296 On Regulating and Measuring Electric Currents. [Jan. 30 y 



adjusted that the lines drawn by the two pencils coincide when no 

 current is passing through the sensitive strip. The passage of a cur- 

 rent through the strip immediately causes 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 tempera- 

 ture 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 temperature (T) ; 



H the heat generated per unit of time at the commencement 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 in- 

 terval, we have by the law of Dulong and Petit — 



H'=(T'-T)S, 



in which S is the radiating surface. Then 



R'C' 2 =(T'-T)S 



C' 3 =(T'-T)|,. 



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

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

 ductor varies as its absolute temperature (which upon the Centigrade 

 scale is 274° below the zero Centigrade) according to a law first ex- 

 pressed by Helmholtz, 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 equi- 

 librium 



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

 temperature or ordinates. 



Tor any other condition of temperature T" we have 



S , m » ™ 



