102 M. A. P. Sundell on Absolute 



By the aid of IV. we easily find the following values of the 

 constants in the other systems : — 



Electrostatic system, 



I 2 



c ~'i (equation 36), c— _£ (equations 40 and 40a); 

 e o 2 



electromagnetic system, 



c— -e (equation 37), c = ^ (equations 40 and 40a); 

 e z 



electrodynamic system, 



2 



-a (equation 37), c=*/2 (equations 39 and 39a). 



C- 



We obtain a formula of induction suited for practical use 

 by replacing the force k in equation (41) by its value calcu- 

 lated from the formula (39 a) or (40 a). 



Since the constant of equation (41) has the value unity in 

 all four systems, it follows that the work performed by the 

 current in unit time is equal to the product of electromotive 

 force into current-strength. Moreover the equation corre- 

 sponding to Ohm's law which determines resistance is of the 

 same form in all three systems. 



The relations of the chief units of the electromagnetic, 

 electrodynamic, and electrostatic systems, together with their 

 dimensions, are given in Prof. Wiedemann's Lehre vom Gal- 

 vanismus und Elektromognetismits, vol. ii. div. 2. pp. 467-471; 

 they are also given for the electrostatic and electromagnetic 

 systems in Maxwell's ; Treatise on Electricity and Magnetism/ 

 vol. ii. pp. 239-245. 



The occurrence of the constant e in so many of the for- 

 mulas connected with electricity would seem to show that these 

 formulae could be derived from some natural law. Wilhelm 

 Weber finds this in his fundamental electrical laic, 



Here - is the quantity of positive or negative electricity 



(measured electrostatically like e x and e 2 ) which traverses the 

 circuit in unit time when the current-strength is equal to the 



electrodynamic unit current, i. e. is equal to - electromag- 



r< ^i i 1 60 « 2 1 



netic unit. Consequentlv we have -= = or — = — , 



1 * a 2^2 lb 2el' 



