106 Lord Rayleigh and Dr. A. Schuster. [May 5, 



If L were zero, or if the rotation were extremely slow, the current 

 would (apart from KM) be greatest when the coil is passing through 

 the meridian. In consequence of self-induction, the phase of the 

 current is retarded, and its maximum value is diminished. At the 

 higher speeds used by the Committee, the retardation of phase 

 amounted to 20°. 



To find the effect of (2) upon the suspended needle, we have to 

 introduce MK and the resolving factor cos (0— 0), and then to take 

 the average. This, on the supposition that the needle remains on the 

 whole balanced at 0, must be equal to the force of restitution due 

 to the direct action of the earth's magnetism and to torsion, i.e., 

 MHsin0+MHT0. Thus— 



R |^^ 2 {GH(R cos + sin 0) + KMR} -MH (sin + r 0) = 0. 



In the actual experiment t is a very small quantity, say t -^qo j an d the 

 distinction between r and t sin may be neglected. 



Bj-Bigg" cot f i+ jgiec »W W -* agL " 2 b q . . (.3). 



1 + t \ GrH / 1 + t 



If we omit the small terms depending upon t and upon MK/GrH, we 

 get on solution and expansion of the radical — 



-*«—*{-S(S-0-*-(ST(S-')''-'«'l 



.... (4). 



The term in tan 4 is not given in the report of the Committee, 

 but, as I learn from Mr. Hockin through Dr. Schuster, it was included 

 in the actual reductions. But the next term in tan 6 0, and one arising 

 from a combination of the correction for self-induction with that 

 depending on M, are not altogether insensible, so that probably the 

 direct use of the quadratic is more convenient than the expansion. 

 At the high speeds used by the Committee the correction for self- 

 induction amounted to some 8 per cent., and therefore cannot be treated 

 as very small. 



If the axis of rotation be not truly vertical, a correction for level is 

 necessary. In the case of coincidence with the line of dip, no currents, 

 due to the earth's magnetism, would be developed. If the upper end of 

 the axis deviate from the vertical by a small angle ft towards the north, 

 the electromotive forces are increased in the ratio cos(I + /3) : cos I, 

 i.e., in the ratio 1 + tan I.yS, I being the angle of dip. A devia- 

 tion in the east and west plane will have an effect of the second order 

 only. The magnetic forces due to the currents will not act upon the 

 needle precisely as if the plane of the coil were always vertical, but 

 the difference is of the second order, so that the whole effect of a 



