248 PROCEEDINGS OF THE AMERICAN ACADEMY. 



From the plot or data compute the mean calorimeter temperature for 

 the time interval m^ — ???i by the expression 



where n is the number of half-minute temperature readings t^, b, c 

 . . . , to- Compute also 



" ^" and 6* = ^ + ^2. ov = ^y + ti. 



to — ti a a 



Then the corrected rise of temperature in the calorimeter will be 



t^ — ti + a (T— 6) (^2 — Wi), 



or if the area method is adopted, 



tn — ti -\- a A. 



Special Case. — "Where B C h sensibly straight, and C J/(Fig. 1) 

 is of short duration relatively to B C, then ij is to be found by pro- 

 longing UD (Fig. 2) to its intersection in /with the vertical through 

 C, the point where the operation ceased, or where £ C begins to de- 

 flect from a straight line. From C onward the exchange has been 

 at the rate oi D E ; hence the ordinate of 1 may be taken as the tem- 

 perature which would have been indicated had all the remaining heat 

 been distributed throughout the calorimeter instantly when the opera- 

 tion ceased. This may be called to. The gain by exchange during 

 the passage from J5 to C is obviously about ^ {r^ -f r^ (jn^ — nti), 

 where jrio is the time corresponding to t^. The corrected rise of tem- 

 perature is then 



Whether this special method is close enough can be determined for 

 any series of measuremfnts by solving a typical example both by it 

 and by the general method. 



Modified Method. 



Procedure. — By computation from approximate or estimated values 

 of the quantities involved, or from a preliminary trial, determine 

 nearly what the rise of temperature in the calorimeter is to be and 

 call this A t. Start with the water of the jacket at, or a degree or two 

 above, the temperature of the air of the room. In the calorimeter, 

 start with the water A t° below that of the jacket, or enough more than 



