136 Mr. G. J. Stoncy on the Adjustments oj the Needle 



uiaguetic meridian, and draw through its centre three rectan- 

 gular coordinates, X perpendicular to its plane through the 

 magnetic east, Y and Z in its plane, Z tovvards the zenith and Y 

 towards the magnetic north point of the horizon. Imagine now 

 a moveable axis Y' to be drawn through the centre of the circle 

 and the projection of the north pole of the needle on the plane 

 of the circle, then taking the radius of the circular current as 

 the unit of length, and dividing its circumference into elements 

 d^, commencing from its intersection with Y', we find by Am- 

 l)ere's theory for the components of the cun-ent's action on the 

 north pole of the needle, 



1—y' coscf) 



X 



= 2p.i I dcj) . 



c 



=2/j,i\ d<f> 



{l+a;'^ + y'^—2y' cos (f)y 

 X cos </) 



( I + x^ + ?/''^ — 2?/'cos 6) '^ 



in which i is the intensity of the current, /j, a constant, and 

 X, y, z, y' coordinates of the north pole of the needle. We have 

 also for the force northwards, 



Y=^ Y'- 



y 



and for the moment to turn the needle round its magnetic centre, 



Xcos^.X-Xsin^.Y; 



2\ being the interval between the poles of the needle, and 6 its 



deviation from the magnetic north. Hence this moment, which 



arises from the action of the current on the north pole, 



xy tan 6 + y'^ 

 •^ • . cos 



1- 



= VXcos^. i #■ 



y 



-3- • • (1) 



^•0 {\+x^+y''^—2y' eos(}))^ 



Assuming now that the magnetic centre of the needle is meant 

 to be at the distance a from the origin along the axis of the cur- 

 rent, but that through want of adjustment it deviates from this 

 position so that its coordinates arc « + «, /8, 7, we find that 

 x=fl + a + Xsin^ 

 y = /3 + Xcos 9 



,/2 = y2 + ^-2. 



i+x^ + y'^ = A^^2h, y ' (^) 



A2 for 1 + a' + 2fl« + X^ + u' -j- /3H 7^ 

 B for Xffsin^ + X,(«sin(? + /8c()s^). 



llcuce 

 writing 



and 



