of Lightning -Conductors. 221 



In practice u may be a number not very different from 

 4 or 5. 



Of the three terms in equation (1), the first and most im- 

 portant depends on no hypothesis as to distribution at all ; 

 the second depends on the assumption of uniform distribu- 

 tion of displacement-recoil in the dielectric, and may there- 

 fore really be greater, but not less ; the third term depends 

 on the magnetization of the conductor itself by a uniformly 

 distributed current, and if the current keeps itself to the 

 exterior surface, as a very rapidly alternating one will, this 

 term vanishes. 



Now that we know S and L, we can easily find the cri- 

 terion for the discharge to be oscillatory, and can determine 

 the rate of alternation. 



The discharge will be oscillatory unless the resistance it 

 meets with exceeds a certain critical value, viz.: — 



V u 



1 30 



where v= , -^. = the velocity of light = — ohms ; 



so the critical resistance is 



R =12o|,>V(21og^-l) ohms. . . (2') 



And inasmuch as in practice h is likely to be much greater 

 than b, and b much greater than a, this is a big resistance, 

 which is not likely to be exceeded by the discharger. For 

 if the line of discharge is a metallic conductor, a is moderate, 

 but then so is R ; whereas if the flash occurs through air, and 

 it is not easy to say what the equivalent R is, then a must be 

 considered extremely minute. 



Suppose h to be a mile, b 50 metres, and a a millimetre ; 

 R comes out about 15,000 ohms. 



I think we shall be right in saying that this far exceeds 

 any reasonable value that can be attributed to the resistance 

 met with by a disruptive discharge. It is generally supposed, 

 indeed, that a conductor and earth must have a resistance 

 of only a few ohms, unless they are to form a considerable 

 portion of the whole resistance a flash meets with. 



In so far as the path consists of different conductors in 

 series, it is a mere matter of summation to take them all 

 into account. 



If the actual resistance falls greatly below the critical value 



