544 JAMES CLERK MAXWELL. 



tional to the product of the strength of the currents, that is 

 to the square of one of them. The pressure excited by the 

 vortices is, cceteris paribus, proportional to their density and 

 the square of their velocity. Suppose we keep the attrac- 

 tion between the wires the same, but change the density of 

 the medium. Then the velocity of the vortices at any 

 point must vary inversely as the square root of the density 

 of the medium. But the velocity of the vortices is propor- 

 tional to the strength of the currents. Hence the strength 

 of each current must vary inversely as the square root of 

 the density of the medium. If then the electromagnetic 

 unit of current be defined as that current which, flowing in a 

 certain wire, attracts an equal current in another given wire 

 with unit force, the unit of current, and therefore the unit 

 of electricity, which is the amount flowing per second across 

 any section of a wire conveying a unit current, will vary 

 inversely as the square root of the density of the medium. 



The ratio of the electromagnetic to the electrostatic 

 unit of electricity will therefore be proportional to the ratio 

 of the square root of the elasticity to the square root of the 

 density of the medium. But this is known to be the velo- 

 city with which a transverse vibration is propagated through 

 the medium. Hence the ratio of these units is a concrete 

 velocity, and is proportional to the velocity of propagation of 

 an electromagnetic disturbance, or of the vortex motions 

 above described, through the dielectric. If the units are 

 chosen according to the ordinary system their ratio is not 

 only proportional to but identical with this velocity. 



In a paper published in the Phil. Trans, for 1868, 

 Professor Maxwell gave an account of an experiment for 

 determining the ratio of the electrostatic and electromagnetic 

 units of electricity where air is the dielectric. The principle 

 of the method lay in balancing the attraction between two 

 electrified discs by the repulsion between two coils of wire 

 in which currents were flowing in opposite directions. One 

 of the discs and one coil was placed at one end of the beam 

 of a torsion balance, the other disc and coil being fixed, but 

 a third coil, conveying the same current as the other two, 



