352 Duane — Velocity of Chemical Reactions. 



(where n is the ordinary index of refraction) are additive 

 functions of the constituents (see Nernst, Theoretische Ghemie), 

 Granting these, it follows that the difference between the 



value of — at any time and its final value must be propor- 



tional to the amount z of cane sugar remaining at that time. 

 Denoting this difference by A we have 



A -5 — - = Jcz 

 ft 2 + 2 



Approximately for small changes 



nVl d (r?—\ \ 6n 



A n^2 = 7U \tf + %) An = (n^2y 



Hence Aft = *—- — - k z 



6ft 



If n (Fig. 3) is the index of refraction of the already reacted 

 solution 



n i __ s * n P _ 8 ™ ( a + ^ a ) 

 n sin a sin a 



= 1 — cot a sin Aa 



approximately, and therefore, 



n. Aft 



COt a Sin Aa = 1 = ■ 



ft ft 



Aft 



u 











ft COt a 









3 



I 





c 







- — ^ot 





O0\/^ 







/^\'/S 









I) 



a a 









If D is the distance from 



the solution to the screen 





• 2/ = 



2/ 

 D 

 = Dsir 



sin Aa 



* 



"~ cos Aa " 



i Aa approximately 



Hence 



17 ft COt a 



ft does not vary more than *1 per cent and if n lies between 



(w. a + 2) a 

 1*3 and 1*4, which it usually does, the expression — is 



practically constant. 



Hence y is proportional to s, or the displacement of the 

 image from its final position is proportional to the quantity of 

 cane sugar in the solution. 



