HOLM AN. CALORIMETRY. 251 



where 6 = some constant temperature (representing that of the sur- 

 roundings, which may not be uniform or known) and a = the rate per 

 degree difference between and t. 



The two quantities a and 6 are unknown, but obviously can 

 be computed from the two pairs of observed values, r^, ti, and rg, t^. 

 For 



r^ = a (6 — tfi) ; 



'-i + 1, 



a 



Both a and 6 are next computed numerically from the data. 6 is 

 best found from the smaller value of r, for the reason that it influ- 

 ences the result most largely through its subsequent combination with 

 values near that one. 



The gain of temperature by exchange, then, in any short interval 

 of time, A, during which the temperature is t, will be a (^ — t) A. 



The rate of gain of temperature is a (^ — t), or ad — a t, so that, as 6 

 is constant, r varies directly as t. Hence the average rate will be 

 proportional to the average value of t, that is, to T, and will be 

 a 6 — a T, OT a (0 — T). The total gain will therefore be this quan- 

 tity multiplied by the duration (???2 — '^i) of this average rate, or 

 a (6 — T) {rrio, — m^^ and the exchange (or " cooling ") correction will 

 be this with reversed sign, viz. : 



-a {6 - T) (w2 - OTi), or a{T-e) {m.,- m^). 



The corrected rise of temperature of the calorimeter will then be 



h-h^ a {T-6) (m.,-m,). 



Obviously (T—6) {m^ — in^) is the area ^0 Oi^ZT minus the area 

 B G H B. This difference. A, in proper units, may therefore be 

 measured on a plot by the planimeter or otherwise, and the corrected 

 temperature rise will then be 



h — tx ■{■ a A. 



Critique of the Methods. 



Three assumptions, beyond that of Newton's law of cooling, are 

 involved in the employment of this method, unless otherwise pro- 

 vided for in the computations into which the corrected rise of tem- 

 perature is introduced. First, that the thermometer indicates the 



