92 Mr. R. Potter on a 'particular Modification 



still only indicated on the second side; but from the com- 

 plexity it assumes there is no means of using it, except by 

 changing it into a numerical equation, by adopting some nu- 

 merical values for y 9 and calculating the corresponding values 

 for x by extracting the required roots. On this account the 

 above is, I believe, the simplest form in which it can be used, 

 and the calculation is, nevertheless, still sufficiently laborious. 

 We may compare the equation to the following : 



(Ax^ — Bx + D) 2 = E# 9 +F; 

 or, A e i*-2AB^ 3 + ^(B 2 + 2AD-E)-2BD l r+D 9 -F = 0. 



For the data, I have taken e = 40 inches, a = *06 inch, 

 and the refracting angle of a new prism (which I prepared 

 with the intention of making micrometrical measurements if 

 the phamomena had come under any known theory) = 33° 18'; 

 the refractive index of the glass being 1*500 very nearly. 



From these I find for the angle of minimum deviation or 

 i —25° 27' 14" nearly. 



For the lower curve e' — c + 2a sin i — 40*0515744. 



x = 2*^— r-= 44*4. 

 F 



2 -i 



/• = 2g' ^ , =44*50174. 

 F 



r _ JL^ __ 44*297241 (= dl). 

 cos i v ' 



e 1 



r ti — : — 44-354361 (= bm). 



1 cos? v ' 



To the point on the same perpendicular — r fi + 2 a tan i 

 - r\i + 2a tan i = 44*411479 = r\ p (= g o). 

 r\ = 44*342340 (= ?r) 

 ' r lp - r\ or 8 = -069139 (= s&) 

 A paths or 3/ = -0634655 (=?/#). 

 * a = -1140052 (= a $ 

 = -0786127 [= at) 

 C = '0691293. 

 Calculating with these, I have taken for y three different 

 values; namely, y — 41 inches, y = 45 inches, and y — 50 

 inches, and arrived at the following equations : 

 For y = 41 inches, 

 •000045968 x* + '00927 1 S 1 x 3 — *0 1 28883 x* — 40*053245 x 



+ 718*6541 = 0. 

 For y — 45 inches, 

 •000024167 x A + 0061 15092.r 3 + -00971671 a; 2 - 38*1 3274* 

 + 787'2133 = 0. 



