222 Prof. Perry on Long-Distance Telephony. 



the ring along its core filament is allowable ; but, as we have 

 seen, this requires that the ring must be an extremely thin 

 one, and in most cases of the coiling of wires for the con- 

 veyance of currents the assumption would be inadmissible ; 

 for, the ideal vortex filament required by the assumption 

 (infinitely thin as compared with the radius of its aperture) 

 finds but a very coarse representative in any coil of wire. 

 We have already given the values of the magnetic force at 

 the centre, 0, of the curve formed by the wire and at the 

 points, E, B, just outside its surface ; these are the analogues 

 of the velocity of the (irrotationally moving) fluid at these 

 points in the case of a vortex ring. The velocity with which 

 the ring itself moves forward is given by Mr. Basset as equal 



— (i g J?_i) ? where / is the strength of the vortex 



(product of the cross-section and molecular rotation), while 



f 

 the velocity of the fluid at is - ; so that the ratio of the 



forward velocity of the ring itself to the velocity of the fluid 

 at the centre, 0, of its aperture is 



8a 

 log — — 1 



2tt 

 which, as Mr. Basset says, is " large " in the case supposed 

 [L e. } a very thin ring) . We must observe, however, when 

 comparing actual electrical coils with fine vortex rings, that 

 for a vortex ring for which a is 1000 times c (which would 

 ordinarily be considered as a " fine " ring), this ratio is not 

 very large : it amounts only to 1*27 ; while for a vortex ring 

 the radius of whose aperture is 100 times that of its cross- 

 section, this ratio is only *9, i. e., the ring moves more slowly 

 than the fluid at its centre. 



XX. Long-Distance Telephony. By Prof. Perry, F.R.S., 

 assisted by H. A. Beeston*. 



WHEN resistance, capacity, self-induction, and leakage 

 are taken into account, this subject is one of con- 

 siderable difficulty. It is given to very few men to be able to 

 discuss complicated mathematical formulas without making- 

 mistakes — the proceedings of Scientific Societies possess many 

 such mistakes detected and undetected — and consequently I in- 

 struct my students to experiment with their formulae, using 

 numerical values for their variables. The consideration of 

 * Communicated by the Author. 



