HOLLOW LIGHTNING CONDUCTOR CRUSHED BY THE DISCHARGE. 135 



steam; this was being done when the storm occurred, the 

 grid being suspended in the well, free from the bottom. 

 From what I could gather at the time, some ten years ago, 

 there appears to have been only one severe flash. The 

 central point on the ball and two of the radiating ones 

 were cut off and the pipe was fused at the goose-neck which 

 connected it with the copper band. This was the only 

 damage sustained. The copper band for a distance of 20 

 feet below the goose neck was tempered to a hardness of 

 a steel band, so much so that in repairing the conductor, it 

 was with some difficulty that the gun metal holdfasts could 

 be made to hold, though these were driven into lead plugs 

 and well caulked. When a holdfast was put in and the 

 band struck to get the buckle out, one or two above would 

 be sprung out of the plugs." 



Electrodynamic Action op the Current. 

 For steady currents uniformly distributed over the area 

 of cross section, elementary considerations show, in the case 

 of a solid cylinder of radius a, that the sum of the mechanical 

 forces acting throughout the matter contained in unit 

 length of the cylinder is given by the expression 4 Il/3a 

 where I is the total current flowing along the conductor, 

 the forces at all points being directed radially inwards in 

 planes at right angles to the axis of the cylinder. Under 

 the same circumstances, for a cylindrical shell of inner 

 radius b and outer radius a, the corresponding expression is 

 4 It (a+ 2b)/ 3 (a + b) 2 , which if the shell is very thin reduces 

 to 11/ a. With alternating currents for a cylindrical con- 

 ductor where a is the radius of the outer surface, J. J. 

 Thomson "Recent Researches," § 268, gives as the maxi- 

 mum value of the magnetic force at a point in the cross 

 section fixed by a radius r 



J ar 



where I is the total current flowing along the conductor 



