THE MECHANICAL EQUIVALENT OF HEAT. 
489 
Remarks on Table XL. 
The column headed “Mean” was obtained by multiplying the numbers in the 
preceding columns of each section by the number of experiments from which they 
were deduced, and dividing the sum of the products by the total number of experi¬ 
ments. The “means” were plotted on a scale such that inch of ordinate repre¬ 
sented a difference of '1 second in T, and the smooth curve in each case so drawn that 
the sum of the positive and negative areas included between it and the experimental 
curve was zero. The curvature is so slight over our range that by assuming T to be 
a linear function of our “ curve numbers ” are not affected when written to four 
figures. 
It will be found that our results (obtained from the “ smooth curve ” values of T) 
are in much closer agreement than might be exjDected from a study of Table XL. 
This indicates that the irregularities are due to some (or all) of the following causes. 
(1.) Errors in the comparative values of the ranges. The effect of such errors 
would be common to all the experiments, and there is evidence that the sixth range 
is too small, the value of T over that range being nearly always too large ; the error, 
however, does not amount to 0°’00L. Again, the ninth range is evidently too great. 
These errors do not affect the result when the values of T over two or three consecu¬ 
tive ranges are meaned (as is done by the smooth curve), the excess in one case is 
then compensated by the deficiency in another. 
(2.) The irregular (as apart from the strictly recurrent) “stickings” of the ther¬ 
mometer ; these, as previously mentioned, must mean out wLen sufficient observations 
are taken over the same range. 
(3.) Irregularities in the temperature of the water ejected through the opening in 
the cylinder on to the thermometer bulb, water from cooler parts of the calorimeter 
being followed by a gnsh of warmer water brought direct from the hot wire. This, 
no doubt, is a fruitful cause of alternate lag and acceleration, but again, it is evidently 
an irregularity which would but slightly affect the results of many experiments con¬ 
tinued through a sufficient number of intervals of time. We have previously pointed 
out that the “ throw ” was irregular throughout Groups B and E, and the effect on 
the individual experiments is very marked ; nevertheless the values of T derived from 
the fifteen experiments in those groups are in practical agreement with the values 
deduced from the experiments in Series II. 
(4.) Personal errors of observation which, from their very nature, are unlikely to 
recur at regular intervals or over identical ranges. These, no doubt, are the origin of 
many discrepancies, the strain on the observer during these experiments being great. 
The cumulative effect of all the above causes of irregularity may at times be large. 
In Series I. differences of 1 in 500 occasionally present themselves, although, in 
Series II., there is only one case in which the difference between the mean and the 
curve-numbers exceeds 1 in 1000, and only two others in which it exceeds 1 in 2000. 
MDCCCXCIII.—A. 3 R 
