210, 211] ELECTROMAGNETISM. 413 



the surface integral, being by Gauss's theorem, 39, equal to o> 

 the solid angle subtended by the current circuit at the point P. 

 The positive side of the shell and the one toward which the normal 

 is to be drawn is the side toward which a right-handed screw 

 advancing in the direction of the normal to the diaphragm, would 

 move when rotating with the current. The line of force is 

 positively linked with the current. Since the potential every- 

 where, except in the substance of the conductor, satisfies Laplace's 

 equation, the force is everywhere solenoidal, and the tubes of 

 force are endless, and are all linked once with the current. 



211. Electromagnetic Units. The determination of the 

 factor A, which is a natural constant, is a matter of experiment. 

 It is extremely small, that is, an enormous number of electro- 

 static units of electricity must pass in unit time in order that the 

 current may produce magnetic forces of appreciable amount. If, 

 however, we choose a new unit for /, defined by the assumption 

 A = 1, so that 



we get a new system of measuring currents known as the electro- 

 magnetic system. The unit magnetic potential is defined as the 

 potential at unit distance from the unit magnetic pole in vacuo, 

 accordingly the electromagnetic unit of current is referred at once 

 to a magnetic pole, instead of to an electrified point. From this 

 definition of the new unit of current we may at once obtain a 

 whole system of electrical units. We define the new unit of 

 quantity of electricity as the quantity passing in unit of time 

 when a steady current of one electromagnetic unit flows. From 

 this definition of unit charge we obtain, as before, new units of 

 field, of electric potential, of resistance, capacity, and the rest. 

 Conversely if, measuring the current in electrostatic measure, we 

 put A = 1 we shall get a new unit of magnetic potential, from 

 which we may obtain a complete set of units for magnetic quan- 

 tities, all referred to the unit of electric charge, instead of to the 

 unit magnetic pole. We may thus measure electric quantities in 

 the electromagnetic system, or magnetic quantities in the electro- 

 static system, or as before, each kind of quantity in its own 

 appropriate system, thus obtaining the Gaussian system. 



