AS EXPLAINED BY THE HYPOTHESIS OF FINITE INTERVALS. 177 



P = ^^^- P^ -p^T^—] ^P'' 



f 1 (w4^1)^l ,. 



9=-">^-[p^ -^s — |V ; 



let the distance between two consecutive particles be denoted by e, 

 and for Sx, Sy, Sz, Sp respectively write €^, erj, e^, to-: ^ being the num- 

 ber of particles along a line through Q perpendicular to the plane of 

 1/x, and similarly of >/, ^ and o-. 



By substituting these values 



„ - ^i^i 1 {n + l).e ]eV 



' l(f + ,= + H— (f + ';' + D~^ 



Now each part of these expressions, with the exception of the factors 



A B 



-^^ and -^33, is a numerical quantity not dependent on the nature of 



the medium, except inasmuch as it requires the medium of symmetry, 



B . . ~' 



and —^ is evidently some mmiber: in fact it is equal to 



A^ ^ ^ 3 X (100,000)' 



by page 28 ; hence the only possible mode of causing p to become 



large in vacuum whilst q is small, at the same time that p is not 



large and q not small, (I speak comparatively) in glass, will be by 



supposing ——^ large, and —;^ small, in the former, whilst the same 



quantities are not so widely different in glass : but e is small in 



all cases ; in order, then, that -;^ shall be large, m — 1 must be positive, 



and that €""' may be small at the same time, and vice versa, e'-' must 



be negative; therefore m > 1 < 3, or if ?j = 2, all the conditions are satis- 

 VoL. VI. Part I. Z 



