BARLOW'S PROBLEM. 373 



Applying this formula to iron, and taking ^ = 500, we get 

 A i 





112 i- 



By giving different values to /?, we find that, as long as the thickness of 

 the spherical layer is greater than a fifth of the radius, the magnetic 

 action on the exterior does not differ by o.oi of that which a solid 

 sphere of the same diameter would produce. 



The older experiments of Barlow are in conformity with the 

 results of this calculation. With spheres of 10 inches external 

 diameter, Barlow found no appreciable difference between the 

 actions of two different spheres, one solid and the other hollow, 



the thickness of the latter being equal to - of the radius. 



2 



On the other hand, the action of the hollow sphere was only - 

 that of the solid one, when the thickness was reduced to about the 



of an inch. Taking the value of ft at 500, calculation would 



30 j 



give about - for the ratio of the two actions. 



391. We have seen (386) that the total action in the vicinity of 

 a solid sphere is 



near the pole, and 



ear the equator. Still taking //, = 500, as for soft iron, we get 



nearly. 



