:66 



NATURE 



[August 15, iSg; 



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 -jiith the writers of, rejected 

 manuscripts intended for this or any other part of NATURE. 

 No notice is taken oj anonvmoiis communications.'] 



The University of London. 



Sir John LibbolK does not seem to me to appreciate in the 

 smallest degree the facts of the position. 



His projKJsal is, as I and others understand it, that the result 

 of the labiiurs of the Staluior)- Commission " should be sub- 

 mitted to Convocation for their approval, to be signijiid as at a 

 senatorial election." 



The words which I have placed in italics propose a new 

 pnxredure which I presume would have to be provided for in the 

 Act. This is what for the sake of brevity has been called the 

 referendum. 



Kor reasons which I have sufficiently set out in my former 

 letter I think the institution of the referendum extremely 

 undesirable under any circumstances, and peculiarly open to 

 objection in the present instance. 



But I think we are now entitled to ask Sir John explicitly what 

 he means when he says " it is the law at present," and that his 

 " constituents highly value this right." In so grave a matter it 

 is difficult to Iwlieve that he is indulging in a mere logomachy, 

 or that he means seriously that the veto exercised under existing 

 conditions and the new referendum are one and the same thing. 



f he meaning of the whole business is, of course, verj' simple. 

 Convocation, in common with the Senate and practically every 

 bo<ly interested in the higher education in London, has expressed 

 its approval of the Report of the late Commission as aflbrding a 

 fasis for the reorganisation of the University. .\s Convocation 

 is not to Ik- moved from its decision expressed in the customary 

 and constitutional way, the leaders of the minority, mainly 

 drawn from the Faculty of Laws, have induced Sir John Lub- 

 txxrk to suggest a fundamental change in our iJrocedure. The 

 hope, of course, is that by this means a different result may be 

 manipulated. I say " manipulated " because I entirely agree with 

 Mr. .\. \V. Bennett, who in his admirable letter clearly indicates 

 the kind of tactics we may expect. .\s the avowed object of the 

 whole scheme is to set aside and nullify the action which Con- 

 vocation has taken, I do not think that the language in which I 

 descriljed it is in any way inappropriate. 



Sir John may be as polite .-is he likes to our intelligence. But 

 what he has done is to constitute himself the instnnnent of those 

 who would destroy the prosiK-cIs of academic study in London, 

 and of making the University of London a belter mechanisn) for 

 the purjiose for which it exists. .\n<l this is not what we hati a 

 right to expect of Sir John Lubtwck. 



Kew, .\ugust 10. \V. T. TillsEi.rox-DvER. 



Note on Quaternions. 



On reading Cayley's fanunis memoir on matrices,' I have 

 noticed in passing that in .Mc.\uley"s- notation we may write 

 in general, 



^"' = V)\ogm, ip"^ — I) log///; 



1^ = I)///, 



^' = Dm ; 



,..(.\) 



^Dlog /// = ^Dlog /// = iji 'D/// = i(("'D/// = L 

 «' « <»' 4 



^^ ■ n invariant of ip, which being the original linear 



<)i is Ilamillonian inverse function, and I is 

 ■r ; they are respectively defined by 



mS\fiv = HtpK^fi^v = Sp'K^'fi'p'v, 

 4i = nip'\ Ip = p. 



Indeed, we may prove the above relation by the variation 

 formula, 



i(> = - (,),S».;.(:i),i. 



3 " L'tilily (if (^u.ilcrnion*, fie," 



3 I cannot refer to llic jiauc, n* I h.'ivc not (he book in hand. 



Sm = - /«,S5^fn,f = - SSp(DmC= - S5(J>fi(,'C 

 * «• 



= - SS<>/^^'/ - S5()>/'^^/ - S5<^k\(i'k 

 = - SSipiipjpK - SS<Pj<pK<pi - SS<pK<piip/ 

 = — SS^i^JipK = 5///. 



If W be any scalar function of (p, and if its independent 

 variable be /// (as it is so in some cases of the problems in 

 elasticity, where /// is the volume-dilatation), we might dispense 

 with the notation D, for we may write in general, 



DW = — +' (B) 



* dm 



-Vlso, if tj be any quaternion function i>f <p, and if its inde- 

 pendent variable be ///, we have again 



JQ = - '^^hip^'C \0 



dm 



For, beginning with Mc.\ulcy"s form, we have 



5(1 = - (3,SS0fD,f = - '-^'S5.fif f 

 ^ am 



= - ^lSS<pi\fi'i + SSa/i^/V + SS(f)Kf k] 

 dm 



= ^5/« = 8(). 

 dm 



SiH'NKicni Ki\iii;\. 

 Japanese Legation, The H.igue, Jidy i6. 



To Find the Focal Length of a Convex Mirror. 



Till-; following method is so much simpler than those ordinarily 

 used, that it may be of interest to your re.iders. 



Use as ol)ject an opaque screen with a hole and pin-point, and 

 painted w hile, or covered with « hitc paper. 



Set up on the bench in line, say, with the left edge of the hole, 

 the convex mirror and an auxiliary biconvex lens of short focal 

 length (six inches or so), and adjust the lens so that the image of 

 the hole and pin-point is formed side by side with tlie object. The 

 centre of the mirror is now at the point at which the image 

 would be formed by the lens alone ; this position may either be 

 calculated or found (after noting the position of the mirror and 

 then removing it) by means of a screen. Thus the radius is 

 easily measured. 



If the focal length of the mirror be greater than / that of the 

 lens, the simplest way of adjusting is to put the lens as close as 

 possible to the mirror, put the object at principal focus of lens, 

 and move the object back until the image is formed as above. 



If, however, the focal length be less, we can be sure of linding 

 the position by putting the mirror at a distance of 4 / from the 

 object, and the lens at 2 /, and moving the lens back until the 

 desired jiosition is reached. 



The following is a simple way of making a direct measure of 

 the focal length of a concave lens: — 



Use an object like the one mentioned above, an auxiliary con- 

 vex lens (say six inches focal length) to produce a ccmvergent 

 Ix'am, and an auxiliary plane mirror, placed beyond the concave 

 Icn.s. 



.\djusl imtil the image is formed side by side with the object 

 as before, then the rays must be emerging parallel to one 

 another from the concave lens, ami hence the convergent beam 

 from the convex lens will (when the concave lens and mirror are 

 removed) form an image at the principal focus of the concave 

 lens. .\ direct measure can thus be made of the focal length. 



I may arid that both methods are very simple in practice. 



Grammar School, M.-iccleslield. ICdwin H' hiun. 



Oceanic Islands. 

 I r is lo be hoperl thai in the i>rogramme of the present govern- 

 ment a place will be found for an item hundile and unimportant 

 in the |>olitician's eyes, but to the biologist of the ulmost 

 urgency- the sending out of a scientific expedition or expedi- 

 tions lo sludy the fauna ami llora of oceanic islands before ihey 

 are exterminated by continental imporlaliims. Let it be granted 

 thai men of science are busy with problems of even greater 

 interest than those which such expeditions might help lo >olve. 

 But aniirng all the ambitious aims of science, it wrnilil be hard lo 

 find one to which rlelay would be more ruinous than lo this -the 



NO. 1346, VOL. 52] 



