156 THE ROYAL SOCIETY OF CANADA 



zero. (This is the case in the double tangent galvanometer, in the 

 electrodynamometer, and in the method to be suggested for the 

 determination of Li and Lo.) In this case our value for TF reduces to 



W=k{aAP,+a,hP,) (5) 



The correction for the finite dimensions of the windings in a coil 

 is such that bi should be multiplied by 



1/2 T" \ 1 4y'^ — r- 



l-\ I — — 15 fe^H e\ + (terms usually negli- 



24\r2 {r^+yy/ 8 {r'-^f~y 



gible) where ei and eo are respectively the depth and breadth of the 

 windings. This value is obtained by integrating our expression over 

 the given cross section of the windings (See §700, Maxwell, loc. cit.). 

 In the case y = r/2, this reduces to 



(1 I + (terms usually negligible) 

 60 ^2 / 



and is thus practically independent of e2, the breadth of the coil 

 winding. The corresponding correction for 65 is negligible in all 

 practical cases. 



§4. The Determination of M, Lj, and L^. 



The methods of determining M are well known and it is sufficient 

 to point out that the presence of L2 with L] in the equations cannot 

 always be neglected. Kohlrausch's method for determining Li is 

 perhaps the best standard method,^ and is suitable provided again 

 that the value of L2 may be neglected or estimated. 



The following method of determining these quantities is suggested. 

 Two (or more) carefully measured circular coils of quite different sizes 

 are set up in such a way that the intersection of their axes is at a 

 distance of half a radius respectively from each coil. A small magnet 

 to be tested is placed so that its axis intersects at the same point. 

 For convenience in calculation and measurement the most suitable 



^In Kohlrausch's method two concentric coils are placed in the meridian and con- 

 nected in parallel. If a current is sent through them and supplementary resistances 

 are adjusted until there is no effect on a very small magnet at the centre, we have 

 Wiîi/oi = «2^2/^2 where n, i and a represent the number of turns, the current and the 

 radius in each case. The magnet to be examined is then substituted for the small 

 testing magnetometer, and the current is reversed. If H cos d is the couple due to the 

 earth's field, it can be shown (if the terms containing Li may be neglected or otherwise 

 determined), that 



L\^{2aiHcot e)/3Trniii{5 cos=5-l) 



\ah a\J 



