78 Dr. J. W. Nicholson on the Effective 



little service. But even with the restriction to wires witli 

 small capacity and leakage, mathematical solutions have not 

 hitherto progressed far. The problem of the concentric 

 main was discussed by Maxwell * and Heaviside f, and 

 afterwards for very high frequencies by Lord Rayleigh %. 

 A practical formula for the resistance of the inner conductor 

 was given by Lord Kelvin §, whose solution is not essen- 

 tially different from that of Heaviside. 



Formula? for the effective inductance in this case have 

 also been obtained by Sir J.J.Thomson ||, and an exhaustive 

 treatment of the whole problem by more simple methods, in 

 which the ranges of application of all the previous formula? 

 are critically examined, has been given by Russell %. 



The investigation of the effective inductance and resist- 

 ance of two parallel wires, one being the return of the other, 

 was made by the author **, and developed, in a later paper ft, 

 in a form capable of more immediate practical use. The 

 upper limit necessary to the capacity was at the same time 

 examined. 



The main problem of importance in which the wires are 

 bent is that of the single helical coil of considerable length. 

 Solutions have hitherto dealt with the case in which the 

 wire is closely wound round a circular cylinder, forming a 

 helix whose pitch is very small. Wien J J first discussed the 

 problem, but assumed that the current distribution is the 

 same at all points equidistant from the axis. Battelli showed 

 that this assumption was not lawful, and the results do not 

 agree with experiment. Shortly afterwards, Sommerfeld§§ 

 investigated the problem in so far as the resistance is con- 

 cerned, and his method was applied later by Coffin || || to a 

 determination of inductance. PicciatilHF gave an independent 

 solution, but like those of Sommerfeld and Wien, its agree- 

 ment with experiment was not very good. The best solution 

 in this respect is that of Cohen***, which appears to be quite 



* Elec. and Mag-, vol. ii. § 690._ 

 t Electrical Papers, i. p. 353 ; ii. p. 64 et set. 

 % Phil. Mag. xxii. p. 381 (1886) ; Scientific Papers, ii. p. 486. 

 § Journ. Inst. Elec. Eng. xxiii. p. 4 (1889) ; Math. & Phys. Papers, 

 iii. p. 491. 



|| Recent Researches, p. 295. 



5[ Phil. Ma?. April 1909; Proc. Phys. Soc. xxi. 



** Phil. Mag. Feb. 1909 ; Proc. Phys. Soc. xxi. 



tt Phil. Mau-. Sept. 1909 ; Proc. Phys. Soc. xxii. 



it Ann. de^Phys. xiv. p. 1 (1904). 



§§ Ann. der Phys. xv. p. 073 (1904). 



Illl Bulletin of Bureau of Standards, ii. p. 275. 



*(1<H 11 Nuovo Cimento (5) ii. p. 35. 



*** Bulletin of Bureau of Standards, iv. no. 1. 



