134 PROCEEDINGS OF THE AMERICAN ACADEMY 



The temperature reaches a maximum nearly at the time 



0" — 0i 



and if 6 m is the maximum temperature, we have the value of 6" as 

 follows : 



d"=T'' = O m + C{t m + c-Q; 



T" = d»+c(t m + c£-£); 



and this is the final temperature provided there was no loss of heat. 



When the final temperature of the water is nearly equal to that 

 of the air, C will he small, hut the time t m of reaching the maximum 

 will be great. If a is a constant, we can put O = a (0" — T a ), and 

 @(tm ~\~ c — h) w ^ ue a minimum, when 



0=°^, or T.= <r-Z=*. 



c ac 



That is, the temperature of the air must be lower than the tempera- 

 ture of the water, so that T a = 0" as nearly as possible ; but the for- 

 mula shows that this method makes the corrections greater than if we 

 make T a =■ 6', the reason being that the maximum temperature is 

 not reached until after an infinite time. It will in practice, however, 

 be found best to make the temperature of the water at the beginning 

 about that of the air. It is by far the best and easiest method to 

 make all the corrections graphically, and I have constructed the fol- 

 lowing graphical method from the formulae. 



First make a series of measurements of the temperature of the 

 water of the calorimeter, before and after the basket is dipped, together 

 with the times. Then plot them on a piece of paper as in Fig. 5, 

 making the scale sufficiently large to insure accuracy. Five or ten 

 centimeters to a degree are sufficient. 



nab c d is the plot of the temperature of the water of the calo- 

 rimeter, the time being indicated by the horizontal line. Continue 

 the line d c until it meets the line la. Draw a horizontal line 

 through the point /. At any point, b, of the curve, draw a tangent 

 and also a vertical line b g ; the distance eg will he nearly the value of 

 the constant c in the formula;. Lay off If equal tor, and draw the 

 line fhk through the point A, which indicates the temperature of the 

 atmosphere or of the vessel surrounding the calorimeter. Draw a 

 vertical line, j k, through the point £. From the point of maximum, 



