100 M. A. F. Sunclell on Absolute 



vis viva, and between the so-called time-integral of force* 

 §kdt and the change of momentum, as well as into certain other 

 mechanical equations which are derived from equation (6). 

 The equations are as follows: — 



A= \ c 2 m(h 2 — hi) = i c 2 (m — « ), 



ji dt = c 2 m(h - h ) = r 2 (q - q ), 

 instead of 



A=4(tt— Mq), 



§kdt = q— g , 

 in the usual systems with three fundamental units. That the 

 equations in question, as well as equation (6), are free from 

 any special constant in the usual systems is, no doubt, to be 

 formally mentioned ; but the circumstance is not of practical 

 importance. For physicists often, and engineers almost always, 

 express both forces and masses in units of weight, and the 

 reduction to absolute units necessary for the employment of 

 the ordinary formulas introduces a constant in a disguised form. 



8. The different systems of electrical measurement arranged 

 by Wilhelm Weber, which are connected with the magnetic 

 system of Gauss, are of special interest. 



We have the following equations between the chief concep- 

 tions of this group of phenomena : — 



/* 2 = c&L 2 , (36) 



2 _„/.T2 



ckL 2 , (37) 



t'=4 (38) 



f 2 = c 



m 

 p 



(40) 



E = c^, (41) 



where /x denotes the quantity of free magnetism or strength 

 of a magnetic pole, c the quantity of electricity, and i the cur- 

 rent-strength; / is the length of an element of the current- 

 path, L the distance between two elements of the current, two 

 magnetic poles, or between a current-element and a magnetic 

 pole; h is the attraction or repulsion between current-elements, 

 magnetic poles, or electric masses. The magnetic pole is to 

 * Thomson and Tait, ' Theoretical Physics,' § 29. 



