August 31, 1905] 



NA TURE 



429 



5.45 a.m., althoiigh the shock started from the focus, 

 1280 kilometres away, at 6.10, they examined their data 

 with due scientific caution, and so discovered that the local 

 time-standard of Bombay accounted for the apparently 

 negative result ; but as they obtained from their newspaper 

 a positive record for the Calcutta seismograph, the appli- 

 cation of the same system of scientific criticism of the 

 time-standards did not occur to them. As a consequence, 

 they arrive at the astonishing result that, whilst the 

 earthquake waves travelling southwards to Bombay had 

 a speed of 4-266 kilometres a second, those which were 

 transmitted south-eastwards had a speed of 0-700 kilo- 

 metres only. 



The rest of the paper consists of " facts " and " infer- 

 ences " of this kind, and whilst most are unimportant, it 

 is desirable, perhaps, to point out that the epicentre de- 

 termined by the authors is far removed from the true 

 one. They have had to stretch their epicentre for more 

 than forty miles to the west to account for the " complete 

 destruction " of Pathankot. I was at Pathankot soon 

 after the earthquake, and found it difficult to discover 

 even a masonry crack in the town ; even a few more news- 

 paper cuttings would have shown the authors that the 

 place was practically undamaged. 



."Xfter picking a few pebbles out of this conglomerate 

 of truth and fiction, one wonders why the paper was ever 

 published at all. The very newspaper from which they 

 obtained their data must have informed the authors that 

 a thorough investigation of the earthquake had been 

 organised by the Geological Survey. As both authors 

 were in Madras at the time, one would imagine that a 

 subject sufficiently interesting for a serious paper in a 

 leading scientific journal would be worth, at any rate, a 

 few more newspaper cuttings, even if a personal visit to 

 the affected area were thought to be, for private reasons, 

 inconvenient. We take it for granted that the long experi- 

 ence of both authors must have brought them into contact 

 with the etiquette observed by scientific men, and that 

 neither would consciously risk the recognised danger of 

 forestalling the results of a thorough investigation by the 

 publication of conclusions obtained from unverified data. 

 But whatever the object, if the editor of a leading scien- 

 tific journal can join in the production of such a paper, 

 the future of scientific literature in Germany may yet give 

 us entertainments as surprising as any of the recent 

 efforts of the Russian Navy. 



Of the Kangra earthquake, as well as of the other 

 Indian questions which have been treated recently in the 

 Cciitralblatt with an equal regard for accuracy, those who 

 wish to know the truth will be provided with details in 

 due season. Within a few days after the disaster occurred, 

 every telegraph operator, meteorological observer, and dis- 

 trict official north of the latitude of Bombay was provided 

 with a complete guide for reporting the resulting pheno- 

 mena, and the reports so obtained have since been supple- 

 mented by a detailed examination of the affected area by 

 five ofificers of the Geological Survey. The observations 

 made will be summarised first in the next part of the 

 records, and the full details will form a special memoir, 

 now in course of preparation. When these reports are 

 ready, it will be seen that the actual facts, though in 

 ways interesting and novel, are scarcely so strange as 

 German fiction. T. H. Holl.4Nd. 



Calcutta, July 20. 



The Transverse Momentum of an Electron. 



When Newton's third law is applied to an electron, it 

 makes 



F = *l + N, (i) 



where M is the " momentum " in the field, or that part of 

 the time integral of the force on the ether which is in 

 the field, or 2 Vdb, and N is the momentum already 

 wasted, whilst F is the applied force on the electron. 

 Similarly, Newton's fourth law (or the Scholium to the 

 third) makes 



Fu = U-l-t-|-W, (2) 



if u is the velocity of the electron, U the electric and T 

 the magnetic field energy, and W the rate of waste of 

 energy. 



Now, both W and N are known in terms of the velocity 

 and acceleration of the charge at any moment by formulae 

 I gave in N.mure, October 30, November 6, 1902. But 

 when applied to (i), (2), these equations do not let us 

 determine M generally in terms of the velocity and 

 acceleration, on account of the variability of the state 

 of the field, and the waste of energy and momentum. 

 M is indefinite. But in long-continued forced circular 

 motion of a charge, U-|-T = o. So 



Fu = W = ^,.Q'a'|6nVK (3) 



(loc. cit.), where Q is the charge, and a the acceleration 



(or «"/R, if R is the radius of the orbit). Also, 



K- = i—u-/-j-. The direct or u component of F is there- 

 fore known. We also have (loc. cit.) 



N = (u/v')\V. (4) 

 Using this in (i), along with (3), we come to 



K=F, = M,, F, = M,, (s) 



where F, is the u component, and F„ the transverse com- 

 ponent, towards the centre. 



Thus only the part k^F, of the direct force is associated 

 with the transverse or centripetal force F„ in keeping up 

 the revolving state, the rest of F,, that is, (fi-/2'")F,, being 

 the wasted part as regards momentum, although the 

 whole of F, is concerned in the waste of energy. 



Now, l»l=VnlVI, if n is the angular velocity. That is,, 



M=M,Ui-(-MiU, + M,aj-|-M,a., (6) 



if u, and a, are unit vectors, making 



u, = («/R)a„ a,= -(»/R)u,. (7) 



.Mso IVI,=o, Ji, = o, because the motion is steady. So we 

 convert (5) to 



k=f. = m, = -M,(h/R)u,, F, = M, = Mi(»/R)aj. (8) 



Finally, although we get no formula for M,, we do 

 obtain a complete formula for M,, viz., 



M, = — fiQ-a/bTrVK-. 



(9) 



NO. 1870, VOL. 72] 



This is the transverse momentum of Q in steady circular 

 motion, without any limitations upon the size of the 

 velocity and acceleration, save the usual ones, >i<v, and 

 a not excessively great in regard to the diameter of the 

 electron. 



It would seem that an integration over the whole field, 

 in which E and H are known (loc. cit.), is required to 

 find M,, the direct momentum. If, however, the acceler- 

 ation is infinitesimal, the known formula for M, in steady 

 rectilinear motion may be employed, viz. ^M^u^T. 



Finally, I have pleasure in saying that Mr. G. F. C. 

 Searle, F.R.S., led me to see that my waste formulae led 

 to the formula (9) for the transverse momentum, by sub- 

 mitting to me a calculation of M, in the special case of 

 infinitesimal acceleration and velocity. He made no use 

 of the waste formula, not being aware of it, but, since in 

 the circumstances the waste is infinitesimal, it did not 

 matter. In fact, 5M,it = T leads to the reduced special 

 value of the transverse momentum when » and a are 

 infinitesimal. The argument became somewhat obscure 

 by the want of comprehensiveness, but the result agrees 

 with (9). Oliver Heaviside. 



August 20. 



A Parasite of the House-fly. 



I SHOULD be very glad if Mr. Hill (p. 397) would send 

 me a few specimens of the Pscudoscorpioncs he has found 

 attached to common house-flies, and 1 will endeavour to 

 identify them for him. There are several genera of this 

 order represented in the British fauna, and it is probable 

 that all the species occasionally attach themselves to the 

 legs or wings of larger insects and arachnids. There is 

 some doubt, however, whether this is a case of true 

 parasitism. It may be that the occasional association of 

 these small arachnids with larger and more rapid arthro- 

 pods is of importance to the species in providing a means 

 for a wider geographical distribution. 



Sydney J. Hickson. 



The University, Manchester, August 25. 



