of Light produced by Quartz. 171 



Before we proceed further we must make a few observa- 

 tions on the nature and relative magnitudes of the quantities 

 contained in the formulae (17.) The capital letters denote 

 quantities depending entirely on the nature of the medium ; 

 and by examining (15.) and (16.) we may see that A, and Ag 

 are sums of which the terms are all positive ; but we infer that 

 the latter is almost indefinitely smaller than the former, be- 

 cause it involves a power of A j; higher by two units, and A x 

 can never exceed the radius of the sphere of influence of a 

 molecule of the medium. The same observations apply to 

 A/ and A'g . The quantities A, Ao, ... A', A'o , ... B, B^, Bg, 

 ... are sums in each of which the terms must be about half 

 of them positive and half negative, hence these quantities 

 must be comparatively small, and their real magnitudes can 

 be learnt only by comparing with experiments the results of 

 the calculation, the basis of which must originally be hypo- 

 thetical. 



The sum B^, which is the principal quantity in the value 

 of <r, is the sum which we have shown in art. 15, p. 426, vol. 

 ix. can always be made to vanish, by taking the axes of y and 

 z in proper directions. Let us suppose this done, and that 

 the other sums in o- are indefinitely small in comparison with 



A; , A/. Let us also suppose -j- to be insensible. Then, by 



substituting the values (17.) in the equation (14.), writing v 



for -J-, transposing, and stopping at the terms explicitly ex- 



pressed in (17.), we get 



v^ = A(— Ag kf — q^ sin b .'&^k^, 

 = K]-K,kf^ sin^.B,^, 



v^ — Af—K^k^—pci^ sin b.'Ec^k^ (^^O 



= A/-A^3A-.;-+ '^"^•^^^^ 



where we have marked v and k with subscript figures, be- 

 cause the values of these quantities must necessarily be dif- 

 ferent in the two equations, while that of « remains the same. 



Suppose 0--, and or sin b^ to be indefinitely small in compa- 

 rison with the quantities to which they are joined in (12.) and 

 (13.), then , 



cosi = ±y-^, (19.) 



«"^ P = --r^S; (20.) 



' <r' cos b ^ ' 



