2 Prof. J. Larmor on Electromagnetic Induction 



secure compactness and completeness, work out ab initio the 

 results that we require. The methods are chosen with a view 

 to deducing the results directly from consideration of the phy- 

 sical quantities involved, with as little appeal to mathematical 

 transformations as possible. 



The solutions given below are all for cases that can be pre- 

 sented in a simple form. A principal object in obtaining 

 them is to examine the circumstances of what may be called 

 electromagnetic screens. 



It has long been known that a plate of soft iron placed in 

 front of a magnet will partially screen the space on the other 

 side of the plate from the influence of the magnet, and that 

 the screening increases with the thickness of the plate. Sir 

 William Thomson has applied the effect in recent times by 

 enclosing his marine galvanometer in a heavy soft-iron case 

 to protect it from the magnetism of the iron of the ship. And 

 lately Stefan has published a paper in Wiedemann's Annalen, 

 in which he investigates experimentally the diminution of the 

 strength of a magnetic field which is produced in the interior 

 of soft-iron cylinders, and compares the results with the indi- 

 cations of Poisson's theory of induced magnetization. 



Now if we have a sheet of conducting matter in the neigh- 

 bourhood of a magnetic system, the effect of a disturbance of 

 that system will be to induce currents in the sheet of such 

 kind as will tend to prevent any change in the conformation 

 of the tubes of force cutting through the sheet. This follows 

 from Lenz's law, which itself has been shown by Helmholtz 

 and Thomson to be a direct consequence of the conservation 

 of energy. But if the arrangement of the tubes in the con- 

 ductor is unaltered, the field on the other side of the conductor 

 into which they pass (supposed isolated from the outside spaces 

 by the conductor) will be unaltered. Hence if the disturb- 

 ance is of an alternating character, with a period small enough 

 to make it go through a cycle of changes before the currents 

 decay sensibly, we shall have the conductor acting as a screen. 

 - Further, we shall also find, on the same principle, that a 

 rapidly rotating conducting-sheet screens the space inside it 

 from all magnetic action which is not symmetrical round the 

 axis of rotation. 



The Earth considered as a rotating body comes under this 

 case ; for the upper strata of the atmosphere are conductors of 

 electricity, whether the conduction follows the law of Ohm or 

 not, and therefore these principles show that this layer must 

 more or less protect the interior from any external magnetic 

 action, not symmetrical round the earth's axis, that might exist- 

 outside it. In the case of a spherical sheet conducting accord- 



