1878.] R. S. BYough—S(ectionnl Areas for LigJitning Bods. 191 



XVI. — On the proper relative Sectional Areas for Copper and Iron Light' 

 ning Rods, — By K. S. Brough. 



So far as mere conductivity is concerned, a comparatively thin wire of 

 either copper or iron would suffice for the loftiest building ; but such a thin 

 conductor would be dangerous, because it would be fused by a heavy dis- 

 charge of lightning. 



Now the problem is to determine what relative sectional areas should 

 be given to copper and iron rods, in order that neither should be more lia- 

 ble to fusion than the other. 



The usual answer given, is, that an iron rod should have 4 times the 

 sectional area of a copper rod.* This result is, I suppose, arrived at in 

 the following way. The conductivity of copper is about 6 times as great 

 as that of iron, but the melting point of iron is about 50 per cent, higher 



than that of copper, therefore — , = 4, is the ratio for the sectional area 



±o 



of iron to copper. 



This simple treatment of the problem, however, is incomplete, because 

 it neglects to take three most important factors into consideration, namely, 

 (1) the influence of the rise of temperature in increasing the electrical 

 resistance of the metal, (2) the difference between the " thermal capacity" 

 or "specific heat" of copper and iron, and (3) the fact that the iron rod 

 being made several times more massive than the copper rod, it will require 

 a proportionately greater quantity of heat to increase its temperature. 

 These omissions introduce an enormous error in the result. 



The effect of the passage of a discharge of lightning through the rod 

 will be to raise its temperature. 



The temperature (T) to which a given length of the rod will be raised 

 will depend on 



(1) The quantity of heat developed by the discharge. 



(2) The mass of the rod. 



(3) The " Specific heat" cr of the metal composing the rod. 

 This may be expressed mathematically as follows : 



T = Const. — - 

 <r m 



where m is the mass of the unit length of the rod, which we shall assume 

 to be uniform in sectional area throughout its length, and H is the quanti- 

 ty of heat developed by the discharge. 



* War Ofl&ce Memorandum by Sir Fred. Chapman, R, E. 

 25 



