28 
PEOF. H. L. CALLENDAE ON THE VAEIATION OF THE SPECIFIC 
temperature, is the change of total heat at constant pressure, and is a quantity of 
the same khid as that measured in the continuous-mixture method. The work 
wliich is generally included in tabulated values of the total heat, is 
supplied as work by the feed-pump, and not as heat in the boiler. It would amount 
to oidy 1 in 500 of the total heat at 200° C., and might be neglected except in the 
most accurate calorimetric work. 
The quantity measured in Regnault’s method was the change of total heat from 
boiler pressure and temperature down to the final temperature of the calorimeter at 
atmospheric pressure, which may be denoted by the expression (E-l-pi’) — (Ei-t-ppij), 
where the suifix 1 denotes atmospheric pressure at the final temperature of the 
calorimeter. The differential of this is the rate of change of the total heat of water 
under saturation pressure, and exceeds the specific heat at a constant pressure equal 
to that of saturation by the expression \y — 9{d^^/d0)p]{d2)/d9)s^^,whlch amounts to 
nearly 0'3 per cent, at 200° C. The specific heat at constant pressure exceeds the 
so-called “ saturation ” specific heat at the same pressure and temperature by the 
expression 9 {dv/d9)p{d2J|d9)^^^, which amounts to O'G per cent, at 200° C. The values 
of the total heat and the specific heat from 100° C. to 200° C. given in the following 
tables, in so far as they represent a reduction of E,egnault’s observations, must be 
taken as representing the total heat of water and its rate of variation under satura¬ 
tion pressure, and not under constant pressure; liut the uncertainty of the reduction 
probably exceeds the difterence in question. 
The quantity measured by Dieterici was the change of intrinsic energy E of 
water from saturation pressure and temperature in the heater to saturation pressure 
at 0° C., whicli may be denoted l)y E —E^. Neglecting the small change of intrinsic 
eiiergy diie to 1 atmosphere at 0° C., tlie quantity measured by Dieterici is less 
than that measured by Regnault by the expression (jpc—pp’u), which amounts to 
0‘43 calorie at 200° C., or 0'2 per cent, on the mean specific heat. His tabulated 
values of the mean specific heat at 200° 0., when reduced to a unit at 20° C., are 
already 0'8 per cent, higher than my reduction of Regnault’s observations, so that 
tlie discrepancy is increased to 1 per cent, at this point if allowance is made for the 
difterence in the quantities measured. The actual specific heat at t tabulated by 
Dieterici is the rate of increase of the intrinsic energy under saturation pressure, 
which is less than that of tlie total heat E+jic under the same conditions by the 
expression \_d { •pv)ld9\^^^ which amounts to nearly 1 per cent, at 200° C. The specific 
heat tabulated by Dieterici already exceeds that deduced from Regnault by 2 per 
cent, at 200° C., so that the discrepancy is increased to 3 per cent, in the value of 
the actual specific heat at this point. The discrepancy is of the same order as the 
whole variation of the specific heat, and is not nnimportant from a theoretical stand- 
jioint. Accurate experiments at these temperatures are very difficult, but it is clear 
that further experiments are desirable, if any theoiy of the variation of specific heat 
is to be framed or tested, 
