520 Prof. J. J. Thomson on the Relation between the 



We see that some of these lines of flow in the neighbour- 

 hood of the column are closed curves ; now the liquid inside 

 any one of these curves will always remain in the neighbour- 

 hood of the column, and if the column is moved will move 

 with it : thus the effective mass of the column will be that of 

 the column plus that of the liquid enclosed by the largest of 

 the closed lines of flow. The linear dimensions of the curve 

 are proportional to m/u, where u is the velocity of the fluid 

 at an infinite distance from the column, and in the strength 

 of the vortex ; (the equation to the bounding line of flow is 



easily seen to be r = — e ™), thus the area enclosed by the line 



of flow, and consequently the mass of fluid inside a cylinder of 

 which it is the cross section, is proportional to m 2 /u 2 ; thus, as 

 the effective mass is increased by this mass of fluid, the expres- 

 sion for the effective mass of the vurtex column will contain 

 a term proportional to the square of the vorticity. Hence, 

 if we regard a Faraday tube as a bundle of vortex filaments, 

 we can by this analogy see that its effective inertia might 

 involve a term proportional to the square of the polarization. 



Relation of the preceding Analogies to the Electrochemical 

 Properties of the Atoms. 



To return, however, to the relation between the electric 

 charge and the electrochemical properties of the element whose 

 atom carries the charge. The illustration given on page 513 

 suggests that when an atom is charged with electricity it 

 acquires a certain amount of potential energy depending upon 

 the sign of the charge and also upon the kind of atom carry- 

 ing the charge. Let us suppose that when an atom of an 

 element A carries unit charge of positive electricity, its 

 potential energy, in consequence of the connexion between 

 the internal motion of the atom and the motion of the fluid in 

 the Faraday tube, is greater by cr A than when it has no charge, 

 while when the atom has the unit negative charge its 

 potential energy is less by <r A than that of the uncharged 

 atom. The quantity cr depends upon the nature of the atom ; 

 in ' Recent Researches on Electricity and Magnetism/ p. 64, 

 it is called the Volta potential of the substance, since the 

 difference of potential between two metals A and B when 

 placed in contact can be proved to be equal to cr A — cr B . 



If the substance A has a charge Q of positive electricity, 

 then in the expression for its potential energy there will be 

 the term cr A Q. If we consider this term alone, then if <7 A is 

 positive an increase in the positive charge will involve an 



