Imagens das páginas

"nebulosity," "nebulous light," and "nebulous matter," when he means luminosity and luminous matter. In ante-spectroscopic days the terms nebula and cluster were used almost indiscriminately, a nebula being looked upon as simply an irresolvable cluster, and this error still survives in many astronomical text-books and compilations, but Dr. Boeddicker should have avoided it. When we consider that the majority of the stars in the cluster which we call the Milky Way are of the Sirian type, we see how misleading is the use of the terms nebulous light and nebulous matter. A. T.

degree. Consider, for example, any rational p(x1, X2, . . . ., Xn) which is not wholly as there must exist a set of substitutions each of leaves the value of unaltered. A substitution t the product of any number of these must also = unaltered: hence the set in question forms a group have here a fundamental point in the theory of s tions, viz., the existence of a group of substitute the correlation therewith of rational functions #2 unaltered by all the substitutions of the gro group is said to belong to all the functions with: unaltered; and these functions are said to form a which is characterized by the group. Thus the

THE THEORY OF SUBSTITUTIONS AND ITS a wholly asymmetric function is the identical gr

The Theory of Substitutions and its Applications to
Algebra. By Dr. Eugen Netto. Translated by F. N.
Cole, Ph.D. (Mich. : Ann Arbor, 1892.)


HE theory of substitutions abstractly considered is concerned with the enumeration and classification of the permutations of a set of n different letters X1, X2,...., Xn. It is scarcely apparent at first sight that a far-reaching mathematical theory could be built on a basis so simple, still less that there should be any connection between this and the complicated question of the solution of algebraical equations by means of radicals. It may be worth while, in order to excite the interest of mathematical readers in the work before us, to mention one or two points in the Theory of Substitutions which will give an inkling of the nature of its connection with the interesting problem just mentioned.

The operation of replacing-say in any function (X1, X2, X)—any permutation of the letters, say X1, X2, X3, by any other, say X1, X3, X2, is called a substitution. This operation is denoted explicitly by (1,2,3) or shortly by a single letter s. Thus sp(X1, X2, X3) P(X1, X3, Xg);

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sisting of the substitution; the group of the symmetric functions consists of the whole of the stitutions of the nth degree; the group of the alır. functions consists of all those substitutions w equivalent to an even number of transpositions, a”. on. It is obvious that every rational function deter: a group of substitutions, and it may be shown thi versely, for every group of substitutions we may it. an infinity of rational functions which are unaltere the substitutions of the group. The significance of correlation between a group and a family of fun depends on the following important theorem, wech in substance to Lagrange. If be a rational fu which is unaltered by all the substitutions of the gre (in other words, if the group of contain the gr ́.... 4) then can be expressed as a rational function. and the elementary symmetric functions C1 = · Ex1, C2 ZX1, X2,...., C# = X], 5g... • • • ^ A particular case of this is the theorem that if the of and be identical, then each can be expresed on rational function of the other, and of the eleme". symmetric functions. A limiting case of this theor the familiar result that every rational symmetric fun” * can be expressed as a rational function of the eleme


and again: If i denote the substitution (3), symmetric functions. As a special example consi..




the two wholly asymmetric functions = →

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= a/x1 + bx2; these both belong to the der: group, since they are changed by every substitut

the letters 19 Xq.

tp(X1, X3, X2) (X3, X1, X2). We may indicate the suc cessive application of the two substitutions s and by multiplying the symbols st in the order of application: thus stp(X1, X2, X3) (x3, x1, x) and ts(x1, x2, X3) (X2, X3, X1). In particular, the repetition of the same substitution may be represented by powers of the symbol; thus s2P(X1, X2, X3) = P(X1, X2, X3). The identical substi=2(a-b) C. − (a2 + b2) C ̧2 + (a+b)C,C,p¦ ¦ − ̧a•


tution (1,2,3) is represented by unity. The total number of different substitutions of n letters is obviously n!; consequently, if we form the consecutive powers of any substitution we shall ultimately arrive at a power sm which will be the identical substitution, m being some positive integer not exceeding n!: m is called the order and the degree of the substitution.

If among the substitutions of any given degree we can select a set which have the property that the product of any two furnishes another substitution belonging to the set, we obtain what is called a group of substitutions. The whole of the n! substitutions of n letters obviously form a group, and the identical substitution by itself forms a group. It is easy, however, to see that in general there are other groups among the substitutions of a given

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Hence can be rationally expre ** as a function of p, C1, C. The actual expression fact

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The application of the theory of substitutions is ** in the first instance to rational functions. Its user: theory of the solution of algebraical equations by re of radicals is based on the following important result theory of irrational functions. Any root of a solvable ex tion f(x)=o can be expressed as a rational integral for tion of certain elements V1, V,...., V1, the coefficiers which are rational functions of the coefficients off. * of primitive roots of unity. The quantities V, V are on the one hand rational integral functions of :** roots of f(x) = o and of primitive roots of unity, and the other hand are determined by a series of equations Vapa Fa(Va-1, Va-2,..., l'e, where pa is a prime number and F is a rational funct of the V-s. For example, in the case of the c


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- 4C23 + C12C22, S = 2C ̧3 −9C1C1⁄2 +27C3, T=9C3 | Das Centralnervensystem von Protopterus annectens; the relations in question are

·− 27A, V1⁄23 = {(S + V3), V13 = {}(S − V3) ;

11 = x1 + w2x2 + wx3, V2 = x1 + wx2 + w2x3,

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T +3w(xz2x3 + xq2x1 + xz2xq) + 3w2(x12x2 + x22x3 +31);

G12+ V1 + V2, x2 = }{C1 + w V1 + w2 V2}, ¥3 = }} {C1 + w2 V1 + w V2} •

ans of this theorem and certain elementary prinof the theory of substitutions an elegant and simple stration can be given of Abel's theorem that the n by radicals of the general equation of the nth is impossible when > 4: see § 217 of the work


ough the theory of substitutions bears, as we have own, on some of the oldest and most interesting of blems of algebra, it has been comparatively little 1, especially by English speaking mathematicians. le has therefore rendered us a service of great ance by translating one of the standard treatises subject. Of the three that were at his disposal ik that he has chosen the one most likely to be to a beginner. While Serret in his "Higher a" and Jordan in his "Traité" treat the theory n abstract and more general point of view, Dr. constantly associates with the substitution the n on which it is supposed to operate. This gives rful concrete aid to the comprehension of the pro1s of the abstract theory and also helps the student p their application. The great danger in subjects generality is that the stream of theorems is apt to the mind of the learner without soaking in, like off the proverbial duck's back.

Vetto's book will be found to contain all the ordieorems regarding the classification of substitutions, existence of groups, transitive and intransitive, ve and non-primitive, simple and compound; the of the algebraic relations between the values of e-valued functions and between functions belongor included in the same family; and also a conle number of theorems regarding special groups. oplications embrace the theory of resolvents in and of the Galois resolvent in particular; the theory of the solvability of equations by means of ; the theory of the group of an equation and a on of the criteria of solvability; besides special ions to the cyclotomic and Abelian equations, and tions three roots of which are connected by a relation.

translation has been admirably done, both from uistic and from the mathematical point of view. d, it is true, here and there passages which were at obscure; but in every case, on comparing with inal, we found the rendering to be absolutely Such obscurities therefore must be charged the author, or to the nature of the subject, or to syncrasy of the critic, and not to the translator. gratulate Mr. Cole on the successful completion duous task, and heartily recommend the result lover of the most ancient and the most beautiful e sciences.

G. CH.

eine vergleichend Anatomische Studie. Von Dr. Rudolf Burckhardt. (Berlin: R. Friedländer und Sohn, 1892.)


HE Mudfishes, Dipnoi, from many peculiarities in their structure, have attracted the especial attention of anatomists and zoologists. Important monographs on Lepidosiren have been written by Owen and Wiedersheim, whilst Huxley, Günther, and Beauregard have described the anatomy of Ceratodus. Serres, in 1863, made a contribution to the anatomy of the nervous system of Protopterus, Fulliquet in 1886, and Parker in 1888, have also added to our knowledge of its structure; and now Dr. Burckhardt has published a wellillustrated monograph on the central nervous system of Protopterus annectens. He had obtained an ample supply of this fish from Herr W. Jezler, a merchant whose business engagements had taken him to the neighbourhood of Bathurst, Senegambia. On more than one occasion Dr. Burckhardt had received living fish, so that he was able to study the microscopic anatomy by the use of the most recent technical methods, and has thus added materially to our knowledge of the brain of this animal.

The author found, in the anterior horn of grey matter of the spinal cord, remarkably large nerve-cells, which possessed both branching protoplasm processes and an axial-cylinder process. In the lateral and posterior horns nerve cells somewhat smaller in size were seen. The medulla oblongata gave origin to nerves which he names hypoglossal, vagus, glosso-pharyngeal, acusticofacialis, and trigeminus. He also describes two slender nerves as abducens and trochlearis, so that the Dipnoi are not, as some have said, destitute of these nerves. The cerebellum formed the anterior boundary of the 4th ventricle. Large nerve-cells, corresponding to those of Purkinje in the mammalian brain, were not seen. The mid-brain was distinct, and gave origin to a root of the trigeminus, to the optic tract and to the oculo-motor nerve: grey matter containing nerve-cells was grouped around the aqueduct of Sylvius.

Whilst Protopterus corresponded closely with the lowest vetebrates in the regions of the mid and hind brains it presented striking peculiarities in the pineal region. The roof of the 3rd ventricle was complicated, and possessed a velum, which represented a middle choroid plexus; a conarium, and a structure like that which Edinger has named “Zirbelpolster." The epiphysis (Zirbel) was attached to the skull by the arachnoid membrane.

The fore brain was well developed, and divided into two hemispheres. He recognized in it a posterior ventral swelling, which, because it contained cells similar to those found in the dentate gyrus (fascia dentata) of the higher brains, he describes as a lobus hippocampi. He distinguished a fissure which separated the lobus olfactorius from the pallial part of the hemisphere, so that he harmonizes the fore brain in its fundamental divisions with the mammalian brain as described by Broca and Turner. He directs attention to an elevation ventrad of the lobus olfactorius, which he calls the lobus postolfactorius. This lobe is also found in the brains of

Selachia and Amphibia, and apparently corresponds to the lobus olfactorius posterior described by His in the human embryo, which forms the anterior perforated spot in the adult human brain. As regards its structure the hemisphere possessed central grey matter containing nerve-cells which lay around the hemisphere ventricle; also a mass of grey matter which he calls corpus striatum ; whilst in the more posterior part of the ventral region of the hemisphere were nerve cells which represented a cortical layer. In the dorsal region of the hemisphere also cortical nerve-cells were found, which were arranged as an inner and an outer layer. The cells of the cortex gave origin to nerve fibres. A definite anterior commissure was present, the fibres of which passed on each side into the lobus hippocampi. Burckhardt, also, figures, as distinct from the anterior commissure, fibres which he regards as the corpus callosum of Osborn. The most important tract of nerve fibres was the basal bundle, which ascended from the spinal cord into the corpus


One of the most interesting chapters in Burckhardt's memoir is that in which he gives an account of the saccus endolymphaticus. Wiedersheim had described in 1876, in Phyllodactylus europeus, a sac with many branching diverticula, filled with otolith-sand and lying in relation to the choroid plexus of the 4th ventricle. Hasse had previously seen in Amphibia a similar structure which Coggi had investigated in the frog. Burckhardt has for the first time observed and figured it in Protopterus. The

saccus communicated by a narrow neck with the sacculus and utriculus of the auditory vesicle, and with its diverticula overlaid the region of the 4th ventricle, and extended as far back as the 1st pair of spinal nerves.

The memoir contains a short chapter on the phyletic development of the brain of Protopterus. Starting with Selachia, he considers that one line of development has been through Protopterus to Ichthyophis, and thence to the Urodela and Anura; another through Ceratodus to Reptilia and Mammalia; whilst a third line is from the Selachia to the Ganoids and Bony Fishes.


The Chemical Basis of the Animal Body. An Appendix to Foster's" Text-Book of Physiology" (fifth edition). By A. Sheridan Lea, M.A., D.Sc., F.R.S. (London: Macmillan and Co., 1892.)

LIKE its parent volume, this well-known appendix has grown in bulk considerably, so that it now constitutes a treatise (separately paged and indexed) on the chemical, substances occurring in the body. It contains numerous references to the text of Foster's" Physiology," and so the two may be most profitably read together.

The plan pursued in the present edition is the same as in former editions; the chemistry of the body is described under the headings of the names of the chemical substances. This plan has its advantages. It for instance gives a completeness to the description of any particular substance, whereas the other plan of describing the facts of animal chemistry, under the headings of the tissues, organs, and functions involves a certain amount of repetition and the facts relating to any one group, such as the proteids and carbohydrates will be found distributed in different chapters. Dr. Sheridan Lea's plan

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has, however, the disadvantage that it dest tinuity. Many of the paragraphs are necessar and one passes from one subject to another with amount of abruptness. The style of the writing ever, interesting and clear, so that this disadva reduced to a minimum. The parts that treat the in a fuller style, such as those in which ferment the origin of urea in the economy, or the to hæmoglobin to bile pigment are discussed, are.. lucid writing.

The book opens with a description of the pr ferments, the most important of physiological s but those of which, from the chemical standp know least. The simpler materials found in the its excreta are treated next. This is the more c part of the book, and the author expresses his m ness to Dr. S. Ruhemann for assistance here. Un whether this part of the work will prove at ordinary students. There is no question that ai students should be educated up to it, but a organic chemistry and structural formule are they are inclined to fight shy of. The concluir, are again devoted to substances of which we physiological rather than a chemical knowledge the pigments.

The figures of crystals, which form a new feath present edition, have been taken from the this notice without alluding to the extensive re Krukenberg, Kühne, and Funke. One cannet t to literature that are given throughout. This a most valuable assistance to all original workers those more earnest students who desire to go je the subject. The references are provided with use index. They are chiefly to German litera

German leanings of the author are seen 2

spelling of sarkosin, kreatin, &c. The final en omitted in the names of the amido acids. It w good thing in the future if international uniform names of chemical compounds were adopted meantime it seems a pity that Dr. Lea has t to use the spellings reconimended by the Cher.. of London.

The author is to be congratulated on having his labours to a successful conclusion, and ve the present volume no better compliment that that it is well worthy of those that have precede.

Chambers's Encyclopædia. New Edition. VoLA

and Edinburgh: W. and R. Chambers, 1822 THE editor and publishers of the present was cordially congratulated on the fact that it hast successfully completed. A better encyclopedi scope does not exist in our own or any other Nominally it is merely a new edition; but in the editor claims in the preface, it must be t to all intents and purposes a new work. One of difficulties in an undertaking of this kind is tosseach subject shall have the degree of attent properly belongs to it, no single subject or gra jects being permitted to usurp space which o otherwise occupied. The editor has grappie difficulty so effectually that few readers will have to complain of any lack of proportion in the le various articles. Another striking merit of that all important subjects have been ett specialists, so that students may have full co the accuracy of the information offered to the matters in which they happen to be partic. rested. The space at the disposal of the wher limited that what they have to say is not, exhaustive, but it is sound as far as it goes, and rally presented with most praiseworthy sma

EBRUARY 9, 1893)


ess. The present volume falls in no respect below
wel of those which have preceded it. Among the
s of scientific articles are Prof. James Geikie, who
with the triassic system and with volcanoes; Prof.
, who expounds the principles of thermodynamics;
R. W. Philip, who writes of tubercle; and Sir F.
well, who has a paper on water-supply.

r Young's Tour in Ireland (1776-79).
1 Introduction and Notes, by A. W. Hutton.
5. (London: G. Bell and Sons, 1892.)


reprint will be of real service to all who study the ion of economic conditions in Ireland, and much ought also to excite and maintain the interest of the al reader. Arthur Young, as every one knows, was narkably accurate observer of such things as lers have opportunities of noting, and his book on d is in its own way hardly less valuable than his celebrated work on France. The work was first hed in 1780, in the course of which two English ns and one Irish edition were issued. Since that Mr. t has not until now been reprinted as a whole. n has done his work as editor admirably, and a useful bibliography has been prepared by Mr. J. P.



Editor does not hold himself responsible for opinions ex-
Neither can he undertake
essed by his correspondents.
return, or to correspond with the writers of, rejected
anuscripts intended for this or any other part of NATURE.
o notice is taken of anonymous communications.]

Some Lake Basins in France.

Ew weeks since M. Delabecque, Ingénieur des Ponts et
sces at Thonon, kindly presented me with a copy of a work
under his superintendence and to a great extent executed
self, to which I should be glad to call the attention of
ts of physiography. M. Delabecque, commissioned by
ench Government, has made a series of soundings of ten
n France, near the Alpine region, and this Atlas records
sults of his work. Contour-lines, in most cases 5 metres
indicate the forms of the lake-basins; the use of varying
Chief among the lakes
n blue makes these more distinct.
ed is the Léman, in the survey of which, as only one shore
nch territory, the Swiss engineers have cooperated. A
of this on a reduced scale, and without colours, appeared
f. Forel's book, "Le Lac Léman " (see NATURE, Nov. 3,
Next in importance come the lakes of Annecy and of
et; the remainder are situated either in the French Jura or
e margin of the outer limestone zone of the Alps, a little
of the Rhone.

luding the Lake of Geneva, which was noticed in the article
entioned, these lakes are especially interesting for their bear-
the difficult problem of the origin of lake-basins. Except
ic de Bourget, none of these can be said to lie in a great
ain valley, or on the probable track of a great glacier. If
heir basins have been excavated by glaciers, we might
expect the Alps and Jura to be "spattered" with lakes, for
peal can be made to exceptional circumstances: while if
ntours of their beds present resemblances to those of the
Alpine lakes, such as the Lake of Geneva, the same
nation ought to apply in the main to both groups.

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hout a reproduction of the charts it is impossible to give than a rough idea of the evidence which they afford, but llowing statements may be helpful. As a general rule the deepen as they broaden, the deepest water being comfound in the widest part. If in the course of the lake ores markedly approach so as to form a kind of "narrow,' col," which sepa. Corresponds with a submerged neck or Atlas des Lacs Français, Ministère des Travaux Publics." jer s name appears on the sheets, but I am informed by M. que that the Atlas can be obtained at Georg's Library, Geneva.

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rates the bed into two basins, rising perhaps 10 metres or more
Not seldom the bed of a lake consists
above their general level.
of a linear series, three to six in number, of shallow basins, so
that a contour line, drawn along the axis of the lake, undulates
"amplitude" of from perhaps 3 to 5
up and down with an
metres. A rather long, blunt-ended oval is the prevalent form
of these lakes, but to this there are exceptions. So far as can be
ascertained the contours of the land above the water-line are
reproduced beneath it. For instance, under the steep slopes of
the Mont du Chat the bed of the Lac de Bourget plunges
abruptly down to a depth of over 120 m. (its greatest depth
being about 145 m.).

Of the Jura lakes, the Lac de St. Point (848.95 m. above the
sea) is rather more than 6 kilometres long, the general width
being rather less than one-tenth of this; a considerable part of
its floor is 30 to 35 metres deep, and its greatest depth is about
It contains no less than 6 basins, parted by "cols
42 metres.
This lake
about half-a-dozen metres above their lowest parts.
is on the course of the Doubs, and lies parallel with the general
strike of the Jura, i.e. from N.E. to S. W. The Lac de
Brenets on the same river, nearly 100 metres lower down, is a
narrow, winding lake, roughly 150 metres wide and perhaps 8 or
9 times as long. At its upper end is a sharply projecting, rather
shallow bay, but the channel of the Doubs can be traced clearly
through this, deepening gradually from 5 to nearly 27 metres and
the whole lake is evidently only an enlargement of the river.

The subalpine lakes are no less interesting, and their testimony generally agrees with that summarised above. Want of space forbids us to mention more than the lake of Annecy. This is deepest (about 65 m.) in its northern and widest part (nearest to the effluent). The sub-aqueous contours on the western side are interrupted, to within about 10 metres from the bottom of the lake, by a prominence, just like a drowned hilly spur. The shallowest soundings over this, near its northern (outer) part, are only 33 metres, and the ground falls rapidly down from 5 to 55 metres. On its northern or "lee" side (assuming a glacier to have followed the course of the water) is a submerged valley over 40 metres deep. The Lake of Annecy exhibits another Near its northern end the bed deepens very singular feature. very rapidly from 30 to 80 metres; this funnel-shaped cavity is less than 200 metres in diameter, and is probably a submerged swallow hole. These notes may, it is hoped, suffice to indicate the importance of this work. The gratitude of students is due to M. Delabecque for supplying them with a valuable group of facts, the collection of which must have entailed great labour. These, however, appear to me not to lend themselves very readily to the support of the glacial excavation hypothesis; but to be more favourable to that which regards the larger Alpine lakes as mainly formed by movements of the earth's crust after the T. G. BONNEY. erosion of the valleys in which they lie.

Dust Photographs. "Breath Figures," printed in IN Mr. Croft's paper on NATURE for December 22 of last year (pp. 187, 188) he states :"Two cases have been reported to me where blinds with embossed letters have left a latent image on the window near which they lay.' The statement is not quite clear as I do not understand whether the letters were in contact with the glass or not.

Perhaps it may be interesting to place on record an observation of my own, made a few years ago, which struck me at the time as curious, but which I have not been able to verify since.

At the stations of the District Railway there is a useful arrangement by which passengers are informed of the destination of the next train. It consists of a shallow box with glass sides into which by a mechanical contrivance boards are let down on which the names of the stations are painted in white letters on a blue ground. The board with the words INNER CIRCLE' At night the box is (or was) is most frequently exposed. illuminated obliquely on either side by a tolerably powerful lamp. One night I was waiting for the train at the Victoria Station. There was some dislocation in the service; the destination of the next train was uncertain and the box was empty. On glancing at it somewhat sideways I was however astonished to see the words 'INNER CIRCLE' on the glass side of the box in quite clear dark letters on a pale illuminated ground. I He drew the attention of one of the platform officials to it. saw it with perfect distinctness, and seemed to think he had

noticed it before. Of course when the apparatus is in full working order there is little opportunity for doing so.

The only explanation I could think of was:- (i) that the light of the lamp had produced some molecular change in the paint coating the notice board; (ii) that this had affected differently the blue and the white paint; (iii) that the same cause had set up some differential electrical condition of the board and the glass; (iv) that a bombardment of particles of the blue paint had taken place on to the glass to which they had adhered; and that (v) the particles so adhering, by dispersing the light, produced the effect of the pale illuminated ground while the spaces occupied by the letters being relatively clean stood out dark. Roval Gardens, Kew, W. T. THISELTON-DYER.

February 1.

MR. W. B. CROFT's paper on Breath-Figures in your issue of

December 22 reminded me of some curious impressions of

monumental brasses which are to be seen on the walls of Canterbury Cathedral. When I saw these impressions a few years ago, it occurred to me that they might have been produced by mere contact, the brass plates having possibly been hung for many years against the walls, in secluded corners, at a time when the Reformers would not let them remain in their proper matrices on the church floor. I had forgotten the particulars of these figures, but Dr. Sheppard, of Canterbury, has kindly sent me the following notes by favour of Canon Fremantle :-"A number of impressions of brasses are in the basement (which is open to the air) under Henry IV.'s chantry in the Cathedral. A very good impression is on the western column of the crypt of Trinity Chapel. On the walls appear the shapes of the effigies. Sometimes the stone is unstained all over the area of the figure, and surrounded by a broad dark smudge: and sometimes the case is reversed, and the figure is the exact negative of the former kind; that is to say, the area of the figure is indicated by an uniform dark tint, whilst the surrounding stone is unstained." Dr. Sheppard suggests that an exact pattern seems to have been made in paper and then fixed to the wall whilst it was brushed over with linseed oil. But this does not account for the white effigies on a dark ground."

I would commend these impressions to the notice of those interested in the subject. It may be that, though some were made intentionally, others are the result of simple contact. F. J. ALLEN.

Mason College, Birmingham, February 4.

Fossil Plants as Tests of Climate.

IN continuation of my recent letter, permit me to call attention to a communication on the bread fruit trees in North America, by Mr. F. H. Knowlton, of the National Museum, Washington, U.S., which appears in your American contemporary Science for January 13. The forty living species of Artocarpus are all confined to tropical Asia and the Malay Archipelago. A. incisa, the true bread fruit tree, and one or two others, are largely cultivated in the tropics. They are small or medium-sized trees with a milky juice, large leathery leaves, and monoecious flowers. The female flowers are long clubshaped spikes, which uniting form one large mass known as the "bread fruit," the interior containing a pulp when ripe like new bread.

The first fossil bread fruit was discovered in boulder county Colorado in late cretaceous rock, and was named by the late Prof. Le Lesquereux Myrica (1) Lessigiana, other fragments he called Aralia pungens. The subsequent researches, or more perfect specimens of Dr. A. S. Nathorst, proved these to belong to one species, Artocarpus Lessigiana. Dr. Nathorst is the discoverer of another species closely allied to A. incisa, which he calls A. Dicksoni, which he obtained from the cretaceous flora of Waigatt, West Greenland, which the previous labours of Profs. Heer and Nordenskiöld had shown to be of a tropical or subtropical character, containing as it does numerous species of ferns of the order Gleichenialeæ, and several species of cycas. CHAS. E. DE RANCE. H.M. Geological Survey, Alderley Edge, Manchester.

Lunar Rainbow in the Highlands.

THIS interesting phenomenon (a very unusual one in this latitude) was observed near here on the morning of the 3rd inst., about six a.m. The moon was two days past full, and was not

shining particularly brightly, being obscured, except 2 able intervals, by driving mist and light clouds. The b ever, was exceedingly well marked, and formed a st beautiful object, stretching as it did completely across western end of Loch Oich, glimmering against the cart ground of the mountains, and sinking into the wate southern shore of the loch. The general colour of the yellow deepening into orange, several of the pristric however, being intermittently visible, especially a tinge on the upper side.

The Abbey, Fort-Augustus, N. B.

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K' tance apart of two dots when they can or distinguished as two, and do not become confused: It is usually reckoned that the normal eye is just just unable to distinguish points that lie one m degree asunder. Now, one minute of a degree angle subtended by two points, separated by the part of an inch, when they are viewed at the reading distance of one foot from the eye. li row of fine dots touching one another, each as a bead of one 300th part of an inch in disc arranged on the page of a book, they would appe" ordinary reader to be an extremely fine and line. If the dots be replaced by short cross st line would look broader, but its apparent contant not be affected. It is impossible to draw any shall commend itself to the eye as possessing the larity than the image of a succession of dots strokes, 300 to the inch, when viewed at the de a foot. Every design, however delicate, that can be with a line of uniform thickness by the best machte most consummate artis, admits of being mimicked coarsest chain, when it is viewed at such a disa the angular length of each of its links shall not one minute of a degree. One of the apparently s outlines in nature is that of the horizon of the se ordinary weather, although it is formed by ware slopes of débris down the sides of distant appear to sweep in beautifully smooth curves. reaching those mountains and climbing up the path may be exceedingly rough.

EENNESS of sight is measured by the arg

The members of an audience sit at such var tances from the lecture table and screen, that possible to illustrate as well as is desirable, the through which a row of dots appears to run tinuous line, as the angular distance between the lessened. I have, however, hung up chains arc beads of various degrees of coarseness. Some will appear as pure lines to all the audience: whose coarseness of structure is obvious to those nearest, will seem to be pure lines when viewed it furthest seats.

Although 300 dots to the inch are required to idea of perfect continuity at the distance of t will shortly be seen that a much smaller numberto suggest it.

writing, makes about 140 dots to the inch. The The cyclostyle, which is an instrument used fot minute spur wheel or roller, instead of a point; the is made on stencil paper, whose surface is covered brittle glaze. This is perforated by the teeth of wheel wherever they press against it. The halfpe sheet is then laid on writing paper, and an inked worked over the glaze. The ink passes throug forations and soaks through them on to the pape consequently the impression consists entirely cis irregular cross bars or dots.

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