BETWEEN THE CONDITIONS OF A CHEMICAL CHANGE AND ITS AMOUNT. 125 
The mean of the values of log log|> — log (f — t) is 3-664, and it will be seen that every- 
one of the values obtained for this difference from the several experiments approximates 
very closely to the mean. Those which exhibit the greatest deviation on either side 
are 3-668 and 3’660; and it is important to ascertain whether these deviations can be 
accounted for by possible errors of experiment. The errors may occur (1) in the 
measurement of the small quantities of sodic hyposulphite, (2) in the management of 
the temperature of the solution, (3) in the estimation of the interval t'—t, which 
depends upon two successive observations of the moment at which the colour of the solu- 
tion changes. If, then, we suppose that the whole deviation is due to an error committed 
in one of these operations, the rest having been correctly performed, we find that it 
might result either (1) from a particular measure of hyposulphite having been one per 
cent, smaller or larger than the rest, or (2) from the temperature having been 0°T3 too 
high or too low, or (3) from an error of three seconds having been made in measuring 
an interval of five minutes. The second of these errors we may perhaps pronounce im- 
possible: the fluctuations of the temperature of the solution seldom exceed 0 o, 05, and 
by balancing a small oscillation on one side of the degree line by a similar oscillation on 
the other, the mean thermometric error during an interval may generally be reduced to 
a much smaller quantity. But neither of the other errors is such as might not possibly 
occur in one or two out of a large number of measurements and observations. It is, 
however, most probable that the maximum deviations from the mean result are due, 
not to any single experimental error, but to the simultaneous occurrence of two or more 
errors in the same direction. For example, it may happen (and in eleven experiments 
it is an even chance that the case will occur) that the measure of hyposulphite is less 
than the mean, the temperature of the solution too high, the first observation made too 
late, and the second observation too soon. All these errors conspire to make the experi- 
ment in which they occur give too high a number for log log — log — t). And such 
a divergence as that in the experiment which gives for the value of this difference 3-668 
instead of the mean 3‘664, would occur if the measure of hyposulphite were a fifth per 
cent, smaller than usual, the temperature 0°-025 too high, and the observed interval one 
second too small. Now all these errors are probable experimental errors. Hence it 
appears that within the limits of experimental error the numerical results here obtained 
accord with the hypothesis before stated. In the case of this reaction, it appears that 
the amount of chemical change occurring at any moment is proportional to the amount 
of peroxide present in the solution. 
It may serve to exhibit the degree of coincidence between the experimental results 
and the hypothesis, if we further compare the intervals actually observed in this set of 
experiments with those calculated from the equation in which the hypothesis is embodied. 
The general equation being log log %j — log(^ — t)— loga+ log log<?, and the mean 
MDCCCLXVII. 
