154 Prof. J. J. Thomson on the Mechanical Force* acting 



the two ions, we must look to the size of the ions and to the 

 charges carried by them, for upon these two factors the 

 velocity itself depends. 



As to the charges on the two kinds of ions, the simplest 

 assumption we can make is that they are equal, for if we 

 assume an unequal distribution we are led into a difficulty in 

 imagining a process whereby the two charges are distributed 

 upon an unequal number of carriers, and so that the charge 

 upon each of those of one sign is just a little different from 

 that upon those of the other sign. 



We are thus led to suppose, as in liquids, that the observed 

 velocity difference is due to an inequality in the size of the 

 two ions. Why the two ions, even if they are formed of 

 groups of molecules, should in a simple gas be of a different 

 size is a question to which definite answers cannot be given 

 in the present state of our knowledge, or rather ignorance, of 

 the relation between matter and electricity, but is one which 

 must be borne in mind in considerations of this relation. 



In conclusion, I desire to express my best thanks to 

 Prof. J. J. Thomson for many valuable suggestions. 



Cavendish Laboratory 

 April 12, 1898. " 





T 



VII. On the Mechanical Forces acting on a Piece of Iron 

 carrying an Electric Current. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, 

 HE subject of the forces acting on a piece of iron carrying 

 _L a current, which is raised by Lord Rayleigh in the 

 June number of the Philosophical Magazine, is one of so 

 much interest and importance that I hope the following 

 remarks may not be considered superfluous. 



To find the force on the piece of iron, let us begin by con- 

 sidering the force exerted hy the system of the iron and 

 currents on an external magnetic system ; this force is equal 

 to the force due to the currents calculated by the same rule 

 as if they were flowing through a non-magnetic substance, 

 say copper, plus the magnetic forces due to the magneti- 

 zation induced or permanent in the iron. It follows from 

 this by the equality of action and reaction that the force 

 acting on the iron will be a force due to the action of the 

 magnetic field on the currents through the iron, this force 

 to be calculated as if the currents were flowing through 

 copper 'plus the force due to the magnetic field on the mag- 

 netization in the iron. From this it follows that if A, B, C 



