Measures for Electric and Magnetic Quantities. 397 



takes place will, as has been insisted by other authors, be 

 distinguished above the rest by simplicity. Such a one may 

 here, in conclusion, be discussed. 



First, as to the time-unit to be employed in the new system, 

 this can be selected at pleasure ; but, since all the systems 

 hitherto considered agree in having a second as the unit of 

 time, there is no reason for choosing any other time-unit here, 

 and we therefore retain the second. 



By this determination of the time -unit the unit of length is 

 also determined, because as such that length must be taken 

 which a point endowed with the critical velocity would travel 

 in one second. This amounts to approximately 30 meridian- 

 quadrants, and is consequently about 30 times the unit of 

 length of the practical system of measures. We will denote 

 it by X. 



There still remains to be determined the unit of mass. This 

 has no influence upon the unit of velocity ; so that any value 

 whatever can be given to it without altering the unit of velo- 

 city; hence it appears to me most expedient so to choose this 

 value that two of the most important electrical units, viz. 

 those of quantity of electricity and intensity of cm-rent, take 

 the same values in the new system of measures as in the prac- 

 tical system. In the latter we have, according to the prece- 

 ding section, to put 



and in the new system, if its unit of mass be denoted by ^, 

 the following equations must hold : — 



0<J =***** ; and [i^=fiMs-K 



Now, if the latter values of [e^\ and [i d ~\ are to agree with the 

 former, the products /j?\* andp^q 2 must be equal, and hence 

 also 



f^=P9, (35) 



from which follows 



P=p{ (36) 



Hereby the determination of fi is reduced to the determina- 

 tion of X., and consequently to the determination of the critical 

 velocity ; and from what has been said above respecting the 

 approximate value of \, it results that /a is approximately ^- - 

 undecimogram or 1 duodecimogram — that is, a three billionth 

 of a gram. 



Phil. Mag. S. 5. Vol. 13. No. 83. June 1882. 2 H 



