390 Prof. R. Clausius on the different Systems of 



[4L -2 ], we get the following expression for the force exerted 

 by two static units of magnetism upon one another at unit 

 distance : — 



The velocity denoted by K, which, so far as the measurements 

 hitherto effected permit a judgment to be formed, agrees with 

 the velocity of light in vacuo, is a quantity so important for 

 electricity that it seems convenient to introduce a special 

 name for it ; and I propose to call it, analogously to a name 

 introduced by Andrews into the theory of heat, the critical 

 velocity. 



Returning now to the consideration of the magnetic forces, 

 according to the above the force exerted between two static 

 units of magnetism at the unit of distance is equal to the frac- 

 tion L J of a unit of force. The force between two dy- 



K 2 J 



namic units of magnetism at unit distance is, on the contrary, 

 according to § 1, equal to a unit of force. Consequently the 



TL 2 T — 2 1 

 latter force is to the former as 1 to - — p — -, or as K 2 to 



[L 2 T -2 ]. Since, then, the forces must at equal distances be 

 as the products of the quantities of magnetism acting upon 

 each other, and consequently in the present case as the square 

 of the dynamic unit of' magnetism to the square of the static 

 unit of magnetism, these two squares must also be as K 2 to 

 [L 2 T -2 ], and the two units of magnetism themselves must 

 therefore be as K to [LT -1 ]. 



In representing this result mathematically, we must not 

 denote the units of magnetism simply by [»?,] and [wi rf ]; for 

 these symbols represent the quantities of magnetism under 

 consideration (taken as units) on the hypothesis that the one 

 is measured with the aid of the electrostatic and the other with 

 the aid of the electrodynamic force. For a comparison of the 

 magnitudes of the two units, however, it is necessary that both 

 be measured by the same measure — and consequently that 

 either the dynamic unit be reduced to static measure or the 

 static unit to dynamic measure. For these reduced values we 

 will introduce a special symbol. To indicate that a quantity 

 whose former symbol supposes dynamic measurement is mea- 

 sured according to static measure we will prefix to that symbol 

 v. s., the initials of valor staticus; and to indicate that a quan- 

 tity whose former symbol supposes static measurement is 

 measured according to dynamic measure, we will prefix to that 



