322 COMPARISON OF RESISTANCES. 



929. CORRECTION FOR TEMPERATURE. The coils of resistance 

 boxes have the value assigned to them only at a special temperature 

 generally given by the constructor ; a correction is necessary if we 

 work at a different temperature. 



Let / be the standard temperature, / the actual temperature, and a 

 the coefficient of variation ; we have 



The boxes should be arranged so that we may know the tempera- 

 ture of the coils. The best arrangement consists in letting the inside 

 of the box communicate freely with the outer air by the apertures O 

 (Fig. 181) in which are thermometers the bulbs of which are near the 

 coils. A difference of temperature of / corresponds to a relative 

 error of 0*0003 or 0*0004, according as the wire is an alloy of 

 platinum-silver or of argentan. 



In the resistance boxes constructed by Elliott Brothers (Fig. 181), 

 the supplementary unit v v' enables us to get the temperature by a 

 very sensitive electrical method. This unit is made of a copper wire 

 wound on an ebonite cylinder and occupying the entire length of the 

 box. The variation in the resistance of the copper being about 0*0039 

 for i that is to say, eleven times that of the wire of the coil 

 the measurement of this resistance by the box itself, with a relative 

 approximation of 0*0001, will indicate the temperature to within a 

 thirtieth of a degree. 



The variations of temperature most to be feared are those which 

 arise from the passage of the current itself; it may be well to give an 

 idea of this by a numerical example. 



The quantity of heat developed per second in each unit of length 

 of a wire of section o> and specific resistance a-, at a difference of 



U) 



potential E for unit length, is equal in mechanical units to El = E 2 - , 



E 2 o> 

 or in thermal units to - , where J is the mechanical equivalent of 



J " 

 heat. If p is the specific gravity of the metal, c its specific heat, and 



therefore ly = the thermal capacity for unit volume, the rise of 

 temperature d& corresponding to the time dt is given by equation 



= - -dt, or -r = -r --- 

 Jo- dt J yo- 



