ON THE VELOCITY OF CHEMICAL REACTIONS 23 



Approximately for small changes 



Hence A^=-^^ — 5 — —kz 



If /I (Fig. 3) is the index of refraction of the already reacted solution 



n^ sin /S sin(aH-A«) 



n sin a sin a 



= 1 — cot a sin A* 

 approximately, and therefore, 



cot « sm A<3;=1 — — '-^ 



7?/ n 



■ A A'«' 



or sm /\,a= ^ — 



n cot a 



Fig. 3. 



If D is the distance from the solution to the screen 



y sin A« 



D cos A« 

 . • . y =: D sin A* approximately 

 Hence 



7/ = — ^^ ^— k z 



•^ n^ cot « 



71 does not vary more than -1 per cent.; and '\in lies between 1-3 and 



(w3 + 2)2 . 

 14, which it usually does, the expression ^ ^ — — is practically 



constant. 



Hence y is proportional to z, or the displacement of the image 

 from its final position is proportional to the quantity of cane sugar 

 in the solution. 



Whether or not y is proportional to z in any particular case 

 should and can be tested experimentally as follows: Take equal 



