4 
304 LORD RAYLEIGH AND MRS. H. SIDGWICK ON THE ABSOLUTE 
§ 18. The modification referred to relates to the position of the induction coils 
relatively to the disc. In the arrangement with which we have been dealing hitherto, 
the mean planes of the coils are nearly coincident with that of the disc, and the 
accuracy of the final number depends upon an exact knowledge of the mean radius of 
the coils. It has, on the other hand, the advantages of being practically independent 
of measurements parallel to the axis, and of giving the maximum coefficient of induc¬ 
tion. In the new arrangement the coils are separated to such a distance that the 
result is nearly independent of a knowledge of the mean radius. How this may come 
about will be readily understood by considering the dependence of the coefficient of 
induction M upon A, when a and b are given. It is clear that M vanishes, both when 
A is very small, and also when it is very large; from which it follows that there must 
be some value of A for which the effect is a maximum, and therefore independent of 
small variations of A. 
In carrying out this idea, it is not necessary to approach the above defined state of 
things very closely ; for of course we have in reality a good approximate knowledge of 
the value of A. In our apparatus the distance of mean planes was about 30 centims., 
so that b = about 15 centims. (A=26, «=16). From the calculations in § 25 it 
appears that with the actual proportions 
+\1 
"M 
= + •12 
db 
+ !■ 
da 
a 
so that the error of A enters in quite a subordinate degree. The positive coefficient of 
c/A shows that with the given coils and the given disc the separation was somewhat 
too great to secure the utmost independence of c/A. 
§ 19. The success of this arrangement depends principally upon the degree of 
accuracy with which b can be determined. The two rings upon which the coils are 
wound were held apart by three equal distance-pieces, against which they were firmly 
pressed by wooden clamps. The distance-pieces were hollow, of massive brass, and 
the terminal faces were carefully turned. Central marks upon them facilitated the 
adjustment of the coils into the symmetrical positions. The distance of mean planes 
does not however depend solely upon the distance-pieces. Even if we could assume 
that the mean planes are symmetrically situated relatively to the grooves in which the 
wire is wound, we should still have to take account of the thicknesses of the flanges. 
All uncertainty in this matter is eliminated by following the plan adopted by Glaze- 
brook of reversing the rings (without interchange), and then repeating the measure¬ 
ments. Whatever may be the situation of the mean planes and the thicknesses of 
the flanges, the mean result thus obtained corresponds to a distance equal to the 
length of the pieces plus half the total outside thicknesses of the rings. These 
quantities can all be measured with great precision, and as easily after the coils are 
wound as before. Full particulars are given in § 24. There can hardly be a doubt 
but that the determination is much more accurate than that of the mean radius of a 
