THE MECHANICAL EQUIVALENT OF HEAT. 
423 
if the thermometer was to be used for the determination of changing temperatures. 
We believe that no calibration can be considered satisfactory unless made under the 
same circumstances as those in which the thermometeris to be used. As an illus¬ 
tration of our meaning we may mention that the range 87‘5 to I27'5 = 0°'975 C. 
when the thermometer was stationary, but = 0°‘973 C. when rising at the normal rate 
of our experiments, ^.e., in addition to calibration for inequalities in the bore, a ther¬ 
mometer used under circumstances similar to ours must be calibrated for “ sticking ” 
and for certain periodic alterations in the rate of advance which are probably due to 
the behaviour of the glass bulb. Whatever may be the case with other thermometers, 
a close and prolonged study of the thermometer has rendered it certain that the 
rate of advance of the column (when the rise in temperature is uniform) is influenced 
by other conditions than mere irregularities in the bore, but that these changes in 
rate will, under the same conditions, almost always recur at the same places. 
During 1891 the times of rising every 10 millims.* throughout the whole range 
were observed and the observations repeated on more than thirty occasions with 
varying rates of rise. Nearly half of these observations were taken with the alloy 
wire, whose resistance did not increase as the temperature rose, the remainder with 
a platinum wire. During this series of observations the weights of water were 
different, the supply of heat was trebled, the exterior temperature was shifted from 
the bottom to the top of our range, the pressure changed from I to 760 millims., 
and, in fact, all the conditions were altered. The times of rising 10 millims. under 
all these different circumstances were thus determined at 42 points in our range, and 
the results plotted; the mean path in each case was, of course, diflerent, but the 
deviations from it were regular in their occurrence and similar in them nature. Such 
deviations as invariably occurred throughout all the altered conditions must have 
had their oiugin in the thermometer itself. 
We hope to publish some of these curves in our further communication for, although 
the changes in the curves themselves are great, the steady repetition of lag and 
acceleration is both curious and interesting. This year these differences recurred 
with another coil and a different method of stirring. 
The mean values of these deviations, which were repeated throughout the whole 
I of the exjDeriments, were expressed in terms of the curve-reading at each point and 
plotted as ordinates on a straight line,t and the remainder of the calibration com¬ 
pleted in the usual manner. The effect of the application of the resulting corrections 
to the numbers obtained from our J experiments is a sufficient proof of the accuracy 
of the method. An error of 0°’001 C. in the comparative value of any of our ranges 
would produce a difference of from '4 to ’7 second between the “ mean times ” given 
* 10 millims. on thermometer E* = 0°’25 C. approximately. 
t E.g., if t" was observed time over a small range 6^ — 0^, and if t' was the value over that range 
as given by the smooth curve, then f'/t' was plotted as ordinate and f (dj — 0Q as abcissa, and the 
areas thus obtained were integrated, &c. 
