NA TURE 



[November 6, 1902 



compilation which represents much hard work and which 

 will serve to stimulate interest in that division of the 

 county, inasmuch as it indicates a somewhat unexpected 

 wealth and variety of plant forms. Mr. J. J. Marshall 

 has furnished a list of the mosses of the Riding. 



A Revolution in the Science of Cosmology. By George 

 Campbell. Pp. 210. (London : Sampson Low, 

 Marston and Co., Ltd., 1902.) 



In spite of the author's description of himself as " a 

 professor and teacher of the natural sciences for many 

 years," this attempt to revise the generally accepted 

 theory of planetary evolution shows a very imperfect 

 acquaintance with scientific principles. The leading idea 

 is that the earth was never in a molten condition, but is 

 now undergoing the process of fusion in consequence of 

 the pressure of the external strata on the interior mass. 

 The sun also is declared to have once been an opaque 

 body, and to represent more or less what the earth and 

 other planets will become. In this connection it is only 

 necessary to point out that while a gaseous mass con- 

 tracting under the influence of its own gravity will rise 

 in temperature, there is no ground for extending this 

 principle to masses which are liquid or solid. 



Among the other unacceptable ideas met with is that 

 which accounts for a prehistoric change in the polar 

 climate by supposing that the North Pole of the earth was 

 "suddenly" turned from the sun and remained in that 

 position for ages, having ceased for the time being to 

 rotate on its axis (pp. 35 and 140). Again, on p. 64, 

 speaking of the Whirlpool nebula, it is stated that "the 

 violent agitation of the mass must result in a very low 

 temperature," whereas a high temperature would be 

 expected. 



The author appears to have a vague idea that elec- 

 tricity plays an important part in the development of 

 worlds, and that "atoms of interstellar space" repre- 

 sent the primary state of all matter, but he makes no 

 contribution of value to the subject. 



The Reliquary and Illustrated Archaeologist. Edited 

 by J. Romilly Allen. Vol. viii. Pp. 287. (London : 

 Bemrose and Sons, Ltd., 1902.) Price 12^. net. 

 STUDENTS of any branch of archaeology will find some- 

 thing to interest them in this volume. The periodical, of 

 which the numbers issued during the present year are 

 included in the volume, is " a quarterly journal and 

 review devoted to the study of the early pagan and 

 Christian antiquities of Great Britain ; mediaeval archi- 

 tecture and ecclesiology ; the development of the arts 

 and industries of man in the past ages ; and the survivals 

 of ancient usages and appliances in the present." Notes 

 on interesting and important papers contributed to some 

 of the separate numbers of the Reliquary have already 

 appeared in these columns, so that it is only necessary 

 to say here that the eighth volume, with its numerous, 

 well-produced illustrations, would make a handsome 

 addition to the library of the student of antiquities. 



Earth and Sky. A Second and Third Grade Nature 

 Reader and Text-Book. By. J. H. Stickney. Pp. 

 viii + 118. (Boston, U.S.A., and London: Ginn and 

 Co., 1902.) Price is. 6d. 

 THIS is a reading book for young children. Its object is, 

 the author says in his preface, " to bring before chil- 

 dren's minds their own relation to the natural world in 

 such a way as to appeal to imagination and reflection." 

 The lessons will probably prove interesting to those for 

 whom they are intended, but they do not sufficiently en- 

 courage the child's own activity. It is not enough to tell 

 young pupils about natural objects ; they should be en- 

 couraged to observe for themselves, instead of being 

 content with the descriptions of others. 



NO. 1723, VOL. 67] 



LETTERS TO THE EDITOR. 



[ The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of NATURE. 

 No notice is taken of anonymous communications.'] 



The Waste of Energy from a Moving Electron. 



The subject of the dynamics of a moving charge being of 

 considerable interest now, I have thought the following may be 

 useful. I have shown thai a charge Q on a sphere of radius A, 

 when suddenly jerked into motion at speed u, generates a spherical 

 electromagnetic shell of depth 2A, in which the magnetic force 

 H tends to the value given by 



2AH: 



J3 



4irR 



u sin 9 



(1) 



-cos 8 



when R, the distance from the initial centre of Q, is great. 

 Along with this H, we have perpendicular electric force in the 

 shell, according to E = ,ur'H, or vectorially, E = VvB, if v is the 

 vector velocity of the shell. The angle 6 is that between u and' 

 R. The energy wasted by this shell equals the energy left 

 behind, that is, U-U n + T, if U is the initial, U the final 

 electric energy in the field, and T the final magnetic field 

 energy. On its first formation, H and E in the shell are 

 different ; they then include in accumulated form all the H and 

 E which are left behind by the shell as it expands. The applied 

 force impulse follows from my formula for the force on the ether,, 

 viz. T = (d/dt)VD'B per unit volume. Denoting the time integral 

 by M, then M = M 1 + M„, where M., belongs to the shell 

 ultimately, and is lost, whilst M, is left behind in the field. We 

 have T=^Mai and U - U = iM.,« ; so that altogether 



JM« = U-U n + T. (2) 



Both HI, and M, 2 are parallel to n. 



If, now, a second impulse acts, changing the velocity from u, 

 tou 2 say, another spherical shell is generated. Disregarding the 

 part left behind, (1) above shows that the magnetic force in it is 



2AH = . Q . / »» sin9 "' sin9 V (3) 



4* R \,-Scos9 1 -- 1 cos eJ 



when the direction does not change. More generally, substitute 

 the vector change in the quantity on the right side of (1) 

 properly vectorised. Then the change in 9 will be allowed for 

 as well. 



The energy lost in this second shell may be calculated by (3). 

 It amounts to 



( u„ -a, \ v- J J 



where P is the potential function 

 O 



Ac\ 3 s' is' / 



4ttA<t 



(4) 



(5) 



investigated by Searle and Morton. Take « = o, «j and h 2 to 

 obtain P , P lt P 2 . It may be shown that the substitution of two 

 impulsive changes in the same direction for a single one reduces 

 the waste ; that is, the one impulse u„ wastes more energy than the 

 two successive impulses ft, and » 2 - u v In fact, the saving is great, 

 and ten equal partial impulses in succession waste not much 

 more than one-tenth part of that wasted by a single impulse of. 

 size equal to their sum. There is a residuum, however, and 

 that is what appears as continuous waste when u varies 

 continuously. 



When Am is small 



Q sin 9 Au 



~^ R ( 1-? cos eV 



2AH = 



(6) 



and now the waste of energy in the shell wave corresponding 

 to Aft is 



.«> (A«) 2 



I2ttA 



(-5) 



(7) 



The magnetic force in the above shells is uniform in the depth 

 of the shell, when the impulse acts strictly at the front of a shell. 



