250 PROCEEDINGS OF THE AMERICAN ACADEMY. 



ri (positive for a rising, negative for a falling temperature), expressed 

 iu degrees per minute. 



For the data between D and E, i. e. through the observations for 

 the final few minutes, which will lie sensibly along a straight line, is 

 deduced similarly the final rate /v 



Let ti be the temperature at the point B, the beginnino- of the 

 operation. Call this the initial temperature. Then rj is the exchange 

 rate at t{. Let mj be the corresponding time. Let f^ be the tempera- 

 ture at the earliest minute or half-minute at which the line has become 

 straight, that is, at which the fourth stage has been sensibly attained, 

 e. g. the point 1). Call this the final temperature of the calorime- 

 ter, and 711.2 t^^e corresponding time in minutes. Then u will be the 

 rate at t^. 



The average temperature of the calorimeter between ???i and ni^ is 

 next found as follows. Drawing through the points the be-t re|)re- 

 sentative line B C M D, read off its ordinates at each half-minute 

 (better each quarter-minute) from Wi to m,2. Instead of a plot the 

 corrected data may be used directly. Call these temperatures a (=<i), 

 b. c, d, . . . , n {= (2), then the average temperature will be 



?2 — 1 L2 2 J 71 — 1 



This is, of course, the well known process. A slightly better one 

 is to read off the temperature at the end of the first qua7-t€r-imnute 

 after mj, then at intervals of a /<«//-minute (viz. at |, |, etc.) up to m^, 

 which must therefore be selected at a point an even number of quarter- 

 minutes from ???|, as there must be a quarter-minute interval at each 

 end. The average of these also gives T. 



By Newton's law of cooling, the rate of gain or loss of heat by a 

 body through exchange with surroundings is directly proportional to 

 the difference of temperature between the body and the surroundings. 

 In calorimetry, provided that the heat capacity of the calorimeter and 

 contents is not changed materially during the process (by the insertion 

 or removal of substances), the rate of gain of temperature through 

 exchange is proportional to the rate of gain of heat, so tliat the cool- 

 ing correction may be applied directly to the temperature, instead of 

 to the heat. 



Under this condition, the rate of exchange of temperature when the 

 calorimeter is at any temperature t will be 



