n 



136 DK. K. H CKimTHS AND MR. EZER GRIFFITHS ON Till! 



of the heating coil for that value of the current, then 



r _ nE 

 R'' 



Potential difference at the ends of 3-ohm coil is 



x a 



If Si, * 2 , ..., * be the potentiometer readings corresponding to 1, 2, 3, 4, ..., 

 number of Cd cells balanced at the ends of the heating coil, then 



p 



S H = K ^ x a. ; where K is a constant. 

 R 



Hence, 



By plotting n 3 horizontally since the heating effect is proportional to the square 

 of the electromotive force and the quantity n/s B vertically, but reduced in such pro- 

 portion that for n = it is unity, we get the relation between SB,, the increment of 

 resistance, and n 3 . The resulting points fall (within the limits of experimental error) 

 on the straight line, <SR = ten*. These observations were repeated when the tank 

 temperatures were C. and 97 C., and for both the copper and iron blocks. 



In the locality of C. the temperature coefficient of manganin is positive, as shown 



by the relation 



At C., SR = 0-0 5 52n 2 . 



About 100 C. manganin has a negative coefficient and it was found on reducing 

 the results that SR was negative. 



At 97 C., SR = -0'0 5 86n 2 . 



These equations represent the extremes of SR in our range, for at intermediate 

 temperatures, owing to the locus of R being concave downwards, the factor k was 

 smaller and vanished altogether between 50 C. and 60 C. 



It may be pointed out that for the highest rate usually employed, viz., that due to 

 8 cells, the correction on account of SR amounted to only 3 parts in 10,000, corre- 

 sponding to a temperature change in the wire of 10 C. As the values of SR at both 

 C. and 97 C. indicated that the rise in temperature of the wire depended on n 2 only 

 and was independent of all other conditions, we could, from the curve giving the 

 relation between temperature and resistance, calculate the relation between R and 

 rt 1 for any temperature within our range. 



The value of R was the one directly determined by the dial box when the heating 

 effect was insignificant, the current through the coil being in that case 0'0015 

 ampere. 



