190 Mr. T. Gray on the Size of Conductors 
where « is the coefficient of change of specific resistance with 
temperature. That is to say, for any conductor the rise of 
temperature depends directly on the square of the current and 
on the specific resistance of the material, and, if we neglect 
the variation of specific resistance with temperature, inversely 
on the rate of cooling and the section of the conductor. 
If we assume 50° C. as the maximum rise of temperature, 
we have for the section of the conductor, 
c 2 m+oo») . 
50r 
For bare copper rod we may take r as being very nearly 
- rfr multiplied by the number of units of radiating surface 
in the unit length, or 
_ TTdJ 
r ~ 5000' 
where d is the diameter of the rod, and J Joule's mechanical 
equivalent of heat, which is, approximately, 4*2 x 10 7 in C.G.S. 
units. Hence, by substitution, 
3*14 x 4-2 x 10 7 , c . 1A4 , , K , 
r= 5000 *=«** W* • • ( 5 ) 
Now, as S is 1700 and a nearly "0039, we have 
2 2030 _l-54 cl_ 
13-2 xWd~ 10* X d' 
It must be remembered that c is here taken in C.G.S. 
ird 2 
units ; and hence, putting for A —r— , and taking c in amperes 
and reducing, we get 
»-j£* W 
Now the value of C found from equation (2) is for bare copper 
60 amperes per square centimetre. Let us assume that the 
maximum value of c will be 100 amperes per square centi- 
metre, and we have to find for what value of d or c we have 
^4-m P) 
From (6 J and (7) we get at once 
A 4 x 10 3 
7rx442 
