NA TURE 



THURSDAY, NOVEMBER 14, 1912. 



ELECTRONS AND THE ELECTRO- 

 MAGNETIC FIELD. 



Electromagnetic Radiation and the Mechanical 

 Reactions arising from it. Being an Adams 

 Prize Essay in the University of Cambridge. 

 By Dr. G. A. Schott. Pp. xxii + 330. (Cam- 

 bridge : University Press, 1912.) Price 185. net. 

 PROF. SCHOTT'S original essay is, in this 

 book, supplemented by a series of valuable 

 appendices, which amply justify the delay in its 

 publication. The work is deductive in plan ; its 

 foundations are the electromagnetic equations of 

 Maxwell and Hertz, together with the Larmor- 

 Lorentz expression for the mechanical force on a 

 moving charge. The " retarded potentials " of the 

 electromagnetic field are transformed so as to yield 

 Schott's solutions, in the form of "modified 

 Fourier integrals," and most of the calculations 

 are performed from these as starting point. They 

 lead simply, and with considerable mathematical 

 rigour, to many results obtained by other writers ; 

 in particular, the " point laws " of Li^nard and 

 Wiechert are deduced, and are used to illustrate 

 the general features of the electromagnetic field in 

 a number of special cases. The exact calculations, 

 however, are more readily executed with Schott's 

 expressions, and various simple cases of motion 

 of electrons are thus dealt with, as, e.g., uniform 

 or uniformly accelerated rectilinear motion. 

 Periodic motions, such as uniform circular motion 

 of a single electron, or of a ring of electrons, are 

 also discussed. More complex cases, like pseudo- 

 periodic or aperiodic motions, cannot be solved 

 completely, but the distant field is approximated to. 

 Specially interesting are the problems relating to 

 the pulse theory of the X-rays, and the precessional 

 motion of a ring of electrons, as applied to Ritz's 

 theory of the Zeeman effect. 



The velocities of the electrons are not restricted 

 to be less than the velocit}' of light, chiefly because 

 the mathematical expressions require no such con- 

 dition (though the work is far simpler in the 

 restricted case). It is pointed out that no experi- 

 mental evidence, either way, has been brought to 

 settle the question of the possibility of velocities 

 exceeding that of light ; if the Lorentz mass- 

 formula were universally true, indeed, the question 

 would be decided in the negative, but this formula 

 has been verified (by Bucherer) only for velocities 

 considerably less than that of light. Moreover, 

 the theory of relativity, which is based on this 

 formula and has proved useful in explaining 

 aberration phenomena and the behaviour of 

 moving optical systems, neglects the loss of energy 

 NO. 2246, VOL. go] 



by radiation from accelerated charges ; this, how- 

 ever, becomes very important for velocities 

 approaching that of light. 



In the appendices several theorems are 

 proved which lead up to an interesting dis- 

 cussion of the possible mechanical explanations of 

 the electron. It is shown that the Lorentz de- 

 formable electron is more easily explained mechani- 

 cally than the electrons of Abraham and others, 

 as it only requires an invariable hydrostatic 

 pressure of the aether over its surface to enable it 

 to subsist. This pressure is estimated (p. 269) as 

 10-^ atmospheres. Moreover, the mass-formula 

 for such an electron is practically the only one 

 which can be applied in the mathematical theory 

 of the mechanical forces and the radiation. 



For the mathematician the book abounds in 

 problems and suggestions of interest and 

 importance ; especially does it clearly display the 

 need for the cooperation of the pure analyst in 

 the study of the summation and convergence of 

 the difficult series and integrals which occur in 

 its investigations. The physicist will, perhaps, 

 find it rather tedious to unearth the physical con- 

 clusions (which are pointed out from time to time 

 in the course of the work) from the mass of com- 

 plicated mathematics in which these remarks are 

 involved. The great value of the book would have 

 been increased if the physical bearing of the results 

 had been summarised in an extra chapter ; this is 

 done to a slight extent in the preface. A greater 

 number of numerical calculations would also have 

 been advantageous in giving a clearer grasp of 

 the results, but the great labour required for such 

 an undertaking sufficiently explains the omission. 



THE LAND AND ITS LORE. 

 (i) Common Land and Inclosure. By Prof. E. 

 C. K. Conner. Pp. xxx + 461 + 5 maps. 

 (London: Macmillan and Co., Ltd., 1912.) 

 Price I2S. net. 

 (2) Byivays in British Archaeology. By Walter 

 Johnson. Pp. xii + 529. (Cambridge : Univer- 

 sity Press, 1912.) Price los. 6d. net. 

 (i) QCIENTIFIC studies of the history of land- 

 »^ holding have a peculiar importance at the 

 present moment, when legislative innovations in 

 ownership are so widely mooted on o priori 

 grounds. By supplying valid inductions from the 

 past, science here, as in other spheres, provides 

 the statesman with a solid foundation for political 

 principles, and a sure test for fallacious schemes. 

 The entire history of English agriculture, so far 

 as it is connected with national progress and 

 advance in civilisation, is bound up with "com- 

 mon " and inclosure, and the passage from the 



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