348 
PROFESSOR 0. REYNOLDS AND MR. W. H. MOORBT 
divergence from the boiling-point, with care and experience it would be possible to 
bring the mean result in a number of trials within a close approximation of 
212° Fahr. 
On the other hand, there has been no means provided of regulating the tempera¬ 
ture of the water entering the brake. This is determined by the rate at which the 
water passes through the iced coil and the temperature at which it entered, as deter¬ 
mined by the temperature in the town’s mains, which varies from 38° in the winter to 
55° in the summer. Thus the temperature in the light trials would be from half to 
a degree above 32°, and that of the heavy trials from a degree to two degrees. 
In calculating the heat of each trial the actual difference with the correction for 
the thermometers is taken, but if, as is shown by i^revious investigations by Fegnault 
and others, the specific heat at and near 32° is less than the mean specific heat 
between 32° and 212° by something like 0‘5 per cent., there would be errors in 
taking the results so obtained as the mean specific heat between 32° and 212°. 
Owing to the extreme difficulty of determining the specific heat over a very short 
range of temperature to such high degrees of accuracy as ‘01 per cent., the experi¬ 
mental evidence as to the exact value of the specific heat within a few degrees 
of 32° is but vaguely surmised from the general fall of the specific heat with the 
temperature. 
The law of the thermal capacity of water between 0° C. and f, as deduced by 
Regnault from his experiments, is avowedly vague as to the lower temperatures. 
It shows no singular point at the maximum density, as would be expected; and 
Rankin deduced another law from these experiments, making the minimum specific 
heat coincide with the point of maximum density. Also other experimenters have 
obtained higher specific heats near 32° than are given by Regnault’s formula. It 
would seem probable, therefore, that the difference between the specific heat at 32° 
and the mean between 32° and 212°, as given by Regnault’s formula, is too large. 
In that case, the correction obtained by this formula in order to reduce the specific 
heat between the observed temperature in the trials to that between the standard 
points, would probably be too large, and thus afford an outside limit of error. 
Thus, putting 5 for the meau specific heat between 32° and 212°, 5 (l + X) for 
the specific heat between T^° and 212°, when Ti° is small compared with 180°, and, 
by Regnault, taking 5 (1 — 0'005) for the specific heat at Ti°, then the total heat 
from Ti° to 212° is 
6‘(1 + X) (212 - T°) = s (180 - {T° - 32) (1 - 0'005)} 
or, neglecting (T;^ — 32)^, 
= s (212 - W) (1 - X O-OOo;, 
X = 0-005 = 0-000028 (T,° — 32). 
180 
