Ox THE ABSOLUTE UXIT OF ELECTKICAL KESISTAXCE 157 



calculation of M is in parallel circular coils of equal size and of as 

 small sectional area as possible. For measuring E a tangent galvano- 

 meter is needed, and we shall then have 



E= ^ tanfl. 



6r 



where H is the horizontal intensity of the earth's magnetism at the 

 place of the tangent galvanometer, and G the constant of the galvano- 

 meter. 



For measuring Q we must use the ballistic method, and we have 



. 



which for very small values of ), becomes 



^ G' - s ' ' 



H' ~W Tain*? I + *A - * A 2 ' 



where H' is the horizontal component of the earth's magnetism at the 

 place of the small galvanometer, G' its constant, T the time of vibra- 

 tion of the needle, and X the logarithmic decrement. 



The ratio of H' to H can be determined by allowing a needle to 

 vibrate in the two positions. But this introduces error, and by the 

 following method we can eliminate both this and the distance of the 

 mirror from the scale by which we find 0' and the error of tangent 

 galvanometer due to length of needle. The method merely consists 

 in placing a circle around the small galvanometer and then taking 

 simultaneous readings with the current passing through it and the 

 tangent galvanometer, before and after each experiment. Let and a' 

 be the deflections of the tangent galvanometer and the other galvano- 

 meter respectively, and let G" be the constant of the circle at the point 

 where the needle hangs, then 



TT JJ I 



-^ tan a = -^j- tan a', 



and we have finally 



TT G tan a' tan 6 \ 



R=M- 



T G 71 ' ta.na sin*0' l+JA U' 



which does not contain H or H', and the distance of the mirror from 

 the scale does not enter except as a correction in the ratio pf sin # 

 and tan a'; and, as a and can be made nearly equal, the correction 



