CAPACITY FOR HEAT OF METALS AT DIFFERENT TEMPERATURES. 149 



bridge-wire division could be calculated, and also tan <f>, the slope of the resulting 

 straight line obtained by plotting dd/dt against 6. 



If there were no losses or gains by radiation, the resulting lines would be 

 horizontal 



As the rate of rise due to radiation depends solely on the difference of temperature 

 between the metal and the surroundings, the lines representing the observed values 

 of SO/St for the various rates of electrical supply have all the same inclination to the 

 horizontal, within the limits of experimental error. 



The equation of the line representing an experiment, where n standard cells are 

 Iwlanced at the ends of the heating coil, is seen to be 



* +< r (8 + 8 -8)= n>E> 



where 



$8/&t is the observed rate of rise, 

 8 is the temperature indicated by the thermometer, 

 8 is the temperature of surrounding envelope, 



8, is the lag of the observed temperature for the particular rate behind the 

 temperature of the " radiating " surface. 



(The determination of this lag is discussed below.) 



Hence, by dividing throughout by n 3 , we have 



:3-? + 5<H-4)- 



JR(MS+m.)' 



The right-hand side would represent the rate of rise due to the electrical supply 

 with a potential difference of one standard cell 



i $6 



Hence, if we can determine the particular value of . at the temperature which 



n ot 



we denote by N , when the second term of the equation vanishes, we have the rate 

 of rise due to the electrical supply only. 



1 88 



Plotting . against the observed temperature due to the various values of n, 

 n 6t 



we obtain a series of straight lines whose tangents vary inversely as n*. 



Now, for each experiment thus plotted, there is a certain point on the line where 



1 Xfi V* 



- . -- represents TTt ... r alone, and this would correspond to the temperature 

 n" St JR(MS+mx) 



N at which there are no losses or gains by radiation, i.e., when the mean temperature 

 of the surface subject to radiation is coincident with the temperature of the 

 surroundings. As the co-ordinates of this point are the same for all rates, the lines 

 would intersect at one point if either the observed 6 was the actual temperature 

 of the " radiating " surface, or the lag was constant for all. 



