24 UNIVERSITY OF COLORADO STUDIES 



quantities by weight of a solution that has already reacted and of 

 one that is just beginning to react. Mix them together and obtain 

 a curve as above. This mixture is equivalent to a solution that has 

 reacted half way, and the total change in the position of S^ as indi- 

 cated by the curve should be ^ that in the case of the original solu- 

 tion. Such a curve photographed for the inversion of sugar proved 

 the proportionality to within about ^ of a per cent. If y is found not 

 to be proportional to 2 a number of mixtures must be made with vary- 

 ing quantities of new and old solutions, and the relation between y 

 and z determined. 



The distances between the lines on the photographic plate cor- 

 responding to the different instants of time can be measured by 

 means of a micrometer microscope of low power. I have found it 

 more satisfactory, however, to place a glass scale over the plate and 

 take the readings with a small lens, illuminating both scale and plate 

 by means of a mirror below them. 



The following table contains the results of such measurements 

 on the plate representing the inversion of sugar. The first column 

 contains the time t expressed in minutes; the second, the distances 

 y in centimeters between the curve and the line drawn 24 hours 

 later (the value of y for z^=0 being extrapolated), and the third, the 

 percentage of cane sugar left in the solution: 



