496 Galvanometer Design — Waste Space near the Needle. 



near one, of needle and turn, this integral will be made up of two 

 parts of opposite sign, the change of sign occurring at the 

 point where = 90°, i. e. where the field is tangent to the 

 needle. Denoting as positive th« total moment from the centre 

 to that point, the value of the integral will have the positive 

 sign when this part numerically preponderates, the negative 

 sign when the moment due to the field beyond that point is 

 the greater. The balance will depend on the diameter and 

 distance of the turn relative to the needle-length. For a turn 

 in immediate proximity to the needle, it is obvious that the 

 moment will be nil when a is somewhat less than half-way 

 from o to n, i. e., when the turn-diameter is somewhat less 

 than Z, half the needle-length. Rough experimental trial 

 confirms this deduction. The further removed the turn is 

 from the needle, the less becomes the negative part of the 

 integral relative to the positive part. Hence the bounding 

 surface for null effect would have a diminishing vertical 

 diameter, and the volume would presumably be not far from 

 that of a sphere of diameter 21, as above stated. 



In deciding whether it would effect any sensible gain to 

 wind this space and connect it in reverse order, it may be 

 noted that a shell of a thickness of nearly half the radius of 

 the sphere extending from the null surface inward would 

 have almost no effect one way or the other. Moreover, some 

 space immediately about the needle must unavoidably be left 

 vacant. The remaining space would thus be so small that 

 the gain would be almost insignificant. The answer is thus 

 clearly in the negative. 



The null bounding surface deduced by Professor Ayrton 

 and others was the locus of the turns whose diameter and 

 distance from the needle were such that the field of each w T as 

 tangent to the needle at the poles, as it would be for the turn 

 a x a 2 with the needle at the position n! s'. The deflecting 

 moment at this position is not nil but decidedly positive. 



As far as it concerns galvanometer design the outcome of 

 the discussion may be put into two sentences : — 



1. It is practically useless to wind turns within a distance 

 of about one-quarter of the needle- length of the coil centre : 



2. To increase sensitiveness, the needle must be made as 

 short as is consistent with torsion of suspension. 



The second inference is, of course, the direct one from 

 Maxwell's formula for the strength of field at the centre in a 

 graded coil, re-enforced by the fact that the use of a finite 

 needle annuls the effect of the otherwise most efficient part of 

 the coil. It means needles much shorter than the customary 



