!70 



NATURE 



years ; and the whole source of confusion lies in the failure of 

 those responsible for the British Associatit>n RejKirls of the time 

 to insert the author's initials— the Allmans having been ap- 

 parently referred to indifferently as merely " Professor " and 

 " Dr." 



While thus my precise statement concerning George James 

 AUman's claim to distinction which is involved must be dis- 

 sociated from his memory, perusal of his published writings still 

 justifies us in regarding him as a scientific botanist of renown. 



It has been pointed out to me that my reference to the late 

 Beete-Jukes might be interpreted to mean that he was a pro- 

 fessor in Trinity College, Dublin ; and, in event of this possi- 

 bility, I would remark that no such idea was intended. George 

 lames AUman was appointed professor of botany in Dublin 

 University, in succession to William .MIman, in 1844 ; resigning 

 the appointment in 1S56. (oseph Beete-Jukes became director 

 of the Irish branch of the Geological Survey in 1S50 ; and 

 during the whole period of George Allman"s occupancy of the 

 Dublin botanical chair, the late Samuel Haughton was professor 

 of geology. The allusion to the late Beete-Jukes wasintroduced 

 into my notes by the kindness of a relative of the late George 

 Tames AUman, and it is inaccurate as concerning the word 

 "" Professor," as I now find to be also the case with the word 

 " Regius " as applied to the Dublin chair itself (which I owe to 

 the obituary notice in the Tinus of November 28, 1S9S). " Pro- 

 fessor" (line 19) and "Regius" (line 18) must accordingly be 

 deleted from my article by those who would make further use 

 of it ; and I would remark that by "Grumera" (column 4), 

 Gunnera is meant. 



My best thanks are due to Mr. Britten, Mr. Griffith, and 

 Prof. Percival Wright, for friendly assistance and advice in this 

 interesting little bibliographic research, the limitations of which 

 I appear to have by no means exhausted. G. B. Howes. 



Royal College of Science, London, S.W., January 9. 



Since the above was written, we have received the following 

 from Prof. AUman. — Ed. 



When writing the above I did not recoUect that my father 

 — many years later — read at the meeting of the British Associ- 

 ation in Dublin (1835) a paper "On the Mathematical 

 Relations of the Forms of the Cells of Plants" (Brit. Assoc. 

 Rep. 1835, partii. p. 79). This paper is erroneously attributed 

 to Dr. George James AUman in the Catalogue of Scientific 

 Papers of the Royal Society of London. — G. J. A. 



January 16. 



The Density of the Matter composing the Kathode 

 Rays. 



The question of the size, charges and velocities of the carriers 

 in the kathode rays has been made the subject of investigation 

 by Prof. J. J. Thomson, Lenard, and others. I do not know 

 whether it has been noticed that, by taking the values which 

 have been obtained for the ratio of charge to mas.s, and for the 

 velocity of the particles, in connection with the observed fact that 

 a shaft of rays from a plane kathode retains its cylindrical form 

 unaltered as it passes across the tube, we can arrive at a limiting 

 value for the mass per unit volume of the matter composing the 

 rays. 



Take for simplicity a uniform circular shaft of charged 

 particles travelling with velocity h. Let the mass per unit 

 volume be /«, the charge per unit volume e, the radius of the 

 section a, and the velocity of light v. The shaft constitutes a 

 current of slrength tu . ira". The magnetic force at the 

 boundary is 



lira 

 If we take unit volume at the boundary, it will be subject to 

 an electro-magnetic force, inwards, 



= H . c:i = 2irae-ir. 

 The same unit volume will be acted upon further by an electro- 

 static repulsion outwards of amount iitath? in electromagnetic 

 units. 



Hence the resultant force on it will be 



Ziiac(v" - »<■■') outwards. 

 Now if f be the radius of curvature of the outer boundary, we 

 have 



= 2itae'\v- - II-), 

 P 



NO. 1525, VOL. 59] 



or the curvature i 



[January 19, 1S99 



<:)'"■ C-0 



We know that this curvature is small. 



Taking the numbers given by Lenard (IVied. Ann., 65, 

 p. 504), we may put, roughly, 



- = 2Trir . 36 . 15 . 10'- . m 

 P 



= ma X 3"4 X 10''. 



Therefore at must be smaller than order 10"'^, whereas thc^ 

 average density in the tube, that of air at the pressure of a frac- 

 tion of a millimetre, is of the order 10*". 



If we do not suppo.se that m and 6- are constant, but take them 

 as functions of the distance from the axis of the shaft, we arrive 

 at the above limit for the average density. 



(Queen's College, Belfast, January 9. W. B. Morton. 



Attraction in a Spherical Hollow. 



Among the papers of the late Prof. Peter Alexander, of 

 Anderson's Medical College, Glasgow, I find the enunciation 

 of an interesting theorem in attraction. " The attraction on a 

 particle of unit mass, in a spherical hollow in a sphere of 

 uniform density, is at all points of the hollow parallel to the 

 line joining the centres of the sphere and hollow, and is of 

 constant magnitude equal to Jirio-K. Where i- is the distance 

 between the centres, a the density of the sphere and k the 

 attraction of unit mass on unit mass at unit distance. ' 



I venture to give the following informal proof. Let A be the 

 centre of sphere which may be supposed to be indefinitely 

 great, and B a particle at the centre •>( the spherical hollow. 

 Then the attr.action on H is towards A, and is proportional to- 

 BA if the hollow be indefinitely small (see Dr. Tarleton's- 

 " Introduction to the Theory of Attraction," p. 13). But the 

 removal of the spherical mass round B as centre in no way- 

 alters the attraction on the particle B. This prove? the theorem 

 for the central point. If the centre of the sphere were at c the 

 attraction on 11 would then be Bc in the same way. Let the 



particle be now placed at c any point in the hollow. Produce 

 CB to meet the hollow sphere at l>. If the spherical hollow be 

 enlarged so that i is its centre and CD its radius, the foice of 

 attraction on <■ will now be CA. Restoring the mass to the- 

 space between the new and the original hollows, subjects the 

 particle at c to an .additional force, equal and opposite to BC. 

 Hence the force exercised on the particle at c in the original 

 hollow is CE, which is par.illel .and equal to BA. 



This furnishes a good example of the theorems {i7i,i., pp. 60 

 and 94), that if one or other the amount or direction of the 

 attraction within unoccupied space be constant, then must both 

 be so. 



There is probably a formal rigid proof of his theorem among 

 my brother's papers. He told me that some practical applic- 

 ation might be made, by having the hollow just touching the 



