Systems of Physical Units. 101 



be supposed to be in the line drawn from the centre point of 

 the element acting on it, and at right angles to it ; the two 

 current- elements which act upon each other are to be regarded 

 as parallel to each other and at right angles to the line joining 

 their centres. 



The complete formulas are 



ck=^ sine, (39 a) 



ck=- Y? (cose— § cos 6 cos X : . . . (40a) 



where e, 6, and Q x are known angles. Equation (41) relates to 

 the morion of a closed circuit in the neighbourhood of cur- 

 rents or of magnets ; i is the strength of the induced current, 

 k the electrodynamic action of the inducing currents or mag- 

 nets on the induced conductor, estimated according to the 

 direction of the motion; h is the velocity of motion, and E the 

 induced electromotive force. 



Since the units of length, time, velocity, and force are 

 already fixed by a system of fundamental equations, we have 

 sis equations connecting the four new conceptions, jjl, c, i, 

 and E. In forming the corresponding fundamental equations 

 we must therefore retain two constants. The electrostatic (or 

 mechanical) system is obtained by retaining the constants of 

 equations (36) and (40). In the electromagnetic system we 

 retain the constants of equations (37) and (40). A very conve- 

 nient system is obtained by retaining the constants of equations 

 (38) and (40) ; this system may be called the Gauss-Weber 

 system: it is completely worked out in Kohlrausch's Leitfaden. 

 Lastly, we have the electrodynamic system with the constants 

 of equations (37) and (39). The values of the constants are as 

 follows in the Gauss-Weber system: — c=\ (equations 40 and 



40 a), and c== - (equation 38), where e is the total quantity 



of electricity (positive and negative) passing per second with 

 the unit current of this system. Weber and Kohlrausch have 

 found 



lxl010 millimetre^ - 



second v ' 



* Wiedemann, Lehre vom Gahanismu-s und Elektromagnetismus, vol. ii. 

 div. 2. p. 457. Weber himself takes into account only one form of elec- 



31 x lfl x0 

 tncity, and puts therefore e =- — * (more exactly 15-537xl0 10 ) 



— (Abh. der koniql. sacks. Ges. der Wissensch. rol. iii. Also in 



second 

 Zollner, Principien einer eleTdrodynarmsehen Theorie, pp. 93-131). 



