22 UNIVERSITY OF COLORADO STUDIES 



gelatine films, for practically the same shrinkage takes place on one 

 plate as on another. The shrinkage, too, reduces all the ordinates of 

 the curve in the same proportion, and if the relative positions of the 

 images are always determined by measurements on a photographic 

 plate no correction need be applied to the ordinates. 



The object of having two wedge-shaped compartments is to 

 reduce the dispersion of the light passing through them as much as 

 possible, indeed white light from an incandescent lamp can be used. 

 The solution in the wedge a h d is the same as that in a c d except 

 .that in it the reaction has already taken place. Under these circum- 

 stances the indices of refraction in the two wedges are very nearly 

 equal and a slow change of a few degrees in temperature does not 

 displace the image Sj since such a change affects the index of re- 

 fraction in both solutions practically to the same extent. 



In the above described experiment the dimensions of the appa- 

 ratus were as follows : SL (Fig. 1) = 150^°^; LS^^ 250<='^; al=V'^\ 

 ad = ^'S*^^; L5 ^ 15*=™, approximately. The breadth of the slit in 

 front of the figure was -2™™, and its distance from the figure about 



That the distance of the image S^ at any time from its final 



position after the reaction has been completed is very approximately 



proportional to the amount of cane sugar left in the solution at that 



time, may be seen from the following reasoning: The proof is based 



upon the assumptions that the density d and the specific index of 



n2 1 1 , . 



refraction „ , ^-, . ^ of the solution (where n is the ordinary index 



n^ ^ Z d ^ '' 



of refraction) are additive functions of the constituents (see Nernst, 

 T/ieoretische Chemie). Granting these, it follows that the difference 



between the value of ^ at any time and its final value must be 



71^ -\- 2 -' 



proportional to the amount s of cane sugar remaining at that time. 

 Denoting this difference by A we have 



