Resistance according to an absolute Standard. 231 



two circles, let it be supposed that the circle A is so twisted as 

 to be at right angles to AB, in which case the area of the plane 

 of the projection is irrr. Let this rotation take place in a short 

 time s, in such a manner that the area of the plane of the projec- 

 tion of the circle increases uniformly in this time from to irrr. 

 Prom the magneto-electrical lavjs, an electromotive force results 

 which the terrestrial magnetism T exerts upon the rotated cir- 

 cular conductor A during the time s, and which, according to 

 the unit of measure explained in the preceding paragraph, is ex- 

 pressed by Ee, in which the number e is determined by the 

 equation e _!^ T 



s 

 By this electromotive force a current is produced in the time 5 

 passing through the whole closed conductor, whose intensity, 

 according to the unit explained in the preceding paragraph, is 

 expressed by iL. This current passes also through the circle B, 

 and acts from here on a distant magnetic needle in C, whose axis 

 of rotation lies in the plane of the circle at right angles to the 

 direction of the earth's magnetism. Let C lie in the produced AB 

 (that is, the line joining the centres of the circles A and B). It 

 follows now from electro -magnetic laws, that the momentum of 

 rotation exerted on the needle at C by a current passing through 

 the circle B, is equal to the rotation exerted by a bar-magnet 

 placed in the centre of the circle in such a manner that its mag- 

 netic axis is at right angles to the plane of the circle, if its mag- 

 netism M, expressed according to absolute measm-e, is 



If, further, the magnetism of the needle in C expressed in the 

 same measure = m, and Bc = B, and <f) the angle which the mag- 

 netic axis of the needle in C makes with the direction of the 

 earth's magnetism AB, the momentum of rotation exerted by 

 the bar magnetism M on the bar magnetism m is expressed, 

 according to known magnetic laws, by 



Mm , irrr . , 



-pg . cos 9 = ^3-. t?ncos(p. 



From which it follows that if K is the inertia of the needle, the 

 acceleration of the rotation is 



ddcb irrr im . 



and therefore that if the needle were previously at rest, and 

 <£ = 0, the velocity of rotation at the end of the short time s is 

 d<j) _ 7T/T im 



