192 R. S. Brougli — On the proper relative Sectional [No. 4, 



We may take cr = 0*1013 for copper, and = 1218 for iron. These 

 figures were only verified by Dulong and Petit up to 300" C. It is proba- 

 ble, however, that their ratio, with which we are only here concerned, 

 would not greatly alter at higher temperatures. At any rate, comparing 

 the specific heat between 0° and lOO'' C, with that between 0° and 300° C, 

 we infer that any alteration would be in favour of iron, i. e., that the speci- 

 fic heat of iron would increase in a quicker ratio than that of copper. 



Adopting the centimetre as the unit of length, the mass of one centi- 

 metre of the rod = p a, where a is the sectional area of the rod in square 

 centimetres, and p = 8"9 for copper and = 7'8 for iron. 



Further, assuming the quantity and duration of the discharge to be 

 constants, H = Const, x R, where E is the resistance of the unit length 

 of the conductor. 



But II = - , where X is the specific resistance of the metal per cubic 

 a , 



centimetre at its temperature of fusion. 



We may take the melting point of copper as 1400° C, and that of 

 wrought iron as 2000° C* ; and, in order to find A. assume that Dr. William 

 Siemens's formula, which he verified to 1000° C, holds good,t viz. — 



A t = X, (0026577 t i + 00031443 t — 0-29751)^ 



for copper I 



X t = X, (0072545 t i + 00138133 t — 123971) [ 



for iron J 



The temperature t in these formulae is to be measured from the abso- 

 lute zero, so that we have t = 1673 for copper, and t = 2273 for iron. 



The value of X^ per cubic centimetre of copper is 1*652 Microhms, and 

 per cubic centimetre of iron is 9827 Microhms. J 



Thus the value of X t per cubic centimetre of copper becomes 10 Micr- 

 ohms at 1673° C, and per cubic centimetre of iron becomes 107 Microhms 

 at 2273° C. 



Hence H = Const. — for copper 

 a 



107 



and H = Const. — — for iron 

 A 



* Bankine's Tables. 



t Bakerian Lecture., 1871. 



X Jenkin's Cantor Lectures, from Mathiessen's experiments. 



