270 Wadsworth — Determination of Specific 



2d. There is another class of errors in 0, not due to errors of 

 reading, but which are even more important than these, viz : 

 errors due to 6 never reaching its maximum value required by 

 theory because of the heat received or lost by radiation. 

 Hence m as observed, will not be the true value suitable for 

 use in (2), but some value lower than this; unless indeed, we 

 start with a temperature so low that the final temperature is 

 less than that of the air; in which case 6 n will be too high. 

 To eliminate this error, due to radiation, several methods have 

 been proposed. 



(a) Those methods which take account of the temperature 

 of the external air. 



The simplest of these is that of Rumford (compensation 

 method). This is to determine by preliminary calculations the 

 rise of temperature in the calorimeter while the body is cool- 

 ing and make the initial temperature of the water as much 

 lower than that of the surrounding air as the final temperature 

 is higher. The fallacy of this method lies in the fact that the 

 time required for the last part of the operation is much longer 

 than that required for the first. If we make the initial tem- 

 perature of the water %(@ — t) lower than the external air, we 

 will come nearer to " compensating " for radiation. 



(b) Methods of Jamin and Regnault. 



Both of these methods depend on a series of observations 

 begun four or five minutes before and continued as long after 

 the introduction of the heated body into the calorimeter. 

 Radiation is proportional to three factors, — time, excess of 

 temperature, and surface. For any given calorimeter, then, 

 the loss per unit of time is a constant x(# — /3), where /3 is the 

 temperature of external air or calorimeter jacket. The lower- 

 ing of temperature due to this loss is, therefore, A {6 — /3), dur- 

 ing each unit of time for which 6 — j3 is the mean excess of 

 temperature. 



Let a series of readings be taken at intervals x^ a? a , a? 8 , a? 4 , a? B , 

 etc., from the instant of immersion to the time when the reading 

 of the thermometer becomes steady, giving a series of temper- 

 atures V # 2 , # 3 , # 4 , etc. Then during the intervals a? 2 — a? 15 x 3 — 

 x„ etc., the mean excess of temperature is 



And the loss of temperature then is 



V = (^-/»)(*.-*,)A 



for the interval (a? 2 — x t ) 







for the interval (a? 3 — as 3 ), etc., etc. 



