168 HENET A. KOWLAND 



a small probable error, and as it is a much larger coil, it seems best to 

 give this number twice the weight of that found by calculation : we thus 

 obtain 



(7 = 1833-19 

 as the final result. 



It does not seem probable that this can be in error more than one 

 part in two or three thousand. 



Telescope, scale, &c. The telescope, mirrors and plane-parallel glass 

 were all from Steinheil in Munich, and left nothing to be desired in 

 this direction, the image of the scale being so perfect that fine scratches 

 on it could be distinguished. The telescope had an aperture of 4 cm. 

 and a magnifying power of 20 was used. The scale was of silvered 

 brass, one metre long and graduated to millimetres. 



Induction coils. A coil was wound in a groove in the centre of each 

 of three accurately turned brass cylinders of different lengths. Two 

 of them only were used at a time, by placing them end to end, the ends 

 being ground so that they laid on each other nicely. The two coils 

 could be placed in four positions with respect to each other, in each of 

 which they were very exactly the same distance apart. This distance 

 for each of the four positions, was determined at three parts of the 

 circumference by means of a cathetometer, with microscopic objective, 

 reading to ^ mm. The mean of all twelve determinations was the 

 mean distance. In using the coils they were always used in all four 

 positions. The probable error of each set of twelve readings was 

 -001 mm. The data are as follows, naming the coils, A, B and C : 



Mean radius of A = 13-710, of B = 13-690, of C = 13-720. 



Mean distance apart of A and 5 = 6-534, of A and (7 = 9-574, of 

 B and (7=11-471. 



N= 154 for each coil, == -90, y = -84. 

 For A and B we have 



M= 3774860- + T V (74250- 66510-) = 3775500- 

 The remaining terms of the series are practically zero, as was found 

 by dividing one of the coils into parts and calculating the parts sepa- 

 rately and adding them. 



For A and C 



M = 2561410- -f T V (34000- 27230-) = 2561974- 

 For B and (7 



M = 2050600- + T V (27500- 19800-) = 2051320- 

 The calculation of the elliptic integrals was made by aid of the tables 

 of the Jacobi function, q, given in Bertrand's ' Traite de Calcul Inte- 



