214 KEPOET— 1897. 



During the time that the ring was unwound the linear coefficient of 

 expansion of the marble was measured by Messrs. Spiers, Twyman, and 

 Waters, three of the students of the City and Guilds Central Technical 

 College. The experiment was attended with difficulty, for it was far from 

 easy to bring so large a mass of a badly conducting substance to the 

 same temperature, but ultimately the result 0*000004 per 1° C. was 

 obtained. 



At the conclusion of the resistance observations recorded further on, 

 the silk ribbons and the protecting layer of paraffin wax were carefully 

 removed until the silk covering of the wire appeared, and the diameter of 

 the coil was measured along two directions at right angles to one another. 

 The maximum difference between four measurements was only five 

 hundred-thousandths of an inch, and after the introduction of the proper 

 temperature corrections, the mean value of the outside diameter of the 

 coil was found to be 



21-04687 inches at 20°-4 C. 



This result is about one part in ten thousand larger than the calcu- 

 lated value given above, and the difference is probably due to the silk 

 covering of the wire having swollen slightly when the wound coil was 

 brushed over with melted paraffin wax. In the calculation, therefore, of 

 the coefficient of mutual induction we have considered it more accurate 

 to use the value obtained by direct experiment. Subtracting from that 

 value — 21 •04687 — the thickness of the double silk-covered wire — 0-01914 

 — we have for the mean diameter of the coil from axis to axis of the loire 



21-02773 inches at 20°-4 C. 



Shortly before the last set of resistance measurements was carried out, 

 the edge of the phosphor bronze disc was ground in position so as to be 

 made quite true with the axis of rotation, and immediately after the com- 

 pletion of the investigation the diameter of the disc was measured and 

 found to be 13-01435 inches at 19°-5 C. Messrs. Spiers, Twyman, and 

 Waters had previously determined its linear coefficient of expansion to 

 be 00000125 per 1° C, so that its diameter was 



13-01451 inches at 20°-4 C. 



During 1896 Mr. W. G. Rhodes, when he was an Assistant at the 

 Central Technical College, carried out the long calculation of the co- 

 efficient of mutual induction between the coil, as wound with bare wire, 

 and the disc by using the method given in the paper in the ' Philosophical 

 Transactions ' above referred to, and with the following values : — • 



Diameter of coil or 2 A =21*02673 inches. 



Diameter of disc or 2 « =13-01997 inches. 



Axial length of helix or 2 x =5-025 inches, 

 ix'umber of convolutions or w=201 

 He found 



M= 18056-36 inches. 

 = 45862-33 centimetres. 



This calculation was checked by Mr, Mather and independently by 

 one of the authors, 



Now it can be shown that for the above values of A, a, x, and n 



$^=1-246 — + 2-343 ^ + 0-0997—, 

 M A a X 



