assure him (or it), however, that the omission has been in no way connected with those "queer notions of honour, and justice, and fairness," which he conceives to be rife in our times. Why should I seek to wrong the honoured dead? And who would gain in this case by the injustice? The present Astronomer Royal? Surely no. To add this small matter to his real claims to our esteem would be

To gild refined gold, to paint the lily,

And throw a perfume on the violet. Neither, I am sure, has any other writer who has overlooked Flamstead's claims, desired to do him injustice. On this point I would merely remark, "Rest, rest, perturbed spirit."

But now

we'll shift our ground," by the Ghost's good leave. Our visitor from Valhalla remarks that "a stir was lately made about what was represented as a new method of investigating the motion of the solar system in space, and instead of a new there was brought forward an old acquaintance (known to Science since the times of our grandfathers)." Here the spirit of Flamstead refers obviously to the Astronomer Royal's method. I am sure that Prof. Airy would desire greatly that if his method be indeed so ancient, the fact should be made widely known. I myself am particularly anxious to be set right on this point, about which I am at this very time writing. For though I care more about explaining this and the other methods than about their history, yet it is desirable to be accurate even in historical details.

If I may say so without offence, I would remark that a ghost was not needed--certainly not the ghost of the first Astronomer Royal-to teach astronomers that the opposition of Mars in 1877 will be exceptionally important. At page 25 of my "Sun" I have already pointed this out, and I dare say others have done likewise.

I hope the " great injustice to which our ghostly corre

spondent refers as endured by him in life, does not relate to his difficulties with Newton, for at the present time the opinion of Brewster on this point is in vogue-not Baily's; and the warmest a dmirers of Flamstead are those who least desire to moot the subject. R. A. PROCTOR

Brighton, Nov. 4

Creators of Science

PERMIT me to do my little towards clearing up a most unfortu nate confusion of thought respecting the intellectual ranks of mathematicians and metaphysicians, which is, in my experience, widely prevalent. We may safely divide the mathematicians into three orders (1) Inventors, (2) Experts, (3) Readers or Students, so as to discriminate from one another those who create systems, those who manipulate with them, as "ministers and interpreters of nature"-just as easily and familiarly as Professor Tait (e g.) employs and applies the theory of Quaternions-and those who have merely studied into an understanding of an author or subject. It was an expedient of the late Sir William Stirling Hamilton to confound all these orders, and from the heterogeneous lump to extract-if not extort-testimonies to the worthlessness of mathematics as a mental discipline, without the least discrimination of their sources.

On the other hand, the metaphysicians cannot be trichotomised; for, even in the present advanced state of metaphysics, there is no class of philosophers corresponding to the mathematical experts, the reason of which explains why examiners in mental science do not set problems. There are, in fact, only two classes of metaphysicians: I., Creators; II., Students, more or less thoroughly ver eu in the systems of the leaders, and more or less accepting or rejecting, with more or less reason, those creations. Accordingly, when on May 17, 1869 (I think that was the date), Professor Tait, at a meeting of the Royal Society of Edinburgh, challenged the metaphysical world to produce a metaphysician who was also a mathematician, he not being able at the moment to call to mind a single instance, he was to be understood as asking for a person of the order 1, who was also in the class I. Professor Calderwood's reply, then, was not wholly unexceptionable, for of the three names he adduced, viz., Descartes, Leibnitz, and Hegel, the last was that of a reader of mathematics, and not of a mathematical inventor. The challenger might have spared the respondent the trouble of reply, had he known what De Morgan wrote in Notes and Queries, 2nd S. vi. 293-4, where are distinguished five mathematical inventors, as facile principes: viz., Archimedes, Galileo, Descartes, Leibnitz, and Newton; and in which Aristotle, Plato, and D'Alembert are allowed a very high rank in mathematics. Had the inventor of Quaternions been then dead, I have little doubt that De Morgan would have

added to the five the name of Sir William Rowan Hamilton, who, besides being a mathematical inventor of the very first rank, was also a diligent and accomplished student of Plato, Kant, Reid, and the other Hamilton, and a writer on Logic; i.e., as good as D'Alembert as a philosopher, and perhaps better than he as a mathematician. Now, it is not a little curious and very instructive to observe that, pace Platonis, the two who were creators of strictly defined metaphysical systems, viz., Descartes and Leibnitz, are the only two among the five metaphysicians adduced by De Morgan who belong to the highest rank as mathematical inventors.

It is quite incredible that a man of Professor Tait's learning (I say here nothing of his judgment) should not have been aware of the identity of Descartes (the poor dreamer !) and Cartes, the founder of the Cartesian Geometry; still more so that he should not have known that the immortal analyst, the co-inventor of the Differential Calculus, was the most eminent metaphysician native to Germany before Kant. It was, then, not "ignorance,' but "ignoration," on the part of the Scotch mathematician, that was involved in his challenge; and that challenge was doubtless intended as mere badinage, at the expense of a science which he had taken no pains to understand.

Descartes' "Animated Machines"

As you open your valuable columns to philosophical discussions, may I request you to publish the following remarks on a passage in Mr. Lewes's popular "History of Philosophy" (Vol. ii. p. 148 of the new edition), where he confesses himself puzzled, along with other critics, to account for Descartes' theory that animals were only animated machines. "I am not prepared," he says, "with a satisfactory explanation." I cannot but think that a careful perusal of the "Discourse on Method" (Part 5, sub. fin.) and of the treatise on les Passions de l'âme, makes Descartes' reasons perfectly clear. In the first place, the use of the word machine has misled most of his critics, and if the story of Malebranche and his dog be true, even this great disciple had grievously mistaken the principles of his master. For in the last-named treatise Descartes endeavours to show that such feelings as joy, grief, fear, &c., though in us accompanied by really mental acts (pensées), are produced by physical causes, and produce physical effects apart from the mind. Descartes would therefore never have denied to brutes any of the bodily sensibilities which we possess; and says expressly that he calls them machines in a special sense-machines made by the Deity, and therefore infinitely more subtle and perfect than any which we can construct. He says that we could not ourselves be ranked higher in the scale of beings did we not possess the gift of language, the phenomena of which can only be accounted for by an internal principle different in kind from those which appear to guide the lower animals, though there are also those passions in us which we have in common with them.

But to come to the psychological reasons for the theory. Historians of philosophy before the 18th century should be particularly alive to theological idola, even in sceptical writers; much more so in good Catholics like Descartes. Just as Berkeley put forward prominently the theological advantages of his Idealism, so Descartes indicates plainly in his "Discourse on Method" (loc. cit.) that these were the chief reasons of his theory. "Next to the error of those who deny the Deity, which I have already refuted, there is none more apt to seduce feeble minds from the path of virtue than to imagine that the soul of beasts is the same as ours. But the locus classicus has, I think, escaped Mr Lewis, and will be found in a letter to a Lord (supposed to be the Duke of Newcastle), the 54th of the 1st volume in the original quarto edition. Descartes there specially answers objections made to him on this point, and in the way above indicated; adding however the following passage: "Yet it may be said that although the beasts perform no action which convinces us that they think, nevertheless, as the organs of their bodies do not differ much from ours, it may be conjectured that some sort of thought is joined to these organs, such as we experience in ourselves, but much less perfect;

to which I have no reply to make, except that if they thought as we do, they must have an immortal soul as we have, which is not likely, as we should apply the argument to all animals, such as sponges, oysters," &c. I am sure these ideas are not unfrequently repeated in his correspondence, as for example, in one of his replies to Morus (vol. i. No. 67 of the 4to edition, in Cousin's Edition, x. p. 204 et seq.). He there even talks of two souls, an âme corporelle which is the cause of passions and affections, and an incorporeal principle of thought, which he elsewhere says was infused by the Deity into man at the first moment of his existence. also observes, I think logically enough, that as no boundary line can be drawn elsewhere, we have no choice between conceding a soul to oysters or refusing it to all animals save man. I am not however concerned to defend the validity of his reasons, but rather to contribute this information as an historical point of interest. J. P. MAHAFFY

Trin. Coll., Dublin, Nov. II

Plane-Direction

He

I THINK "plane-direction" is the best of the competing names. The planes of cleavage in a crystal are the "planedirections" in which it is most easily split. They cannot be called either "aspects" or "positions." The opposite faces of a cube certainly cannot be said to have the same "aspect."

If a rigid body receives a movement of translation, it retains something unchanged. What is this something to be called? It might be called "lie" or "set," but both names are equivocal. Two equal and similar figures possessing this something in common might be very well described as similarly laid,' "similarly set," or "similarly placed." We may say that they have "similar positions," but we can scarcely say that they have “the same position;" for change of position is commonly held to include movements of translation as well as of rotation, and a point is usually defined as having position but not magnitude. I think it is worth while to consider whether "position" cannot be restricted to the more limited sense, place being employed in the wider sense.

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In a special sense it is true that two "Richtungs" determine a third (perpendicular to them both), and that two "Stellungs determine a third (also perpendicular to both); just as two points may be said to determine one plane (bisecting their joining line at right angles). In all these instances the fact is that not one only but many are "determined,' but all except one come out in pairs or multiples of two. It is this one, which has no fellow, that is in a special sense "determined."

I think it is paradoxical and misleading to state, without qualifying words, that two linean directions determine one planedirection; inasmuch as two linean directions really serve to define as many different pairs or multiple pairs of plane-directions as we please, and if we are permitted to distinguish the two linean directions by different names, three plane directions can be separately defined by them without any ambiguity. Similar remarks, of course, apply to the other half of the proposition. J. D. EVERETT Rushmere, Malone Road, Belfast, Nov. 11

the rule for finding the directions of the resultant of two forces acting on a point. The reviewer says that this deduction, "if true, would assert that the attraction of the sun and the earth upon the moon might be transferred to any heavenly body in space which happened to be in the line of direction of the resultant of the forces." If the restriction laid down with emphasis in the book, and printed in italics as quoted above, be not ignored, this is a legitimate inference, and if the point to which the forces are transferred parallel to themselves be rigidly connected with the moon, any conclusion having reference to the magnitude or direction of the resultant action on the moon derived as a consequence of the imaginary transposition of the point of applica tion of the forces will be correct.

2. In finding the direction of the resultant of two parallel forces, the same transposition of the point of application is employed, and, of course, it is understood with the same proviso. This proof your reviewer qualifies as "meaningless," whereas I feel sure that, taken in connection with the original axiom and the deduction above referred to, it would be accepted by any mathematician as both intelligible and correct.

3. The next statement is that the definition of a rigid body is given as a property of forces. This is not so, but the whole theory of statics, when developed independently of dynamics, rests on the properties of a force and the properties of a rigid body jointly.

4. The reviewer next dwells upon a curious error which unfortunately escaped my notice until it was pointed out but a short time ago by a schoolboy, and which forms one of three corrections on a slip of errata. Any student would, however, have been able to make the correction for himself by the help of the preceding pages and the applications to the following exercises, a circumstance which I think an unprejudiced critic should not have overlooked.

5. Your reviewer next remarks that a student who tries an experiment with a block and tackle would naturally be surprised at finding that the result of experiment does not agree with that of the theory, and adds, "nor can we find a single word in the book which would enlighten his difficulty." The reviewer cannot have read section 71.

6. The subjects included in the book are such as comprise the course described in the curriculum and examination papers of the University of London, and if occasionally the discussion of unpractical arrangements of mechanical powers is required, I am not answerable. Indeed, I hope to see the day when a reform of this part of the curriculum will necessitate my rewriting the work on an entirely different plan, namely, one according to which kinematics forms the first part, kinetics the second, and statics the third, the propositions of the third part being special cases of those of the second. But that at present it answers the purpose for which it is intended, is proved by the fact that all the questions set this year can be answered from it.

So far as most of the facts and illustrations are concerned, "I am but a gatherer and disposer of other men's stuff," and a writer of an elementary text-book to suit the requirements of a particular examination could not easily be more.

The tone of depreciation with which the writer of the article has been pleased to refer to the work, so directly opposed to a previous notice of the same book in the same journal, seemed to me to call for some reply, and I should wish to describe more fully the objects I have aimed at in compiling the work, but that I know I have already taken up enough of your valuable space. RICHARD WORMELL

ONE OF THE GREATEST DIFFICULTIES OF THE DARWINIAN THEORY

SIR IR JOHN LUBBOCK has done good service to science in directing attention to the metamorphoses of insects, by admitting freely the great difficulty in conceiving "by what natural process an insect with a suctorial mouth, like that of a gnat or butterfly, could be developed from a powerful mandibulate type like the Orthoptera, or even from that of the Neuroptera" (NATURE for Nov. 9, page 28). Such "difficulties" have struck many from the first, and it is in no small degree encouraging to those who love the liberty of science, to find that the time is ap

proaching when difficulties may be brought under consideration and discussion.

"There are," Sir John Lubbock remarks, "peculiar difficulties in those cases in which, as among the Lepidoptera, the same species is mandibulate as a larva, and suctorial as an imago." The power of mastication during the first period of life being an advantage, on account of a certain kind of food being abundant, and that of suction during the second, when another kind of food prevailed, or vice versa, is suggested as a possible explanation of the origin of species which are mandibulate during one period of life and not during another. In such cases it is said we have "two forces acting successively on each individual, and tending to modify the organisation of the mouth in different directions." It is suggested that the change from one condition to the other would take place "contemporaneously" with a change of skin. Then it is urged that even when there is no change of form, the softness of the organs precludes the insect from feeding for a time, and when any considerable change was involved, "this period of fasting, it is remarked, would be prolonged, and would lead to the existence of a third condition, that of pupa, intermediate between the other two."

There is much that is assumed in this reasoning; but I shall now venture to call the attention of naturalists to one point only, namely, the analogy between the period of fasting caused by the temporary softness of the organs while the caterpillar changes its skin, and the more prolonged fasting period when the organs undergo that more considerable(!) modification involved in the change from the mandibulate to the suctorial type of mouth. The change from a small mandibular apparatus to a larger one seems to be compared with the change from a mandibular to a suctorial apparatus-the change of skin of the caterpillar with the change of skin when the caterpillar becomes the pupa, and the latter the imago-the temporary softness which prevails when the little mandibles grow into bigger mandibles, with the temporary softness which prevails while the mandibles become converted (!) into the suctorial mouth. But these changes are surely of different orders, and the operations of a different nature. The mandibles do not change. The one type of mouth does not pass through gradations of any kind into the other kind of mouth. But one abruptly ceases, its work having been discharged, while the other is developed anew. As compared with the change of skin of the caterpillar, the change of skin from chrysalis to butterfly is indeed a "considerable change." It would require an amazing intelligence to premise from the study of a caterpillar that from it, after certain changes of skin and periods of rest, would emanate a butterfly.

It is very well to suggest that "in reality the necessity for rest is much more intimately connected with the change in the constitution of the mouth"; but what, I would ask, is the evidence of the connection implied? Between the change from the small mandibles to the large, and the change from the latter to the suctorial apparatus, there can be no comparison-no analogy, for the suctorial mouth is developed anew during the pupa state, and its formation is not commenced until all traces of the mandibles are gone. Nay, every tissue of the caterpillar disappears before the development of the new tissues of the imago is commenced. The muscular and nervous systems of the latter are as different from those of the former as are the digestive apparatus, the oral mechanism, and the external covering. These organs do not change from one into the other; but one, having performed its work, dies, and is removed entirely. Not a vestige of it remains. Its place is occupied by formless living matter, like that of which the embryo in its early stages of development is composed; and from this formless matter are developed all the new organs so marvellously unlike those that preceded them; and others unrepresented at all in the larval stage, make their

appearance. To explain, according to Mr. Darwin's theory, the "period of change and quiescence" intermediate between the caterpillar and imago states of existence, is likely to remain for some time a very difficult task. If the difficulty cannot be resolved until the period of quiescence during which the imago is formed, is proved to be analogous to the periods of quiescence during the change of skin of the larva, the life history of a butterfly will remain for a long time a puzzle to Mr. Darwin and those who believe in the universal application of his views. LIONEL S. BEALE

ON THE RECURRENCE OF GLACIAL PHENOMENA DURING GREAT CONTINENTAL EPOCHS

IN the August number of the Geological Society of London I published two papers "On the Physical Relations of the New Red Marl, Rhætic Beds, and Lower Lias," and "On the Red Rocks of England of older date than the Trias." In the latter I attempted to prove that for the north of Europe and some other parts of the world, a great Continental epoch prevailed between the close of the upper Silurian times and the end of the Trias or commencement of the deposition of the Rhætic beds; in other words, that the Old Red sandstone, Carboniferous strata, Permian beds, and New Red series were chiefly formed under terrestrial conditions, all, with the exception of the Carboniferous series, in great lakes and inland seas, salt or fresh.

The Permian strata, in particular, appear to have been deposited under conditions to which the salt lakes in the great area of inland drainage of Central Asia afford the nearest modern parallel.

While brooding over the whole of this subject for several years past, I have often been led to consider its bearing on those recurrent phenomena of glacial epochs which now begin to be received by many geologists.

The phenomena of moraine-matter, scratched stones, and erratic boulders, whether deposited on land by the agency of glaciers, or in the sea and lakes by help of floating ice, are evidently intimately connected with the contemporary occurrence of large areas of land, much of which may, or probably must, have been mountainous.

The late Mr. Cumming, in his History of the Isle of Man, "hints at the glacial origin of certain Old Red conglomerates in that island, conceiving that the bony external skeletons of some of the fish of the period may have been provided to enable them to battle with floating ice. In lectures and in print I have frequently stated my belief that the brecciated subangular conglomerates and boulder beds of the Old Red sandstone of Scotland and the north of England are of glacial origin, so distinct, indeed, that when these masses and our recent boulder clay come together, there is often actual difficulty in drawing a line of demarcation between them. I frequently felt this diffi culty years ago, when, commencing the Geological Survey of Scotland, I mapped the strata in the country south of Dunbar, and the same difficulty was occasionally felt by others in the valley of the Lune, near Kirkby Lonsdale.

If, as I believe, the Old Red sandstone was deposited in inland Continental waters, the Grampians, as a mountain tract, bordered these waters, and they must have been much higher then than now; not only because of the probably greater elevation of the whole continent, but also because the Grampians formed land during the whole of the Upper Silurian epoch, and suffered great waste by denudation, then and ever since. The glaciers of these mountains marked an episode in Old Red sandstone times, and yielded much of the material of the boulder beds of the Old Red sandstone.

In these regions and in North America, the Carboniferous

strata were evidently formed under the influence of "a warm, equable and moist climate," and I know of no glacial phenomena in connection with this epoch.

But respecting Permian times I attempted in 1855 to prove the existence of ice-borne boulder beds during part of that epoch, and by degrees this opinion has been more or less adopted. These boulder beds were derived by glacial transport from the mountains of Wales, which then, also, were necessarily much higher than now. As the Old Red boulder beds were formed during a glacial episode or episodes of parts of that epoch, so the Permian boulders mark another glacial episode occupying part of Permian time, just as our last great glacial epoch formed an episode in those late Tertiary times of which the present time forms a part. At the time of the publication of this paper, I conceived the Permian boulders to have been deposited in the sea by the agency of icebergs, but I now consider them to have been deposited in inland lakes.

This, if true, formed a second glacial epoch, of unknown intensity, during the long continental period that lay between the close of Upper Silurian and the beginning of Liassic times.

During the Triassic period there is no certain sign of glacial phenomena in the British area.

I have elsewhere attempted to show that at the present day there is an intimate connection between past glacial phenomena and the occurrence of lakes, large and small, many of which are true rock-bound basins.

I further believe that this cause would be found to characterise ancient Continental recurrent glacial epochs through all past time, if perfect data were accessible, or had been preserved from destruction by denudation and disturbance of strata. In the Paleozoic cases mentioned above, there is, in my opinion, an evident connection of some kind between inland lakes and glacial action, and in stating this it must be borne in mind that I do not consider the Old Red and Permian strata of Britain to have been deposited solely in two lake basins during two epochs, but in various basins during each of two special eras of geological time. For example, the Magnesian Limestone beds of Yorkshire and Northumberland were formed in a hollow quite distinct from the great conglomerates (locally called "brockram") and sandstones of the Vale of Eden. Prof. Harkness in 1856* showed that in the South of Scotland Permian beds, partly formed of brecciated conglomerates, lie in rocky hollows entirely surrounded by lips of Silurian and Carboniferous strata, in fact, in rock basins; and he attributed this singular circumstance to a sinking in of the Silurian strata in each case underneath the Permian rocks.

Ever since the publication of my paper, in 1862, on the Glacial origin of certain lakes in rock basins, I have suspected that these Permian rock basins may also have been scooped out by the agency of glacier ice. I connect this view with my paper on Permian glaciers, published in the Geological Journal in 1855, but as I have not yet seen the country where these hollows lie, I have not been able either to verify or disprove this supposition. I expect, however, that some day this view will be proved, not for these areas alone, but for others of larger area and very different date, which as yet I have only partially examined, in other European countries.

The unravelling of nearly all stratigraphical phenomena of every geological age resolves itself simply into attempts to realise ancient physical geographies, and we may rest assured that those forces that are now in action have played their part in the world sometimes with greater, sometimes with less intensity, through all known geological time, as far as it can be studied by an examination of the rocks that form the crust of the earth. If glacier ice scooped out many lake rock-basins in the latest great glacial epoch, it did the same during glacial epochs of earlier date. A. C. RAMSAY

* Geol. Jour., vol. xii. p. 254.

THIS

WOOD'S "INSECTS AT HOME”*

HIS bulky volume of 670 pages appears to us to be altogether a mistake. It is far too voluminous and too uninteresting for a beginner, while for the more advanced student it is almost valueless, being a very incomplete compilation from the works of well-known writers. It consists of brief and imperfect descriptions of a selection of, perhaps, one-twentieth of the insects inhabiting Great Britain, with occasional notices of their habits and economy, and extracts from a few entomological works. These descriptions are generally introduced by such words as "Our next example," "We next come to," "We now come to," "Next in order comes," "Next on our list is," &c. &c.; and for the most part are mere amplifications of short technical characters, conveying a minimum of useful information, with a maximum expenditure of words. Let us take two examples at random. At p. 76 we have two-thirds of a page devoted to a beetle :

"Our first example of the Staphylinidæ is one of the finest, in my opinion the very finest, of that family. It is called scientifically Creophilus maxillosus, but has, unfortunately, no popular name, probably because it is confounded in the popular mind with the common black species, which will be presently described. Its name is more appropriate and expressive than is generally the case with insect names. The word Creophilus is of Greek origin, and signifies 'flesh-lover,' while the specific title, maxillosus, signifies 'large-jawed.' Both names show that those who affixed them to the insect were thoroughly acquainted with its character and form, for the Beetle is a most voracious carrion eater, and has jaws of enormous size in proportion to its body. The colour of this beetle is shining black, but it is mottled with short grey down.

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In some places this Beetle is tolerably plentiful, but in others it is seldom if ever seen. It can generally be captured in the bodies of moles that have been suspended by the professional mole-catchers, and, indeed, these unfortunate moles are absolute treasure-houses for the coleopterist, as we shall see when we come to the next group of Beetles. A figure of this insect is given on woodcut No. viii. Fig. 3. It is the only British insect of its genus which is distinguished by having short and thickened antennæ, smooth head and thorax, and the latter rounded."

The descriptive portion of this characteristic passage could be easily compressed into two or three lines. In the other twenty we are told that the original describers of the insect were well acquainted with it, that the public are not, and that moles caught by professional mole-catchers are unfortunate!

Turning to page 447, we have a moth described as follows:

"The first family of the Geometræ is called Urapterydæ, or Wing-tailed Moths, because in them the hinder wings are drawn out into long projections, popularly called 'tails.' In England we have but one insect belonging to this family, the beautiful, though pale-coloured, swallowtailed moth (Urapteryx sambucata). The generic name is spelt in various ways, some writers wishing exactly to represent the Greek letters of which it is composed, and others following the conventional form which is generally If the precisians are to be followed, the word ought to be spelt Ourapteryx.

in use.

"There is no difficulty in recognising the moth, the colour and shape being so decided. Both pairs of wings are delicate yellow, and the upper pair are crossed by two narrow brown stripes, which run from the upper to the lower margin. These stripes are very clear and well defined, but besides these are a vast number of very tiny