THE MEASUREMENT OF RESISTANCE 221 



therefore 



a = + 0.00392 



b = - 0.000000588. 



On account of its use in resistance thermometers, the variation of 

 the resistance of platinum with temperature is important. 



Mean Temperature Coefficient. Denoting particular tem- 

 peratures by subscripts, it is usual to write formula 21 thus 



R tl = #o(l + ft/i) (21o) 



where 



p tl = a + bti + c*! 2 . 



It will be seen that @ tl is the mean, or average fractional rate of 

 increase of resistance per degree between and t\, referred to 

 the resistance at 0, for 



R tl Ro 



0ti is called the mean temperature coefficient of resistance increase. 

 To compute the value of a resistance at any temperature, t, 

 from that at some given temperature, ti, 



Rt, = Ro(l +hfi); 



R t = fl (l + 0,0; 

 therefore 



Temperature Coefficient of Resistance. As in general the 

 graph connecting R t and t is curved, the true rate of increase of 

 resistance will have a particular value at each temperature, 

 consequently a very small temperature interval must be used in 

 computing it. 



The temperature coefficient of resistance increase at any tem- 

 perature is the fractional rate of increase of resistance for a 

 very small temperature increment referred to the resistance at 

 that temperature. It will be denoted by a; then 



. . . 

 ' l R tl \dtJt, 1 + of i + bti* + c*i 3 + . . . ( ' 



Rti + A< Rti 

 a tl = ~~~ -- approximately. 



