A/A' WILLIAM SIEMENS, F.R.S. 



205 



the strip immediately onuses the pencil attached to the lever to 

 move away from the datum line, and the distance between the two 

 lines represents the temperature of the strip. This temperature 

 depends, in the first place, upon the amount of current passing 

 through the strip, and, in the second place, upon the loss of heat 

 by radiation from the strip ; which two quantities balance one 

 another during any interval that the current remains constant. 



If C is the current before increase of temperature has taken 

 place ; R the resistance of the conductor at the external tempera- 

 ture (T) ; H the heat generated per unit of time at the com- 

 mencement of the flow ; R' the resistance, and H' the heat, when 

 the temperature T' and the current C' have been attained ; 



Then by the law of Joule, H' = R'C' 2 . But inasmuch as the 

 radiation during the interval of constant current and temperature 

 is equal to the supply of heat during the same interval, we have 

 by the law of Dulong and Petit, H' = (T' - T) S, in which S is the 

 radiating surface. Then 



R'C' a =(T'-T)S 



But T' - T represents the expansion of the strip, or movement of 

 the pencil m, and considering that the electrical resistance of the 

 conductor varies as its absolute temperature (which upon the 

 Centigrade scale is 274 below the zero Centigrade) according to a 

 law first expressed by Clausius, and that we are only here 

 dealing with a few degrees difference of temperature, no sensible 

 error will be committed in putting the value of R for R', and we 

 have the condition of equilibrium 



rvS o 



C = m_. 



C' = 



5> 0) 



or, in words, the current varies as the square root of the difference 

 of temperature or ordinates. 



For any other condition of temperature T" we have 



C"'=|(T"-T) 



Jtk 



