Resistance according to an absolute Standard. 229 



from which it follows that if the numbers / and m are determined 

 by measurement, i can be directly obtained without a special 

 measurement. 



From these three relations we get, finally, 



e fft 



W— — = — : 

 % sm 



hence if the four numbers /, s, m, t are determined, the number 

 w is also directly obtained. The number/ is obtained by mea- 

 suring the area of the plane embraced by the conductor ; s is 

 found by measuring the time ; and there only remain the num- 

 bers m and /, which are obtained by measuring the bar mag- 

 netism by the method described by Gauss in the above paper. 

 The unchangeability of the unit of measure for electric resistance 

 can accordingly be guaranteed so long as the four given measures 

 (space, time, and the units of measure for the earth's magnetism 

 and for bar magnetism) are obtained unchanged. But it by no 

 means follows that the maintenance of these four given measures 

 is a necessary condition for the unchangeability of the unit of 

 measure of electric resistances ; the simple maintenance of that 

 unit of measure for velocities is sufficient for the purpose. 



Eor if tT is the earth's magnetism, on which the electromotive 

 force depends, which acts upon the closed conductor whose resist- 

 ance has been measured ; if, further, m'M is the magnetism of a 

 bar (whose magnetic axis is parallel to the direction of the earth's 

 magnetism, while the straight line drawn from its centre to the 

 centre of the plane enclosed by the conductor is normal thereto) 

 which, according to magnetic laws, would, from a great distance, 

 exert the same action as tT the earth's magnetism ; and, finally, 

 if Rr is the length of the straight line drawn from the middle of 

 this bar to the middle of the plane enclosed by the conductor, we 

 have, according to the Intensitas, the simple relation 

 m' 



Substituting this value of t in the equation for w, we have 

 ft m' 1 

 7 ,a m s 

 If, finally, r'R is the side of a square whose area is equal to the 

 area of the plane enclosed by the conductor, from which is ob- 

 tained the relation 



f=r¥, 



and substituting this value of/ in the above equation, we have 



J;\ 



IV- 



