Sim: ( Ialvanometer 381 



11. The shape of the terminals, the nature of the insulation, and the method of 

 connection to the ends of the coils and the concentric or coaxial cables which formed the 

 leads to the battery and measuring devices are shown in Figure 14. Each of the terminal 

 loops was made as nearly like the others as practicable, and each lies in the axial horizontal 

 plane. The intensity each produces in this plane is thus vertical. Moreover, at all 

 points along the axial vertical plane the vertical intensities of the loops neutralize one 

 another in pairs. The marble insulators, carrying the brass terminal blocks, were 

 treated with hot paraffin, but not just like the spool. The cables were specially made 

 from stranded and braided copper wire, with cotton and rubber insulation, by the Bel den 

 Mfg. Co., and their ends were carefully tinned before being soldered to the terminals. 

 They were left about 35 ft. long each, the conductors of each cable, equivalent to Nos. 

 21 and 22 wire, B. and S. gage, being soldered to a double binding-post on a block of 

 ebonite. ' 



The marble spool was mounted as shown in Figures A and B in the brass saddle already 

 described and was held in position by four brass screws coming up vertically through the 

 saddle from beneath. 



In much of the work on the marble spools, coils, etc., we have profited greatly 

 by the experience gained at the National Physical Laboratory. 2 



12. The ideal Helmholtz coil consists of two equal coaxial circular turns of linear 

 wire, the axial distance between whose planes is equal to half their diameter. The 

 magnetic field near the center of such a system of two circles traversed by the same 

 electric current in the same direction is very nearly uniform. If, as is approximately the 

 case in the coils of the instrument described here, the diameter is 30 cm., the axial 

 intensity at a point on the axis 0.5 cm. from the center does not differ from that at the 

 center by as much as 1 part in 400,000. Even for a distance of 1 cm. the difference 

 is less than 1 part in 42,000 (13). 



If, therefore, we substitute for each circle in the ideal Helmholtz pair, 30 cm. in 

 diameter, any number n of circles of the same diameter distributed axially over a range 

 even as great as 2 cm., the axial distance between corresponding circles in the two groups 

 being always 15 cm., each of these pairs will produce at the center of the system the 

 same axial intensity as that due to a central pair within less than 1 part in 42,000. If 

 the circles in each group are uniformly distributed, the intensity at the center of the 

 system will be n times that due to a central pair within much less than 1 part in 80,000. 



Furthermore, it is clear from what precedes and the general form of Ampere's 

 expression for the magnetic intensity due to a current element, that any circle of a 30 

 cm. coil may be distorted by a purely axial displacement of any part or parts, provided 

 that this displacement does not make the extreme width of the group to which it belongs 

 greater than 2 cm. and that the corresponding part of the other group is distorted in 

 exactly the same way, without affecting the axial intensity at the center by as much as 

 the small quantities mentioned above. Either group, moreover, or a distortion in 

 either group, may evidently be displaced angularly about the axis without affecting 

 the axial intensity at the center at all. 



As a special case, the two groups forming a Helmholtz pair 30 cm. in diameter 

 may be wound in equal regular helices as much as 2 cm. in axial length, the axial distance 

 between corresponding points on the two helices being 15 cm., and yet the axial intensity 

 at the center may be calculated with an error less than 1 part in 84,000 on the assumption 

 that each pair of spiral turns produces at the center of the system the same axial in- 

 tensity as the ideal 30 cm. Helmholtz pair produces at its center. 3 



1 These cables have given entire satisfaction only when the portions which move when the coil is turned in azimuth 

 have been hung from above approximately vertical. Otherwise the change of resistance due to the distortion produced by 

 the motion affects the current more than is admissable. 



* Ayrton, Mather, and Smith, Phil. Trans. A, vol. 207, 190S, p. 463; and F. E. Smith, Ibid., vol. 214, 1914, p. 27. 



3 With regard to the equivalence of circular current sheets and spirals for the axial intensity at points on the axis in 

 the general case, see J. V. Jones, Roy. Soc. Proc. vol. 63, 1S98, p. 204. 



