March 31, 



1892] 



NATURE 



513 



It will be found that the determinant is equal to 



Also 



(2 



U 



c\k + K))8 

 - (U' - u 



c-ar'), 



whence the condition of permanence becomes 



(/>(« . . .«3)<p(U . . . Hj) = <l>{u' . . . co's) - (f.(U' . . . n'3) ; 



a condition which is satisfied when 



(p = m{u^ + v"^ f if^) + A«i- -r.Baij." + .Cci>3-. 

 A simpler case of verification, involving exactly the same 

 principles, is obtained by replacing the spheres by circular disks 

 confined to one plane. Here there will be only 6 co-ordinate 

 velocities, u, v, w, U, V, n, and the notation may be preserved as 

 before, only 



= ?■', k = ^; 

 A A 



w = Pn + /ft 



and neglecting v and V, the velocities resolved in the tangent, as 

 before, we have, now, the factor multiplying the determinant 



I 



reduced to 



and the determinant to 4 rows 



{2 + f--»(K + k)\ 

 and columns instead of 8, which will readily reduce to 

 -(2 + c2(K + k)Y. 



There is, therefore, really nothing vague in Boltzmann's 

 treatment : all that it does is to show on general dynamical 

 principles that the functional determinant must be unity in all 

 ca^e-;, and therefore avoid the labour of evaluation. 



What has been thus done for the collisions of heterogeneous 

 spheres and circles may be equally well done by the application of 

 the Boltzmann method to colliding systems of any number of 

 degrees of freedom ; it will be found that there is no vague- 

 ness in the process, although, of course, the analytical difficulty 

 may be greatly increased with the circumstances of different 

 cases. And what I understand to be the meaning of the Boltz- 

 mann-Maxwell law of partition of energy will, I believe, be 

 found to be true in each case. I understand that law to assert 

 that when the kinetic energy of each system has been expressed, 

 as it always can be, as the sum of it squares, as V{-, Pj", . . . P«-, 

 each of the P's being a linear function of the « generalized 

 velocity components, the average value of each of these squares 

 is the same in the special or equilibrium state. For example, 

 where the system is a single rigid body with 6 degrees of freedom 

 and twice the kinetic energy is 



M(m2 -f v"- + 7a") + AftJi" + Bo)./ + C«3", 

 the average kinetic energy in the special or equilibrium state 

 contributed by each translation is ^ of the whole, and the 

 average kinetic energy contributed by each rotation component 

 is the same. It does not appear to me that the law asserts 

 more than this, or that any application that has been sought to 

 be made of it requires anything more than this. 



These conclusions are confirmed by Mr. Burbury in the paper 

 to the Royal Society already mentioned, and by an entirely 

 independent treatment. 



I have purposely limited myself to the consideration of collid- 

 ing elastic systems treated by the conventional laws of impact, 

 because one such case had been specially singled out in the 

 British Association Report, and I believe that in all such cases 

 the Boltzinann-Maxwell law of partition will be found to hold 

 good. The most general cases contemplated by Boltzmann and 

 Maxwell, involving the considerations of forces between parts of 

 the molecules themselves, with continued interchange of Kinetic 

 and Potential Energies, as well as intermolecular and external 

 forces, demand further space than could reasonably be asked of 

 you. H. W. Watson. 



Berkeswell Rectory, Coventry, March 21. 



is very largely due to compulsory Greek. Anent this, all that I 

 said was that the danger of a Pagan revival was the besi argu- 

 ment for compulsory Greek ; I did not say it was a ^wrf argu- 

 ment. About going to Colleges and Universities, I did not say 

 that the student should go to a College and not to a University, 

 if he ever had time and ability to benefit by University training. 

 Very few can do this, hardly any undergraduates ever do ; and 

 what I deprecate is that University Professors should be expected 

 to waste their time in making cripples run — that is what College 

 teachers and private coaches are paid fordoing. Some Univer- 

 sities, as, for example, that of Dublin, are too poor to pay 

 double sets of teachers, but that is their misfortune, and should 

 not be a precedent for a rich country like England, nor for the 

 wealthiest city in the world, like London. 



As to Prof. Ayrton's forgetting the debt due to those who 

 studied useless subjects, I chode him for it because he sneered 

 at useless subjects. If he still sneered Ft useless subjects, I 

 would chide him still, even though he whited his prophets' 

 sepulchres by using the whole scientific hierarchy to name his 

 units after. As to my forgetting the debt due to the practical 

 applications, my letter was too short to include everything in it. 



Anyway, I entirely agree with Prof. Ayrton that the business 

 of technical schools is to teach useful knowledge, and further, 

 that the enormous majority of mankind are most fortunately 

 employed in doing useful things, and should not be asked to 

 waste their time on trying to do useless ones. 



Geo, Eras. FitzGerai.d. 



The Functions of Universities. 



As it is most desirable that students of all classes should, as 

 far as possible, be in contact with one another during the 

 impressionable years of training, it is eminently desirable that 

 schools of engineering should be connected with Universities. 

 It is distinctly contrary to public policy that the present denomi- 

 national education of students of different professions in special 

 seminaries, whether they are ecclesiastical, or medical, or 

 engineering, should be encouraged. The existing separation of 

 professional and commercial education is most mischievous, and 



NO, TI70. VOL. 45] 



A New Comet. 

 In last week's Nature (p. 484) I announced the discovery of 

 a new comet on March 18, and an editorial note was appended 

 to my letter as follows : " This is stated to be Winnecke's 

 comet." Will you kindly allow me to point out that this state- 

 ment is based on a misconception, for the two comets alluded to 

 are situated in widely different regions of the sky, and cannot 

 possibly be identical, as a comparison of the following positions 

 will show : — 



March 18, 1892. 



R. A. Decl. 



Winnecke's Comet 191° ... + 31° 



Denning's Comet 341 ... +59 



Bristol, March 26. W. F. Denning. 



P.S. — The following is an ephemeris of the latter comet 

 computed by Dr. Birdschof for Berlin midnight : — 



R.A. Decl. Light. 



The comet reaches its perihelion on May 12. 



W. F. D. 



ON INSECT COLOURS. 



■T^HE Editor of Nature has been so kind as to invite 

 ■*■ me to give in these cokiiTins a short summary of 

 certain investigations that I have been for some time past 

 engaged in, upon the behaviour of various insect colours 

 when tested by chemical reagents. A full account of 

 these experiments, of the methods of working, and of 

 the reagents used, has been published in the Entomo- 

 logist,^ to which journal I must refer my readers for any 

 details that they may desire. Here, space will allow me 

 only to give in a condensed form the broad results. It is 

 necessary to say, however, that the remarks in this article 

 have reference only to the colours of the Lepidoptera ; and, 

 further, of the imagines only. The experiments have 

 been made by immersing the wings for one hour in the 

 following reagents: strong hydrochloric acid ; 50 p.c. nitric 

 acid ; 45 p.c. sulphuric ; strong acetic ; strong ammonia ; 

 25 p.c. potassic hydrate ; and 10 p.c. sodic hydrate. 



I April 1890 to September 1891. 



