48 ILLINOIS ACADEMY OF SCIENCE. 



The argument, first employed by J. J. Thomson in 1897, is 

 very simple and makes only the following assumptions : 



(i) Newton's Third Law of Motion. 



(ii) The ordinary equation for centrifugal force acting on 

 a particle. 



(iii) The usual expression for the distance traversed by a 

 particle starting from rest, and acted upon by a constant accel- 

 eration; and 



(iv) The result of Rowland's Berlin experiment. 



Let us imagine a small particle of matter of mass m, carrying 

 an electric charge e, to be fired with speed v into a magnetic field 

 of strength H. If the direction of motion of the particle is per- 

 pendicular to the magnetic field, the path of the particle will be a 

 curved line whose radius of curvature we may call r. 



Now the result of Rowland's Berlin experiment may be 

 expressed as follows : 



^ 



/^ 



e V ^ dx = idx 



dt 



\r 



^ H 



f 



-^ 



so far as the magnetic effect of a convection current is concerned. 



And hence, in the case of this minute charged projectile we are 

 practically dealing with an element of an electric circuit idx, at 

 right angles to a magnetic field H. 



As we know from the behavior of the ordinary electric motor, 

 the force on such an element — such an "inductor," if you 

 please, — is Hid x, or H e v, dynes in a direction perpendicular 

 to the vectors H and v. This same force, the force which com- 

 pels the particle of mass m to travel in a curved path, may be 



tn V 

 called its centripetal force, and as such is measured by 



Equating them we have : 



Hev = ^' Eq. (i). 



Next let us suppose one of these charged particles to be fired 

 into an electric field, in a direction at right angles to that of the 

 field. 



