II. ELECTRICAL RHEOMETRY. 53 



rent is in the direct ratio of the square of the intensity, and the increase of resist- 

 ance may be expressed by x ^ qF^. Hence it is evident that instead of tlie 

 formula assumed 



we ought to assume this other 



E 



F: 



U + qF-'' 

 if for E we wish to use the measured length of the wire. 



This being well understood, it is easy to show that the influence of this cause 

 should produce an apparent diminution of the ratio of forces given by experiments. 

 For let the central intensity be expressed by i, and that at the other place (p) by 

 F, we shall have 



/{p) i Ji + qF'' 



But i "^ F therefore if for a first apj)roximation we suppose in this correction 



F 

 F ^ — , which is permitted on account of the smallness of q, we shall have 

 M 



J? -\- ^ 



fic)~ ^ F' r r \r^ E')' 



•^ V y r + q^- 



r 



Overlooking, therefore, the correction for heat, we must have the ratios — greater 



r 



than those of the functions, when R > r, and the contrary \i R <. r, which agrees 

 with experiment. Indeed, the ratio is found to be less when the resistance at 

 the centre is greater than in the other position p, as it appears from the numbers, 

 at 4 tenths of the axis perpendicular to the plane of currents in the globe. On 

 these principles, and after the differences obtained, one might calculate the cor- 

 rections to be presented for the increase of resistance due to the temperature, but 

 before undertaking this, it would be necessary to examine more deeply several 

 points on which this explanation is founded, which for the present we shall omit, 

 it being an entirely new and interesting field for very important disquisitions. 



I shall conclude this paragraph with a very interesting remark. Using Wheat- 

 stone's method for determining the resistance of a battery, we found it several 

 times difierent, according to the length of constant wire which was coiled on the 

 rheostat. The preceding observations give us the explanation of this fact, because 

 no account was taken of the increase of resistance for the heating of the wire. 

 Much more : these experiments may afford the value of the co-efficient of resistance 

 by temperature, as it is very easy to understand. 



14 



