JAN. 19, 1923 WHITE: ELECTRIC HEATING OF CALORIMETERS 21 
to the time of G is the head during the temperature rise plus that 
during the approach of equilibrium, or: 
n—L 
KT? 
a | {a — Kt) dt 
the 
é Kt 
or = | (a — qt Ya +| ar - 
which gives for the true integrated thermal head for the interval 
T +n: 
of" =aP iF hcg pertanng iS cio  -aiehaacila -E@-n (3) 
2 6 2 2 
with a term containing K? omitted. For calculating an equivalent to 
this the temperatures at times A and G’ in the figure are given. It is 
then a method which sufficiently combines accuracy and convenience 
to assume that the temperature, starting after an interval of Ly 
minutes from A, rose at a uniform rate for 7’ minutes to the tempera- 
ture G’H, and then remained constant at that temperature for n —L 
minutes. That is, the temperature rise is simply multiplied by 
17+” -—L. Now the temperature at H actually is, in accordance 
with (2): 
w(t =a ( Be -») (4) 
Hence, using the approximation just suggested, the calculated thermal 
head is: 6". 7" = of ( - S I —K(n - 1 (Fan as | 
which is, again omitting terms containing K?: 
grt a gh ERD (n —L) —KT(n—-—L)—-—K(n - DH 
The difference between this and (3) is the error of the approximation 
made in calculating. It is: 
\~ (n — L) of (n — a 
6 (¢T’) = qTK -- (6) 
12 2 2 
The calculated thermal head is too small by this amount. A glance 
at (3) shows that this error is over half of the real change in $7” 
due to the leakage. 
With T = 4,n — L =1, K = 0.003, this error causes a final error of 
0.000,036 g7', which is safely negligible even in work of 0.1 per mille 
