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XIX. On the Price of the Factor of Safety in the Materials 

 for Liqhtninq-rods. By Professor Silvanus P. Thompson, 

 'D.Sc* 



IT is possible to determine in an absolute manner what 

 metal is best for securing safety by a system of lightning- 

 conductors, for a given prime cost. In the calculations that 

 follow it is assumed that the duration of the lightning-discharge 

 is so brief that there is no time for appreciable radiation or 

 convection of heat from the surface of the conductor, or for 

 conduction into other bodies ; and that the conductor is devoid 

 of self-induction. 



Safety is dependent, other things being equal, upon the 

 difficulty of fusion of the conductor. The difficulty of fusion 

 of the conductor varies directly as the fusing-point of the ma- 

 terial (or, more strictly, as the difference between this tempera- 

 ture and that of the surrounding air, assumed here to be 15° C), 

 and inversely as the temperature-rise occasioned in it by the 

 discharge of electricity, the amount of which is supposed to be 

 given. The temperature-rise varies inversely as the specific 

 thermal capacity of the material, and directly as the heat 

 developed in it. The heat caused by a given discharge of 

 electricity varies directly as the total electric resistance of the 

 conductor. The total electric resistance of the conductor 

 varies directly as the specific electric resistance per unit cube 

 of volume of the material of the conductor, also directly as its 

 length, and inversely as its area of cross section (supposed 

 uniform throughout). The area of section varies directlv as 

 the volume and inversely as the length (supposed given). 

 The volume varies inversely as the density of the material and 

 directly as its mass. The mass of the conductor varies directly 

 as the total cost, and inversely as the cost per unit of mass, 



Hence, writing/ for the temperature of fusion above that 

 of the surrounding air (assumed at 15° C), s for the specific 

 thermal capacity, p for the specific electric resistance, I for 

 the given length, d for the density, k for the cost, in pence, 

 per pound of the material of the conductor, it at once follows 

 that 



Safety varies as total cost x / ' s — - • 



pxdxl'-xk 



Hence, as the total cost and the length are supposed to be 



* Communicated by the Physical Society : read January 28, 1888. 



