PRACTICAL STANDARDS FOR ELECTRICAL MEASUREMENTS. 241 
nuthorised and requested to retain the custody of the Electrical Standards 
of the Association, and to remove them from Liverpool to London when 
he takes up his post as Director of the National Physical Laboratory. 
The removal of the Standards and the investigations of a Platinum 
Thermometry will necessitate some expenditure during the year. 
The Committee therefore recommend that they be reappointed, with 
the addition of Sir William Roberts-Austen and Mr. Matthey, and with a 
grant of 25/. in addition to the unexpended balance (300/.) of last year’s 
grant, and that Lord Rayleigh be Chairman and Mr, R. T. Glazebrook 
Secretary. 
APPENDIX I. 
The Mutual Induction of Coaxial Helices. By Lord Ray eicn. 
Professor J. V. Jones! has shown that the coefficient of mutual induction (M) 
between a circle and a coaxial helix is the same as between the circle and a 
uniform circular cylindrical current-sheet of the same radial and axial dimensions 
as the helix, if the currents per unit length in helix and sheet be the same. This 
conclusion is arrived at by comparison of the integrals resulting from an applica- 
tion of Neumann’s formula; and it may be of interest to show that it may be 
deduced directly from the general theory of lines of force. 
In the first place, it may be well to remark that the circuit of the helix must 
be supposed to be completed, and that the result will depend upon the manner in 
which the completion is arranged. In the general case the return to the starting- 
point might be by a second helix lying upon the same cylinder; but for practical 
purposes it will suffice to treat of helices including an integral number of revolu- 
tions, so that the initial and final points lie upon the same generating line. The 
return will then naturally be effected along this straight line. 
Let us now suppose that the helix, consisting of one revolution or of any 
number of complete revolutions, is situated in a field of magnetic force sym- 
metrical with respect to the axis of the helix. In considering the number of 
lines of force included in the complete circuit, it is convenient to follow in imagi- 
nation a radius-vector drawn perpendicularly to the axis from any point of the 
circuit. The number of lines cut by this radius, as the complete circuit is 
described, is the number required, and it is at once evident that the part of the 
circuit corresponding to the straight return contributes nothing to the total.* 
As regards any part of the helix corresponding to a rotation of the radius through 
an angle d@, it is equally evident that in the limit the number of lines cut through 
is the same as in describing an equal angle of the circular section of the cylinder 
at the place in question, whence Professor Jones’s result follows immediately. 
Every circular section is sampled, as it were, by the helix, and contributes 
proportionally to the result, since at every point the advance of the vector 
parallel to the axis is in strict proportion to the rotation. It is remarkable that 
the case of the helix (with straight return) is simpler than that of a system of 
true circles in parallel planes at intervals equal to the pitch of the helix. 
The replacement of the helix by a uniform current-sheet shows that the force 
operative upon it in the direction of the axis (¢M/d.x) depends only upon the 
values of M appropriate to the two terminal circles. 
If the field is itself due to a current flowing in a helix, the condition of 
? Proc. Roy. Svc. vol. 1xiii. (1897), p. 192. 
* This would be true so long as the return lies anywhere in tke meridional plane. 
In the general case, where the number of convolutions is incomp’ete, the return may 
be made along a path composed of the extreme radii yectorcs a”d of the part of the 
axis intercepted between them. 
1899. R 
