February 9, 1899] 



NA rURE 



34i 



hatched embryo wilh its mouth closed, the egg-breaker was seen 

 to form a sharp downwardly directed prominence, projecting 

 freely, and in such a position as to leave little room for doubt 

 that it is the direct agent in rupturing both membrane and shell. 

 It may be added that in the three living specimens in my pos- 

 session all traces of the egg-breal;er have vanished — i.e. in that 

 last hatched within seven days. G. B. Howiis. 



Royal College of Science, London, January 31. 



Attraction in a Spherical Hollovir. 



The theorem of attraction stated by Prof. T. Alexander in 

 N.\TURE of January 19, is a particular case of a more general 

 theorem which I have not seen stated, though very likely it is 

 not new. The well-known theorem of conchts dc glisseiiienl is 

 also a case of it. Imagine two spheres, one of radius r and made 

 of positive or attracting matter of density a, the other of radius 

 1' and made of negative or repelling matter of the same density 

 a, to coexist even if they overlap. In the space common to 

 the two spheres the one kind of matter neutralises the other, so 

 that the space may be considered as empty. The force on a 

 unit particle of positive matter, placed at any point on the circle 

 of intersection ot the two surfaces, is parallel to the line of the 

 centres A, B, of the two spheres and of amount iirff/cc where a is 

 the common density of the spheres, c the distance between their 

 centres, and k is the usual attraction constant. For the positive 

 sphere attracts the particle towanls the centre with a force ^Jircnf, 

 and the other sphere repels the particle from its centre with a 

 force ijTrirKr'. These forces give the resultant ^irff/tt parallel 

 to the line joining the centres of the spheres and from the 

 repelling centre towards the other. 



This resultant force is independent of the radii of the spheres, 

 provided their centres remain at the same distance apart. It 

 follows that the force at al! points within the space common to 

 the two spheres is parallel to the line joining the centres, and 

 has the value just stated. For take any such point P and describe 

 through it spherical surfaces about the centres \, B. The por- 

 tions of the two spherical distributions which lie outside these 

 surfaces exert no force at P. The spheres internal to P give the 

 force \Tr(TKi'. 



If one of the spheres is wholly within the other, we have 

 the theorem of the force within a spherical hollow. It is only 

 necessary in that case to suppose the hollow formed by the 

 superposition of negative matter on the previously existing 

 positive matter, and the result follows at once. 



I may point out that a theorem similar to and including that 

 stated above holds for two overlapping similar ellipsoids, of 

 equal and opposite densities, and having their corresponding 

 principal axes in the same directions, and one pair of these, say 

 the axis of .v of each, in the same line. The centres A, B lie 

 on this Une, and any point common to the two ellipsoids will 

 have coordinates x, j', :, say, when relerred to axes through A, 

 and .r', y, z when referred to parallel axes through B. 



Taking, then, as axes of coordinates the principal axes of 

 each ellipsoid, and considering any point in the overlapping 

 portion, and describing through P about A, B as centres two 

 ellipsoidal surfaces S, S', each similar to the given ellipsoids, we 

 obtain for the components of force on a unit particle due to the 

 positive (say) matter of uniform density <r filling S, the values 

 A,.r, A.J', A.jZ ; and for the components of force at the same 

 point due to the negative matter filling S' the values 



- A,.v', - A,)', - A3- 

 where Aj, A.,, A3 are certain integrals which are here constants. 

 The portions of the two ellipsoids external to P exert no force 

 at P. Hence the resultant force on the particle at P is 

 A,(.v - .v'), that is, it is parallel to the line joining the centres, 

 and proportional to the distance between the centres, and acts 

 from the centre of the repelling towards that of the attracting 

 ellipsoid. 



If the coordinates of B, relatively to the axes through A, be 

 a, 6, I, so that there is not a pair of corresponding axes in line, 

 the components of force in the overlapping space are A, a, A.^^, 

 A3C. The force at every point is \IA{-a- + A./*- -|- A3-V', and 

 is therefore fixed in magnitude and direction. 



With reference to the magnetic experiments, it may be re- 

 called that if within a uniformly magnetised ellipsoid there 

 exist a similar ellipsoidal hollow, with its axes parallel to those 

 of the magnetised ellipsoid, the magnetic force within the 

 hollow is zero at every point. A similar result holds, of course, 

 for a sjihere. Andrew Gray. 



NO. 1528, VOL. 59] 



Larvae in Antelope Horns. 



I HAVE read with interest the communications of your corre- 

 spondents on " Larvce in Antelope Horns" in Nature of 

 September 15, and also another note on the same subject in 

 7'/tL' Entomologisl of July last ; but Nature of June 9, for some 

 reason or other, has not reached me. 



As for many jears past I have been travelling and residing in 

 Central Africa, have shot large and small game, and have made 

 large collections of the heads of buffalos and antelopes, I have 

 thought that it may be worth while to record my own observ- 

 ations in this matter. 



Is it the fact, proved beyond all doubt, that the larvae in 

 question are those of Lepidoptera and not of Coleoptera ? 



My own experience is that, unless preventive measures (such 

 as I am about to describe) have been taken in the first ins'ance, 

 the horns of my specimens become infested with the larvte of 

 what I have hitherto believed to be two small species of 

 Coleoptera— ihe one and smaller of bright metallic-green through- 

 out, the other and larger of dull coal-black above, and white on 

 the underside — which larv* eat their way up and through the 

 horns, throw out cocoons, and continue doing so until the horns 

 are destroyed, leaving nothing but the cores. 



If the heads have been neglected, and left in the open — say 

 either on the ground, or in a tree — the larvae very soon develop 

 and commence their depredations, all the sooner if the heads 

 have been left with the skin and flesh on. 



If, however, these last be removed within a few hours after 

 the animal has been killed, and the bases of the horns and their 

 cores be carefully lathered over with strong arsenical soap where 

 the skin has been cut away from round the horns, and between 

 these and their cores as far up as the hairs of the brush will 

 reach, the! larvae do not develop; and heads thus treated, if 

 properly housed, henceforth enjoy absolute immunity from 

 them. 



I have a collection of antelopes' heads treated in this way now 

 at Machako's, and though of all ages up to ten months old, 

 there is not a perforation or a cocoon in any one of them ; 

 whereas, on the same station, I have noticed that the horns 

 collected by other officers, and not properly cared for, become, 

 most of them, after a time, simply perforated and woolly with 

 cocoons. 



Should the larvre have established themselves, they can readily 

 be killed by pouring paraffin into the horns, and leaving these on 

 end for a day or two so as to retain the oil. 



Never once have I remarked these larva; in the horns of a 

 freshly-killed animal. 



I have, however, occasionally found the larvae of Diplera in 

 the flesh of some antelopes — notably so lately in Masailand in 

 the case of a fine male Grant's gazelle, whose body, otherwise 

 in first-rate condition, after being skinned, presented the 

 spectacle of being ' ' flicked " white with larva; about the size and 

 shape of barleycorns, at intervals of two inches or so. 



A propos of the destructive little Coleoptera once more : — 



On landing in England from Africa in the spring of 18S4, I 

 was at Euston, and amongst my battered and travel-stained 

 baggage on the platform was a large truck-load of bufialos' and 

 antelopes' heads. As I was standing talking to one of my 

 brothers who had come to meet me, an old gentleman, who had 

 lieen narrowly inspecting the load of heads, suddenly stooped 

 down, and concentrated his gaze on one particular spot : then, 

 fumbling in the pocket of his tail-coat, he produced a pill-box, 

 and dexterously boxed something from one of the buffalo heads. 

 It proved to be one of the green beetles ! 



Then turning, and realising that I must probably be the 

 owner of the heads, he politely raised his hat and apologised for 

 what he had done, adding that he had taken a species of 

 Coleoptera which — I think he .said — was new to him. 



I lost no time in assuring him that no apology was necessary, 

 that the obligation lay on my side, not on his ! 



Mr. Lionel Crawshay, my brother (whose address is Brasenose 

 College, Oxford), can, I think, show you specimens of the green 

 beetle, and possibly of the other as well : if not, I shall be very 

 pleased to send you a series of both ; as also, if you wish them, 

 specimens of horns perforated by the larva; and with their 

 cocoons attached. Richard Crawshay. 



Simba Camp, British East .\frica, November 29, 1S98. 



P.S.— As an afterthought, I am enclosing you 2 specimens of 

 the green beetle 2 specimens of the black beetle, and 2 larva;, 

 which I hope will survive the post. R. C. 



