20 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES VOL. 13, No. 2 
For calculating this, the only measurements needed during the cali- 
bration are two, of calorimeter temperature or thermal head, one be- 
fore the heat is started, the other long enough after its end to. allow 
the difference between the converging lines DG and FG to become 
negligible. ‘These data may then be used in accordance with the result 
of the following demonstration: 
If g is the temperature rise corresponding to the heat supplied per 
minute, A the jacket temperature, and K the leakage modulus,‘ 
the temperature, neglecting lags, is easily shown to be: 
us 
eared 
t44(,-$—a)™ (1) 
It will be convenient to write the exponential as a series, giving: 
| | Kt K# 
Pee ee ee 6 “ (2) 
6, — A is O in the present case. Since this expression for calorimeter 
temperature is to be multiplied by K to get the temperature change 
due to thermal leakage, then for water-filled calorimeters, where K is 
seldom much over 0.003, the terms now containing K? and higher 
powers will contain a factor of 0.000,000,027 ¢ or less, and may be 
neglected unless ¢ is uncommonly large. Similarly other terms con- 
taining K? will be omitted later. The physical meaning of the omis- 
sion is this: In defining the temperature pattern, which is to be multi- 
plied afterward by the very small factor K7’, we will take account of 
the change in temperature due to the leakage produced by the 
impressed temperature, but find negligibly small the change in the 
leakage caused by the change due to the leakage. 
If n denotes the time from the end of the heating to the first direct 
thermal head measurement afterward, represented by BG, then the 
time from D to G isn — Ly. Thermal head is the same as the tem- 
perature rise above 6, since it was taken as zero for 6 = 0,. On account 
of thermal leakage, the temperature after 7’ + Ly minutes is not 
D'D which equals qT but, by (2) qT — qT “ ; and aftern — Ly 
minutes more is still lower, or, say, G’H. ‘This is the temperature 
actually observed. Then the true integrated thermal head, ¢7’, 
‘ Thermal leakage modulus, temperature fall per minute per degree of thermal head. 
Thermal head, mean effective temperature difference between calorimeter surface and 
surroundings. 
