 mined by Barlow and Lecount, is the same as would follow from 

 the relative centrifugal motions of different portions of the 

 earth, provided the magnetic axis corresponded with the axis of 

 rotationf; Hansteen suspected, and Sabine practically demon- 



* From Silliman's American Journal for May 1865. The Magellanic 

 Gold Medal was awarded to the author for this memoir. 



t This fact was first announced by me at the Society's meeting, April ] 5, 

 1864. See Proceedings of the American Philosoj)hicalSociety,vol.ix. p. 367. 



