508 ON PHYSICAL LINES OF FORCE. 



infinitely small particles constituting electricity to revolve, but without being 

 free like them to change their place and form currents. 



The whole energy of rotation of the magnetized field would thus be greatly 

 increased, as we know it to be ; but the angular momentum of the iron 

 particles would be opposite to that of the eethereal cells and immensely greater, 

 so that the total angular momentum of the substance will be in the direction 

 of rotation of the iron, or the reverse of that of the vortices. Since, however, 

 the angular momentum depends on the absolute size of the revolving portions 

 of the substance, it may depend on the state of aggregation or chemical 

 arrangement of the elements, as well as on the ultimate nature of the com- 

 ponents of the substance. Other phenomena in nature seem to lead to the 

 conclusion that all substances are made up of a number of parts, finite in size, 

 the particles composing these parts being themselves capable of internal motion. 



PROP. XVIII. To find the angular momentum of a vortex. 



The angular momentum of any material system about an axis is the sum 

 of -the products of the mass, dm, of each particle multiplied by twice the area 

 it describes about that axis in unit of time ; or if A is the angular momentum 

 about the axis of x, 



As we do not know the distribution of density within the vortex, we shall 

 determine the relation between the angular momentum and the energy of the 

 vortex which was found in Prop. VI. 



Since the time of revolution is the same throughout the vortex, the mean 



angular velocity at will be uniform and =-, where a is the velocity at the 



circumference, and r the radius. Then 



A = 

 and the energy E 



= -?- f ta'Fby Prop. VI.* 



OTT 



whence A = p.raV ..................................... (144) 



PhiL Mag. April 1861 [p. 472 of this vol.]. 



