64 Mr. J. Larmor. Theory of Electrodynamics [June 2= 



An actual illustration in which the term involving X is of pre- 

 dominant importance is afforded by a bunch of iron nails hanging 

 end to end from a pole of a magnet ; the adjacent nails hang on io 

 each other lengthways and repel each other sideways, while the 

 action of non-adjacent ones is but slight. 



Tn the electric polarisation theory the specific inductive capacity 

 is K = 14- 4. The results of Quincke, above mentioned, after they 

 had been corrected for an experimental oversight in the direct deter- 

 minations of the values of K by experiments on capacity, in accord- 

 ance with a suggestion made by Hopkinson,* made the electric 

 pressure to be KF 2 /87r, consistently within the limits of experimental 

 error for fifteen different substances. Thus, even in the limiting 

 Maxwell form of the theory, which takes the absolute numerical 

 value of K to be very great, this theory would not fit with the 

 experiments unless X is zero. Even by the purely mathematical 

 device of taking the polarised elements to be right solids closely 

 packed together, it does not seen possible to evade this argument. 



In an actual fluid polarised in the above manner each element 

 might on the average be considered as lying at the centre of a cavity, 

 a sort of sphere of action within which the other molecules in their 

 motions do not approach it further. On averaging the positions of 

 these surrounding molecules during their motions with respect to 

 the one under consideration, we arrive at the conception of a con- 

 tinuous polarised medium with a cavity in it of the form of this 

 sphere of action. If this cavity were an actual sphere, the value of 

 X would be -|TT; and for cavities not very greatly different from the 

 spherical form, the alteration in this value would be insensible. 

 Under no likely circumstances could the value of X come to be zero. 



Thus the limiting Helmholtz polarisation representation of an 

 excited dielectric, though complete as regards electromotive properties, 

 would appear to fail to include the static ponderomotive phenomena 

 of electrification, and requires to be modified into some more con- 

 tinuous mechanism, such as an elastic displacement in an aether 

 loaded with the molecules of the dielectric. 



It may be well to remark that, on account of the extreme smallness 

 of the magnetic coefficient K for all fluids, its square is of no account 

 in comparison, and therefore magnetic pressures are sufficiently repre- 

 sented by the simpler formula | *:F 2 , by means of which Quincke has 

 measured the magnetic constants of various fluid media. 



5. The principal conclusions which have been arrived at are here 

 enumerated. 



(i.) It is shown from experimental results that the stress in an 

 excited fluid dielectric between two condenser plates consists, at any 

 rate to a first approximation, of a tension along the lines of force and 

 * ' Roy. Soc. Proc.,' 1886. 





