BETWEEN THE CONDITIONS OF A CHEMICAL CHANGE AND ITS AMOUNT. 123 
Table I. — Weights of substances taken: — sodic peroxide ‘0127 grm., hydric sulphate 
37T grins., potassic iodide *6 grm., volume of solution 993 cub. centims. Tempera- 
ture 17° C. ; y — residue of peroxide after t mins. ; H — t— the time of a portion of 
chemical change by which y is diminished to y'. 
I. 
II. 
III. 
IV. 
y- 
t. 
y-y’- 
t'-t. 
20-95 
o-oo 
]9'95 
4-57 
l 
4-57 
18-95 
9-37 
i 
4-80 
17-95 
14-50 
l 
5-13 
16-95 
19*87 
i 
5-37 
15-95 
25-57 
l 
5-70 
14-95 
31-68 
l 
6-11 
13-95 
38-20 
l 
6-52 
12-95 
45-23 
l 
7-03 
11-95 
52-82 
l 
7-59 
10-95 
61-12 
l 
8-30 
9*95 
70-15 
l 
9-03 
8-95 
80-08 
l 
9-93 
7'95 
91-27 
l 
11-19 
6-95 
103-88 
i 
12-61 
5-95 
118-50 
l 
14-62 
4-95 
135-85 
l 
17*35 
3-95 
157-00 
i 
21-15 
2-95' 
184-53 
l 
27*53 
1-95 
223-45 
l 
38-92 
0-95 
291-18 
l 
67-73 
The relation between the series of numbers in these columns is represented by the 
curve, Plate VIII. This curve, which is drawn through twenty experimental points, 
corresponds to those which served in our former communication*' to exhibit the rate at 
which hydric permanganate is reduced by hydric oxalate. Along the axis of x is 
measured the time of each observation, dating from the commencement of . the set of 
experiments, and along the axis of y the amount of peroxide present in the solution at 
each of the times. Through each experimental point a line is drawn parallel to the axis 
of x to meet a line drawn through the point next below it parallel to the axis of y. 
These lines represent the quantities measured in each experiment, namely, the interval 
between two successive observations, and the amount of chemical change. 
Starting, then, from the 'point to which our previous investigations had led us, we 
inquired at once whether this curve was. logarithmic, that is to say, whether the amount 
of action had in this case varied directly with the amount of the varying active substance. 
The equation expressing this hypothesis has been shown f to be 
u—ae”**, 
where a is the amount of active substance, u the residue after a time x, a the fraction 
disappearing in a -unit of time, and e the base of Napierian logarithms. To the quantity 
a in this equation corresponds any of the values of y in the preceding Table, to the quan- 
tity u corresponds the next successive value of y in the Table, i. e. y 1 , and to the time x 
* Philosophical Transactions, 1866, Plate XVIII. + Loe. cit. p. 208. 
