NA TURE 



361 



THURSDAY, FEBRUARY 19, 1903. 



ELECTRIC RADIATION FROM WIRES. 

 Electric Waves. Being an Adams Prize Essay in the 

 University of Cambridge. By H. M. Macdonald, 

 M.A., F.R.S., Fellow of Clare College. Pp. xiii + 200. 

 (Cambridge : University Press, 1902.) Price lew. 



THE essay under review consists essentially of two 

 parts. In one of them the author aims at a re- 

 statement of electrodynamic theory in a manner which 

 will avoid what he considers to be the difficulties of the 

 existing dynamical expositions. The other part contains 

 new developments relating to the mode of propagation of 

 electric radiation, its emission and absorption by reson- 

 ating wire circuits, and the dynamical laws of its diffrac- 

 tion by obstacles. 



In illustration of the power of the mathematical 

 analysis that is developed in the latter part, it may be 

 mentioned that the general dynamical problem of diffrac- 

 tion at the edge of a perfectly conducting {i.e. totally 

 reflecting) prism is solved in a few pages at the end of 

 the book (Appendix D) by a method which admits of 

 extension to any transparent or metallic prism the optical 

 constants of which are known. The only case of diffrac- 

 tion in which a rigorous dynamical solution had been 

 previously obtained is that of the straight edge of a per- 

 fectly conducting plate, which is the special case of a 

 prism of vanishing angle ; this had been reached through 

 intricate analysis by Poincare and by Sommerfeld, and 

 the result is now often reproduced as a new departure 

 in mathematical physics applied to problems in theo- 

 retical optics. The very elegant treatment in terms of 

 Bessel functions that is brought to bear by Mr. Mac- 

 donald will remind readers of a previous successful 

 application of essentially the same analysis, namely to 

 the verification of Mr. W. D. Niven's beautiful func- 

 tional solution of the problem of electric distribution on 

 the general type of conductor bounded by two intersect- 

 ing spheres, which was published some years ago in the 

 Pi-oceedings of the Mathematical Society. Features of 

 much interest are bound to arise in the theoretical 

 character of the diffraction at the edge of a transparent 

 or metallic prism of known index ; it is to be hoped that 

 the author will not be deterred by some inevitable com- 

 plexity of computation from following out in detail this 

 natural extension of his results. 



When disruptive electric disturbances take place in a 

 material system, their energy is, in the ordinary course, 

 dissipated by electric radiation into space, in so far as 

 it is not degraded into heat by resistance. That any 

 other state of affairs could exist has not been hitherto 

 contemplated, though it has been known by experience 

 that an electric vibrating system like the ring resonator 

 of Hertz could go on oscillating for very many thousands 

 of periods without much loss. The author claims that 

 it is possible theoretically to have electric vibrating 

 systems absolutely permanent, which would last for ever, 

 so far as radiation is concerned ; that if electric waves 

 are introduced into a nearly complete wire circuit, and 

 if the ends are then connected so as to make the 

 NO. 1738, VOL. 67] 



circuit a complete ring, a portion of the wave-motion 

 will settle down into a steady state in the circuit and 

 run round and round for ever, assuming, of course, that 

 the circuit is perfectly conducting ; that as such waves can 

 only enter through the ends, so the only way of dissipating 

 them is by cutting the circuit and allowing them to 

 escape from the ends. This, even if it is not valid for thick 

 anchor rings, is certainly practically correct for thin 

 wires ; and such systems in which electric oscillations are 

 going on thus radiate mainly from the ends or points of 

 the wires. The nature of the beam of radiation which 

 issues from the end of a straight wire is here investigated 

 theoretically, the form obtained for the wave-fronts 

 around the end being shown to be in close accord with 

 the observations of Birkeland and Sarasin. Fortified 

 with this theoretical analysis, we can form a more vivid 

 and confident idea of how exposed metallic points like 

 those of lightning conductors may gather up stray 

 radiations in the surrounding space, which may then be 

 passed down around a system of properly attuned ioops 

 forming nearly closed circuits in the lower part of the 

 wire, in each of which a selected period can be intensified 

 by resonance and tapped off through a relay system into 

 an appropriate recorder ; and we can even imagine that 

 the direction from which an incident train of disturbances 

 comes may be estimated from the orientation of the 

 plane of the resonating loop which responds to it most 

 intensely. 



The whole theoretical discussion is founded on, and in 

 turn elucidates, an extension of the ancient electric 

 dogma of the power of points into the new field of 

 electric radiation. Closed electric circuits can be placed 

 in relation of radiation and absorption with the surround- 

 ing asther, after the manner of radiating atoms in tem- 

 perature equilibrium, by narrow breaks or attached spikes. 

 The subject is far from being exhausted ; for example, 

 the more complex and probably far more difficult 

 problem suggests itself to compare the radiation that 

 must escape from a sharp bend in the wire carrying the 

 waves with the radiation issuing from its open end. 

 From the standpoint of present interests, the theoretical 

 elucidation of the circumstances on which depend the 

 free periods of resonators of the Hertz pattern formed of 

 simple wire rings with or without knobs at the ends, to 

 which close attention is also devoted in the book, is 

 hardly as important as this other related question of the 

 theoretical conditions governing the emission and absorp- 

 tion of radiation from wire circuits and networks. 



The periods of free electric surging in the dielectric 

 sheets of various forms of condensers are also discussed ; 

 the correction for the open edge of a flat condenser 

 is determined, expressed in the form that by adding a 

 slip of certain breadth to the plates all round the edge 

 the electric field between them may be taken as uniform 

 right up to it. The result comes, of course, from appli- 

 cation of the general principles of the mode of analysis 

 applied in acoustics by Helmholtz in 1859 to the 

 correction for the open ends of organ pipes. 



As developed by our author, the key to the discussion 

 of the oscillations and their free periods, in open wire 

 circuits, lies in the determination of the radiation from 

 the end part of a straight wire when standing electric 



R 



