old numbers came on the waters for want of food. of the greatest delicacy.

coasts they would probably die in our And this sustenance was evidently one Full-grown pilchards have been known to feed up to yielding from three to seven gallons of oil to the hogshead of 3000 fish when having their fill of it. Their food was young Crustacea,, and evidently was the larval forms of some crab or crabs which live on our coasts.

I think a few words will make this plain; in considering the great crab-Cancer pagurus-in the sea, the sexes stand in relation to each other of about one male to eight or ten females, the latter spawning from one to two million eggs. These, when hatched out, pass through several distinct larval changes in the surface of the sea before dropping down on the sea bottom. Creatures having such vast procreative powers, when all the conditions of life are favourable, must produce more young than are wanted to make up for the wear and tear of the race; hence in our first outlook we seem in danger of having a plethora of crabs. But Nature, true to herself, has a police force at hand to prevent overcrowding. This is found in the pilchard, who attacks the crabs in the surface of the sea when in their zoe forms; while at the sea bottom, if they are yet too plentiful, those powerful skates (Raia batis and Raia lintea), with their long, sharp, hard noses, make their appearance among them, routing them out of their hiding places among the rocks, and with their powerful jaws and teeth making short work with these crabs.

Hence, in the olden times, when there was no demand for the female crab, even at sixpence per dozen, and when they lay off our coasts in millions, and again throwing off their countless millions of eggs, there was seldom any lack of either large or small pilchards in our bays in the summer months of the year.

But since the extension of the railway systems throughout our land, and the demand came for all the crabs, not only have the large pilchards been scarcer, but they have so fallen off in condition as not to yield above one gallon and a half of oil to the hogshead, and the French sardine-sized fish has disappeared altogether.

It is certainly very satisfactory at this date to know that Mr. Cunningham has found them in their new haunts further out at sea; and that he has also verified the facts of the size and the ages of the pilchards given in my exhibits at the Falmouth Polytechnic so long ago. MATTHIAS DUNN.

Mevagissey, Cornwall, March 22.

On the Boltzmann-Maxwell Law of Partition of Kinetic Energy.

IN the very valuable Report on Thermodynamics drawn up for Section A of the British Association by Messrs. Bryan and Larm r, and now recently published, there is a remark upon the Boltzmann-Maxwell law of partition of Kinetic Energy, upon which I should like to be allowed to make a few comments. The Report says, in fact, after noticing the attempts to extend the theorem from the case, originally contemplated by Boltzmann, of molecules composed of discrete atoms under mutual forces, to the general case of dynamical systems determined by generalized co-ordinates: It has now been proved beyond doubt that the theorem is not valid in this general form; and quotes as a test ca e a paper by Prof. Burnside to the Royal Society of Edinburgh, on the collisions of elastic spheres, in which the centre of mass is at a small distance, c, from the centre of figure. In this paper, doubtless, results are arrived at, after a vigorous and able treatment, inconsistent with the law now under consideration; but there is, I think, an oversight, pointed out by Mr. Burbury in a paper recently read to the Royal Society of London, which vitiates these conclusions and leaves the matter where it was before.

Prof. Burnside, in fact, has omitted to introduce the frequency factor of collisions in proceeding to take his average, so that, whether his result be correct or not, for the average of all possible collisions, it is not correct for the average of all collisions per unit of time, and it is this last which is important for the test of permanence of distribution.

When this frequency-factor is introduced and the approxima

The process is somewhat intricate, and too long for insertion here.

I should like to make a few additional remarks on a view expressed by Prof. Burnside, which is doubtless widely, but I think not quite reasonably, shared by many eminent mathematicians, to whom this theorem of partition of Kinetic Energy is a stumbling-block.

He says, in the paper referred to, "The method of proof adopted by Watson, following Boltzmann, is so vague as to defy criticism or attempts at verification," but I really think the vagueness consists in the generality of the conclusion and not in the method of proof. To establish a proposition applicable to all conceivable cases of collision, either in a field of no force, or of forces of any kind, requires a method of proof which, whether true or false, must of necessity be as general, or, if you please, as vague, as the conclusion; but, in point of fact, Boltzmann's method adapts itself readily to every case which, like this of Prof. Burnside's, admits of practical treatment. For example, in this very case of the colliding spheres with centre of mass distance (c) from that of figure, Boltzmann's method would assume that the number of spheres with lines of centres in any direction, and with component velocities of translation of C. G. and of angular velocities round the principal axes lying between u, u + du, &c., &c., wg, wz + dwg, was

( u, v, w, w1, wy, wz) du . . . dwz.

Suppose, then, the circumstances of the two spheres to be distinguished, as in Prof. Burnside's notation, by the great and small letters, U, u, &c., î, w, &c., and let the corresponding dashed letters denote these respective quantities after collision. Then, as proved in Prof. Burnside's paper, we have2U + c2(K + k)u +2cw

U'

=

=

2u+c2(K + k)U – 200

2 + c2 (K + k)

20 P

A

.

U-u+ca

2+c2 (K+ k)'

U-u+cw 2+c2(K+ k)'

B 2cR U-u+cw C 2+c2(K+ k)'

=

.

3) du

da3 (U

D's) du'.

pu'... w'z)p(U' . . dî'z (U' — u' +ca"), because, when this condition is satisfied, and only then, can the average number of spheres with velocity components in the undashed state and line of centres parallel to the x axis (which may be any direction), be equal before and after collision, inasmuch as those in the dashed state with velocities reversed enter into the undashed state.

In determining the multiple differential du... dig, we may neglect the consideration of the resolved velocities in the tangent plane, v, w, V, W, inasmuch as they are unaltered at impact, and we have to evaluate the quantity

:

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 cases, 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 vagueness 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 Boltzmann-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 n squares, as P12, P2, 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(u2 + v2 + w3) + Aw12 + Bw122 + Cw22,

P,

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 colliding 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 Boltzmann-Maxwell law of partition will be found to hold

is very largely due to compulsory Greek. Anent this, all that I said was that the danger of a Pagan revival was the best argument for compulsory Greek; I did not say it was a good argument. 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 expe ted to waste their time in making cripples run-that is what College teachers and private coaches are paid for doing. Some Universities, 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 at 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. FRAS. FITZGERALD.

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.

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 denominational 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

me to give in these columns 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 Entomologist, 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 acid; 45 p.c. sulphuric; strong acetic; strong ammonia; following reagents: strong hydrochloric acid; 50 p.c. nitric 25 p.c. potassic hydrate; and 10 p.c. sodic hydrate.

1 April 1890 to September 1891.

First of all, I must draw attention to a very important distinction between colours and colours. It is, of course, clear that a colour may be due either to a pigment or to the physical structure of the coloured body; and it was therefore very necessary for me to find out, so far as possible, which of the colours I might have to deal with were physical, and which pigmental. With regard to some of these, it could tolerably safely be conjectured-merely from the appearance that they were simple physical colours; in such cases, I mean, more especially, where there was a distinct sheen or glow in the colour; and I have been able to confirm various conjectures that had previously been made, both by others and myself, as to these physical colours. But in many other cases-indeed, in the majority-nothing but experiment could decide the question; and in some instances the decision has been as unexpected as disappointing to me. In order now to classify the results that I had obtained, and to introduce as much order and method as possible into my explanations of them, I have already ventured to propose1 the following scheme of colours: (1) pigmental colours; (2) interference colours, which include a very large number of insect examples, besides, of course, the iridescent colours displayed by the wings of dragon-flies, May-flies, &c.; (3) reflection colours, other than the interference colours these will be found to include all the whitewinged species that I have examined; and (4) it seems necessary to have a class of simple absorption colours, in order to include all those cases of black in which no pigment can be found, but, apparently, all the light-rays are absorbed in a dense coating of scales.

The limits of space at my disposal compel me to pass over the colours black and white with the remark that as to the former, with one or two dubious exceptions, it can be affected by no reagents, and I have, therefore, concluded it to be not pigmental, but simply a "physical" absorption colour; full details as to this will be found in the Entomologist. As to white, I have similarly failed to find any pigment, or to obtain any reaction, except with Melanargia galathea, and two or three white-fringed species; in these instances the white is changed to a deep yellow, which presently dissolves in the reagent. The explanation of this I must defer until the phenomena of yellow have been discussed. For the rest, white is evidently simply a reflective colour, and not pigmental. We now have to consider in succession the five colours blue, green, red (and pink), yellow (and orange), and chestnut; and, first of all, I must recur to what was said above on the criteria of physical and pigmental colours. Referring my readers to the condensed tables of results, given at the end of this article, I think-as the results of what I have been able to learn from my experimentsthat the following rules may be laid down. There are certainly two ways in which a pigment colour may be affected, and either effect is conclusive evidence of the presence of a pigment. Firstly, the colour may be dissolved out; the liquid is left more or less deeply coloured, and the wing is white, or colourless.2 This is the case (vide tables) with all the yellows and chestnuts that are sensitive at all to the reagents, and also with the pigment greens in most instances. It is very important to observe that this change from a yellow or chestnut wing to a white one does not imply any change from a yellow pigment to a white one-as might at first be supposed from merely glancing at the records in the tables: it is not so. The change is due simply to a solution of the pigment, which has originally been developed, not from a white pigment, but in a white, ie. previously unpigmented, wing. It will be necessary to refer to this again later in discussing the behaviour of A. galathea. It is scarcely necessary to point out how important a bearing the inter

Entomologist, September 1890.

pretation of such results has upon our view of the nature of white.

To proceed: the second criterion for pigment colour (and this, it is needless to say, cannot concur with the former) is what I have denominated the "reversible" or "reversion" effect; and this I have found only in the case of red, which, I may observe, is out and away the most satisfactory colour to experiment upon. In these cases, the effect of the reagents (but chiefly of the acids) is to convert the red colour into a fine yellow or orange, from which the original red can be completely recovered by appropriate means, as will be explained in due course: here, again, there is indubitably a pigment in evidence. In some cases, however, where there is neither solution nor any "reversion" effects, but yet a (sudden) change from the original colour, it is extremely perplexing to decide whether we have to do with a pigmental or with a physical colour. Instances of this will be found in the tables, among the greens (e.g. Argynnis and Thecla) and the blues (e.g. the Lycanida). In such cases I have not ventured to pronounce definitely in favour of either view, although it appears to me that the evidence is strongly in favour of such colours being simply physical. I do not think that there is the least difficulty, theoretically, in supposing such reactions to take place with mere physical colours; since the wingsurface, when soaked-even by an indifferent or neutral fluid-might well be so affected, at least temporarily, as to alter its reaction in the light rays, i.e. to alter the resulting colour. In such cases, then, we have an element of doubt to contend with.

Then, as to undoubtedly physical colours, there are certain blues and greens which, when examined with the naked eye even, can be seen to be, not a continuous patch of colour, but a mass of so to speak-distinct dots. Speaking now on the strength of my experience with such, I think I am justified in stating that these may safely be pronounced off-hand, without experiment, to be physical. When such colours are tested with the reagents, they may either be entirely unaffected, or the colour may disappear, but reappear (usually quickly) on drying. It may prima facie be retorted, and not unreasonably, that these should be considered pigment colours showing the reversion effect; but-as will be seen after the reversion effect of red has been described— there is really no similarity at all; and there can scarcely be a doubt that these are merely physical colours.

Again, a brilliant metallic-looking colour may bẹ changed to a different colour, or sometimes to a dead brown or blackish (vide tables: green), and this effect may be either temporary or permanent; and yet, from the general appearance of the colour before and after the experiment, one may feel thoroughly assured that it is only a physical colour. And lastly, in such cases, a brilliant blue, e.g., may be unaffected by most reagents (or only temporarily so), whilst such a reagent as nitric acid or potassic hydrate may permanently dull or destroy the colour. This is perfectly intelligible, since in such cases the powerful reagent has no doubt damaged the surface structure. I have thought it only right and fair thus to outline the data on which my conclusions concerning the nature of these colours have been founded,

One or two instances have recently been noticed of partial reversion of a colour originally reddish-brown among the Bombyces These seem to be connecting-links between yellow and chestnut descended colours (see later). 2 Facts in support of this view will be quoted in their proper place. But I may be allowed to say that one's judgment in such cases must be partially founded on observation of appearances and conditions that in their nature do not admit of being described or formulated, but appeal to an observer who has learnt by experience to interpret such indications. It will therefore be understood that, throughout this article, the actual evidence for my conclusions is apt to be somewhat discounted when the attempt is made to briefly convey it in words.

plained under "chestnut," infra.

although feeling that it is very difficult indeed to convey, merely by a brief verbal definition, the practical distinctions that one has slowly learnt from experience to recognize. We will now take each of the colours in detail, although, after this general account of the behaviour of physical colours, there is not much left to say of blue, or even of green.

If now the tables of results be referred to, it will be seen that I have arranged the blues in five different groups; but the differences between the first three-or probably four are so slight that they might almost as well be thrown together. It is, however, somewhat convenient to consider them apart. In the first group the blue is a magnificent velvet blue, with a rich glow. Primâ facie, it is evidently a physical colour (as Wallace, e.g., had pointed out years ago), and its behaviour when tested with reagents leaves no doubt of this. Reagents either are without effect, or cause a temporary dulling which disappears on drying, or plainly and permanently injure the wing, and destroy the beautiful glow or even the colour entirely. In cases of merely temporary dulling, where the full colour returns on drying, I believe that the effect is due simply to the soaking of the wing, and that neutral liquids would produce the same effect. The second group, after the explanations I have already given and the information that I have tabulated, requires very little comment. The various reactions abundantly showed that all these are simply physical (interference) colours. The third group are hardly distinguishable from the second the behaviour of the blue on P. machaon when wetted with a reagent and then dried, is an excellent example of such physical colours as were referred to above. Now, concerning the fourth group, which in all probability should be considered as one with the three foregoing. I presume that most people are familiar with our beautiful and common Vanessa butterflies, the "Peacock," "Admiral," and "Tortoiseshell," and know that the borders of the wing are marked in the two latter (as well as in the "Camberwell Beauty") with spots of blue, while in the " Peacock" there are magnificent blue ocelli. The position of many of these marks strongly reminded me of the special positions of blue in various flowers; and at the commencement of my experiments I was in great hopes of discovering a blue pigment in these l'anessa; but after repeated experiments I was driven to conclude it almost certain that the blue here is simply physical. Its reactions throughout indicate as much; since, on being treated with the reagents, it either is wholly unaffected; or it disappears, but returns on drying; or it pales to a sort of grey that resembles the effect produced in the species of the third group; or lastly, it may in some cases disappear entirely, as I have already pointed out that some physical colours may. Finally, we have in the fifth group, containing the little blue butterflies of the family Lycanida, the only instance I have found of a blue not certainly physical, and even here the evidence is, I think, in favour of a physical colour. The question, however, is an unusually perplexing one; and for a long time I supposed that these were pigment blues, but I am very doubtful about them

now.

There is no solution, and I have no evidence of any reversion effect; the colour is changed certainly, and it is rather significant that in several of the deeper coloured species the artificial colour thus obtained is nearly identical with the normal colour of P. corydon; but such changes in no way preclude the colour being physical. The fact, too, that in several instances the effect was to produce a green or greenish tint now appears to me very suspiciously indicative of a physical colour (cf. Papilio polyctor in group 2). I may add, too, that the reaction of the green in the closely related "Hairstreak" butterfly, Thecla rubi, which I think is in all probability physical, must also be taken into account; for the reaction

Vide, or instance, Grant Allen's "Colours of Flowers."

in that instance is similar in general character to that of these blues.

To sum up, then, the case for this last group of blues, it seems to me that we cannot certainly conclude them to be physical, but the evidence points very stongly to the view that they are-like the other blues-physical and not pigmental. Should this conclusion be correct, I have as yet found no instance of pigmental blue among these Lepidoptera.

We will now pass on to green. It will be seen that in the tables I have divided green into three groups; of these, the first are unmistakable physical colours, exactly analogous to the group of metallic blues, and it is therefore unnecessary to comment further on them. The second group, though not metallic, are nevertheless, I believe, also simple physical colours. Not only can I say of them what was said of the blue Lycanida-that there is not the slightest evidence for any pigment; but I may go further, and say that there is some evidence for the green being physical. The striking characteristic of this group is that every reagent instantly turns the green to a brown or bronze brown, which reaction might, as far as it goes, equally betoken either a pigment colour of the "reversible" nature, or a mere physical colour. That it is of the latter nature is indicated both by the fact that I have observed, no true reversion effect (always defining this reversion effect by the standard example of red), and also since it is possible to produce a similar, though only temporary, transformation by pure water or by alcohol. This, I think, makes very strongly indeed for the colour being simply physical, loth as I am to recognize that the magnificent and interesting greens of such species as the Argynnis fritillaries, and Thecla rubi are unpigmental. Still, my final conclusion, after prolonged and careful consideration, is that these colours are simply physical.

Coming now to the third group of greens, we have here undoubtedly pigment colours, showing the solution effect. There are various degrees of solubility among them, and a varying sensitiveness to different reagents; but the summary, in brief, is that the green pigment is dissolved out, leaving a white, i.e. unpigmented, wing. Here, again, I need merely repeat what has already been said of yellow, and will again be referred to, viz. that the (green) pigment has been developed, not from a white pigment, but in a white, i.e. unpigmented, wing. A further question, however, arises-whether green has been directly evolved as such, or is a second stage in the coloric evolution. If the table be examined, it will be found that in several cases the green has been transformed to yellow or yellowish; and this has occurred too commonly to be otherwise than significant. I am therefore of opinion that green has been evolved from yellow, and that the production of yellow in these cases under the influence of the reagents is a retrogressive metamorphosis comparable with the production of yellow from red. The evidence admittedly is not anything like so conclusive or copious for the inference of this derivation of green, and I should, perhaps, hardly have advanced this view but for the analogy to the standard behaviour of red. As it is, however, it seems to me incumbent to hold--at least provisionally-that these pigment greens have been evolved from yellow. It is, however, very evident as will appear from the following discussion-that the respective relations of green and red to yellow are very different indeed, although there be a community of descent. may be well to point out also that these greens occur in three very different groups of the Macro-Lepidoptera, viz. in the Rhopalocera, the Noctuæ, and the Geometræ. The apparent exception of Cidaria will be referred to later; it

It

I It is especially interesting that in T. rubi this brown is the same as the usual ground colour, constituting the greater part of the wing surface. 2 A discussion in somewhat greater detail of this group indeed, of the greens in general-will be found in the Entomologist for May 1891. 3 Cp. also Entomologist for May 1891.