DETERMINATION OF THE SPECIFIC HEAT OF WATER. 443 
gn (n — 1)v = (2n + 1) A — 3B 
gu(n— 1) (n+ 1)kT = 2B— (n+ 1)A, 
where 
A=u,+tut...+ um 
B= u,+ 2uy +... + nu, 
The last observation being taken, the second period—in which the heat to be 
measured is allowed to enter the calorimeter—begins after a further interval T, and 
it is required to calculate, in addition to the rate of heating &T, the most probable 
value w,,, of the temperature at the beginning of the second period. The above 
equations give 
Une. = U+ (nm + 1)kT 
6B —2(u + 2)A 
n(n — 1) 

In our case, where the rise in temperature was always small and regular, ten or 
twelve observations were considered sufficient to determine the constants, and in 
that case the labour of reduction is small. 
After an experiment the change in temperature of the calorimeter had to be 
observed once more, and a value k’ corresponding to k was again determined in a 
similar manner. From the two values k and k’ the loss of heat of the calorimeter 
during the whole of the experiment could easily be calculated, for the rise in 
temperature during the actual heating was uniform. If the current passed during m 
intervals, each equal to T, and if — k and —F’ denote the rates of cooling during the 
first and last periods, the loss of heat during the m intervals was $m(k+ kh’). A 
small correction was necessary owing to the fact that the observed values of & and k’ 
did not correspond to the temperature of the calorimeter at the beginning and end of 
the second period. 
We have now to examine shortly how far errors in the estimation of the cooling 
correction may arise. Nrwton’s law of cooling is known to be approximate only. If 
we had to deal simply with radiation, we should obtain greater accuracy by adopting 
the law of STEFAN, according to which radiation varies as the fourth power of the 
absolute temperature. We have calculated that the difference introduced by STEFAN’S 
law in the final value of the equivalent amounts to about one part in sixty thousand, 
and considering that the combined effect of radiation and conduction seems to follow 
Newton's law more closely than the effect of radiation alone, we are justified in 
taking that law as correct. In order that the usual cooling correction should apply, 
it is not necessary that the different parts of the enclosure should all be at the same 
temperature, nor is it always necessary that the temperature of the surrounding 
bodies should be constant. If, as in our case, the calorimeter receives its heat at a 
constant rate, the temperature of the enclosure may vary as a linear function of the 
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