3.V 



NA TURE 



[February 15, 1894 



field. This part of the work has a value enhanced by 

 the contributions made to our knowledge of this depart- 

 ment of electrical science by the author himself, both as 

 regards the actual experimental facts and their 

 theoretical explanation. The action of a magnet upon 

 discharges in tubes or bulbs without electrodes 

 is peculiarly interesting. The discharge being oscil- 

 latory in such a case is separated into two distinct 

 portions, consisting of the discharges in the two opposite 

 directions. Thus a ring discharge in a horizontal plane 

 has one part raised, the other lowered by the action of 

 a horizontal magnetic field. Further, as has been observed 

 by the author, the discharge is rendered more difficult 

 when it has to pass across the lines of force of a 

 magnetic field, while it is facilitated when it has to pass 

 along the lines. 



The explanation suggested by the author is ingenious- 

 The gas breaks down along the line of maximum electro- 

 motive intensity, and a discharge occurs which gives a 

 supply of dissociated molecules, which readily convey 

 subsequent discharges. The magnetic field, when at 

 right angles to the line of discharge, acting on the mole- 

 cules taking part in the discharge, removes them from 

 the line of maximum electromotive intensity, and thus 

 the instability of electric strength which the discharge 

 tends to set up is continually being annulled by the 

 magnetic action. 



In the other case it is suggested that if branching of 

 the discharge from the main line takes place, the dis- 

 sociated molecules there formed will be brought into the 

 line by the magnetic action, and would thus increase the 

 facility of the discharge, beyond that which would exist, 

 if there were no field. 



This, as Prof. Fitzgerald has suggested, has an impor- 

 tant bearing on the nature of the aurora, and probably 

 explains the streamers which form so remarkable a 

 feature of auroral displays. These may be simply more 

 than averagely bright discharges along the electrically 

 weaker lines of magnetic force in the rarefied air of the 

 upper parts of the atmosphere. 



A chapter is next devoted to Conjugate Functions in 

 their applications to the solution of electrical problems. 

 This method is very serviceable for the solution of prob- 

 lems of electrical flow in two dimensions, but it can 

 hardly be applied in a syste.natic manner to the various 

 problems which present themselves. 



The theory of functions of a complex variable has 

 been o-reatly advanced since Maxwell wrote, and there is 

 certainly much, as has been pointed out, more especially 

 by Klein, that has direct application to the solution of 

 electrical problems. Prof. Thomson has therefore done 

 well to include some of the general transformations of 

 this theory, with their applications to such problems as 

 the effect of the gap between the plate and guard-ring 

 in Lord Kelvin's absolute electrometer or guard-ring con- 

 denser, different arrangements of piles of plates, and the 

 like. This theory of the condenser he has himself made 

 use of in his determination of v. 



It may be objected that some of the problem s solved 

 by the indirect method employed in this chapter have no 

 very distinct practical application ; but there can be no 

 question of the value of such a discussion. It places within 

 the reach of students who are able to follow it processes 

 NO. 1268, VOL. 49] 



ready to hand by which problems quite unassailable by 

 ordinary methods are discovered and solved; and who can 

 tell when such problems may not become of great practical 

 importance, in the present rapidly advancing state of the 

 science ? 



We are taken next to the subject of electrical waves 

 and oscillations, which in some form or other is the 

 theme discussed in the remainder of the book. The 

 problem of periodic disturbances is very fully treated 

 in a large number of practically important cases. 

 Throughout the analysis the method of representing a 

 simply periodic function in the form IMe^"'" "'"^'^^ where 

 i = y/^ I is adopted. This tends greatly to condensa- 

 tion, and the results are always interpretable at will by 

 properly " realising " the solution. 



First is taken the extremely important case of waves 

 along a cylindrical wire surrounded by a coaxial coating 

 of dielectric, outside which again is an infinitely extend- 

 ing cylindrical conductor ; and this is treated with special 

 fulness. The solutions are expressed in terms of Bessel's 

 functions ; and this part of the book ought to lead to a 

 more general study of the properties of such functions, 

 and their applications to physical problems. They had 

 their origin in a physical problem, and their importance 

 to physicists has gone on increasing with the develop- 

 ment of physical mathematics which has been brought 

 about by the problems disclosed by scientific progress in 

 recent times. 



The theoretical solution of the problem of waves 

 along wires is mainly due to Lord Kelvin, Mr. 

 Oliver Heaviside, and Prof. J. J. Thomson. The 

 solution given long ago by Lord Kelvin of the more 

 limited problem which was then the practical one, appears 

 as a particular case of the general solutions which these 

 physicists have since obtained. The conclusions they 

 have reached are of the utmost interest in connection 

 with telephony, and seem likely to point the way to a more 

 extended use of telephonic communication than has 

 hitherto seemed possible. Lord Kelvin's early solution, it 

 is not too much to say, gave for the first time light on 

 the vexed question of the conditions of success in sig- 

 nalling through submarine cables and, together with the 

 marvellously delicate and simple instruments which he 

 also invented, rendered signalling through such cables 

 commercially possible. Even now the question of ocean 

 telephony has come to the front, and if it succeeds (and 

 who will venture to say its difficulties will not be over- 

 come ?) it will be in great measure a result of the patient 

 researches of men like Lord Kelvin, O. Heaviside, and 

 the author of the work before us. 



The complex variable treatment is adhered to, and 

 contributes greatly to brevity of expression. The treat- 

 ment of the subject is very complete, and though it in- 

 volves some rather complicated work seems very accu- 

 rately printed. The author has apparently pressed for- 

 ward from point to point, taking the path which presented 

 itself at the time, and hence, to one coming after, it is 

 possible to suggest some shortening and smoothing of 

 the way. For example, the values of the electromotive 

 and magnetic intensities are perhaps more compactly 

 investigated by first specialising the fundamental equa- 

 tions for the case of symmetry round an axis, noting that 

 the electromotive intensity reduces to two components, 



