BETWEEN THE CONDITIONS OF A CHEMICAL CHANGE AND ITS AMOUNT. 207 



Table VIII. (continued). 



It will be seen that by varying the quantity of sulphuric acid from 25 to 400 pro- 

 portional parts, the reaction is caused to take place with very different velocities. Under 

 the conditions of the last set of experiments more work is done in one minute than is done 

 in ten minutes under the conditions of the first set. In how orderly a manner the amount 

 of residue diminishes as the reaction proceeds, and the rate of change increases with the 

 proportion of sulphuric acid, is shown by the series of curves on Plate XVIII. fig. 1, 

 corresponding to this Table. Guided by the empirical relation which we had observed 

 in the case of the reaction of proportional quantities, we endeavoured to apply the hyper- 

 bola to these curves also. It soon became evident, especially from those experiments in 

 which the reaction proceeded rapidly and was traced through a greater length, that the 

 rectangular hyperbola was not applicable. A hyperbola with an oblique asymptote 

 corresponded much more nearly to our experimental lines, and a number of equations 

 of the form y'^-\-axy — by=.G were obtained, which gave values of y nearly agreeing with 

 those which had been found. But after calculating the constants of this equation for 

 each series of experiments, we observed, 1st, that the earlier and later numbers never 

 agreed quite so well as the rest, the disagreement with the best possible equation at the 

 two extremes generally rather exceeding the probable error of experiment; 2ndly, 

 that when a curve was produced upwards, as could be done by repeating the series 

 with a larger quantity of permanganate, the divergence became much greater; and 

 Srdly, that instead of the actual numbers falling in an irregular manner above and 

 below those calculated from the equations, — as was to be expected if experimental 

 error alone were the cause of difference, — a regular rise and fall was perceptible, the 

 calculated numbers being in every case lower than the first observation or two, then 

 higher than the two or three following, then lower again for four or five consecutively, 

 and finally rising once more above them. Consequently these equations could not be 

 accepted as expressing truly the course of the reaction, and it was therefore vain to 



