Duane— Velocity of Chemical Reactions. 353 



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

 should and can be tested experimentally as follows. Take 

 equal 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 equiva- 

 lent to a solution that has reacted half way, and the total change 

 in the position of S x as indicated by the curve should be -J 

 that in the case of the original solution. Such a curve photo- 

 graphed for the inversion of sugar proved the proportionality 

 to within about -J of a per cent. If y is found not to be pro- 

 portional to 3 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 

 corresponding to the different instants of time can be meas- 

 ured 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 wdth a small lens, illumi- 

 nating both scale and plate by means of a mirror below them. 



The following table contains the results of such measure- 

 ments 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 f or t = being 

 extrapolated), and the third, the percentage of cane sugar left 

 in the solution. 



1 



y 



jo sugar 



2-3026 







25-5 



25' 



•00535 



15 



21-2 



20-78 





30 



17-9 



17-54 



•00490 



45 



15-4 



15-09 



•00463 



60 



13*25 



12-99 



•00454 



75 



11-3 



11-07 



•00455 



70 



9'75 



9-56 



•00449 



105 



8'5 



8*33 



•00441 



120 



7-4 



7-25 



•00435 



135 



6;4 



6-27 



•00433 



150 



5-55 



5-44 



•00431 



165 



4*85 



4-75 



•00427 



180 



4-3 



4-22 



•00419 



195 



3'95 



3-87 



•00405 



210 



3'6 



3-53 



•00395 



225 



3*3 



3-23 



•00385 



According to Gouldberg and Waage's law the rate at which 



the cane sugar disappears should be proportional to the amount 



clz 

 left in the solution. Hence -— = — k z 



dt 



