k b — k a . b 



is equal to a constant — - — -. Thus, since the attraction of the 



u 6 



the Absurdity of Diamagnetic Polarity. 273 



and the behaviour of B would be entirely determined by the 

 supposed compound layer on its surface. 

 Now if 6 be the angle at any point P -pis. 10. 



of the common surface of A and B 

 between the normal at P, supposed 

 drawn from A to B, and the force, 

 which may be considered continuous in 

 crossing the bounding surface, the super- 

 ficial density of the layer at P which 

 belongs to B will be — 1 6 cos 0, and of 

 that which belongs to A, I a cos 0. 

 Hence the density at P of the com- 

 pound layer is (I o — 1 6 ) cos 6. The ratio of this to the density 



at P of the layer which properly belongs to B, is b T a , which 



h _ 7„ JL 



> 



permanent magnet on B,] due to the surface-layer which 

 properly belongs to B, may be written k b Q, where G would 

 have the same value for any soft body of the same shape and 

 size as B, when placed in the same position, the attraction of 

 the permanent magnet on B, when immersed in A, will 

 be (k b —k a ) G, or equal to the force due to the layer which 

 properly belongs to B, diminished by what this force would 

 be for the gas or liquid, A, displaced by B. 



According to the remarkable caricature of reasoning just 

 noticed, it follows that we do not need to know the absolute 

 value of the coefficient k belonging to any soft substance, but 

 merely the algebraic excess of the coefficient over that of 

 some standard substance. This standard " substance " is 

 often chosen to be a " vacuum/' and its coefficient is put 

 zero. Then, since many bodies are apparently repelled by a 

 magnet pole in a comparatively slight " vacuum " of 2 to 3 

 millimetres of mercury, it is concluded that the coefficients of 

 these bodies, or, rather, the excesses of their coefficients over 

 that of a vacuum, are negative. 



Granting, for the present, the first part of this so-called 

 reasoning, we must point out that a vacuum can only be 

 obtained by removing the air completely from the interior of 

 a closed vessel, and not by merely reducing the pressure to 2 

 or 3 millimetres of mercury. If we were allowed to consider 

 such a comparatively slight reduction of density as consti- 

 tuting a vacuum, we could prove the existence of diagravita- 

 tion ; for if we could find a gas 100 times as light as hydrogen, 

 a balloon could be made which would float in this so-called 

 vacuum. 



