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proposes to bring out triennially. The present two volumes form a continuation, and extend as far as § 5 of the second chapter in the second book. The author proceeds on the same lines as formerly, and places before the reader in a concise way all the new methods of development, measuring lenses, apparatus, &c., from the particulars of constitution which characterize developers down to the latest form of kodak or tie camera. Not only is each subject treated with the greatest care, but illustrations are numerously distributed. That which will add great value to the work as a whole is the insertion of references, for what, after all, is more annoying than having to wade through a great quantity of literature when the presence of one or two words would have eliminated all trouble? W.

The Reliquary: Quarterly Archæological Journal and Review. Vol. VI. (New Series). (London: Bemrose and Sons, 1892.)

THIS Volume consists of the four numbers of The Reliquary which have appeared during the present year. The contents include many things which do not quite come within the scope of NATURE; but it is satisfactory to be able to note that the writers, speaking generally, have done their work in a thoroughly scientific spirit. Mr. J. Lewis André contributes an interesting and wellillustrated paper on leather in the useful and ornamental arts, and a clear account is given by the editor of a part of an early dial, bearing runes, which he was lucky enough to find some months ago in the churchyard of Skelton, Cleveland. An illustration gives a good impression of the general character of the stone, the runes on which, according to Canon Browne, are "Danish." Among the other papers are two articles, by Mr. D. A. Walter, on ancient woodwork, and a discussion, by the Rev. A. Donovan, of some of the problems connected with the career of Columbus.

LETTERS TO THE EDITOR.

(The Editor does not hold himself responsible for opinions expressed by his correspondents. Neither can he undertake to return, or to correspond with the writers of rejected manuscripts intended for this or any other part of NATURE. No notice is taken of anonymous communications.]

Nova Auriga.

ON October 5 the Nova Auriga was again observed under favourable circumstances, and the observation as to precautions in focussing necessary on account of chromatic aberration of the refractor was amply verified. [NATURE, September 22, p. 489, in which note two corrections should be made eighth line, for "varying" read "ranging," and fourteenth line, for "(? F)" read (G)"] The line near C was distinctly seen at times; but the blue and violet lines observed on September 14 were not seen; the three green lines were very distinct.

On October 14 the red line was much fainter, but there was an obvious bright line in the yellow, which may be the line which Dr. Copeland estimated as 5801 on August 28 (NATURE, September 15), or may be that which has been measured several times at the Lick Observatory (Astrophysics, October, p. 717), and appears to have a wave length of about 575. It had escaped my notice before, but I was induced to look most carefully in the yellow by considerations arising out of an attempt to reconcile Mr. Barnard's observations of apparent nebulosity surrounding the Nova, as seen in the 36 inch refractor at Mount Hamilton, with my own observations of September 14. Barnard's "stellar nucleus" was the difficulty. There appears to be no doubt that the Nova is emitting a spectrum similar to that of a planetary nebula, but it seems to me necessary to have further spectroscopic evidence before it is established that nebulous extension can be seen; if it is to be seen with a simple eyepiece, it must be looked for in a reflecting telescope, as the following considerations will show.

Mr.

Prof. Keeler's study of the chromatic correction of the Lick

Refractor shows ("Pub. Ast. Soc. Pacific," Vol. II. p. 164) that the circle of aberration of F light on the focal plane for the D line has a diameter which is in terms of the focal length Coco349. We may take this diameter as very nearly that of the Thus if a star emits only D and F light, and the F light is circle of aberration of D light on the focal plane for the F line. focussed, then the D light will fill a circle nearly 7" in diameter, and the star will look like a planetary nebula with a stellar nucleus. If the star emits light of wave lengths 500 and 575, then interpolation based on Keeler's measurements shows that round a stellar nucleus in the focus for wave length 500 there must be a circle of aberration of nearly 4" diameter.

Mr. Campbell found lines of wave lengths 500 and 575 in the spectrum of Nova Aurige with respective intensities 10 and I. Mr. Barnard describes the appearance of nebulosity as "pretty bright and dense," and as measuring 3" diameter. My own inability to see either the circle of aberration for the yellow line when the green was focussed, or the alleged nebulosity, may be explained in several ways (eg. smaller aperture of object glass, climatic conditions, &c.). The spectroscope could probably decide the question at Mount Hamilton by showing whether the minimum length of any of the lines is that corresponding with 3" diameter on the slit. I have not been able to do more than observe that the yellow line is not visible when the 500 line is focussed on the slit of a spectroscope having an effective H. F. NEWALL. dispersion of two 60° prisms.

Observatory, Cambridge, October 24.

Formation of Lunar Volcanoes.

The

WHILE we have, on the lunar surface, a series of markings so evidently volcanic that no one thinks of applying any other term to them, we have on the other hand no explanation of their mode of formation which will stand examination. explanation given by Messrs. Nasmyth and Carpenter in their splendid work on the moon, founded upon explosive expulsion of lava, fails to satisfy the mind when applied to wide craters with a low wall such as Shickard or Grimaldi, of which there are so many on the moon, and which look more like some disturbance in a semi-liquid surface than an accumulation of volcanic débris.

The umbrella-like eruption figured in Messrs. Nasmyth and Carpenter's book does not represent any phenomenon within our experience, as the erupted material (unless light enough to be driven by wind) invariably falls back int o the neighbourhood of

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the vent, and we could not conceive of its being shot neatly out twenty-five miles on every side to form the familiar ring.

An explanation of the mode of formation founded upon lunar tidal motion occurred to me about seventeen years ago, from observations on a cooling slag; but until the recent publication of Mr. Darwin's work on the history of the tides I was doubtful if that force were sufficient to account for observed results.

I had noticed that the rise and fall of a fused slag through holes in its solidifying crust, formed craters exactly like those in the moon; and I enclose a photograph of a piece of that slag in which is reproduced all the salient features of the lunar surface.

The mode of formation was as follows:

The fused liquid (which was potash "black ash" containing a mixture of substances of very varied melting point) was still giving off some gas, which escaped as at a in Fig. 1, building up

a miniature crater as at b, c, d. But the crater vent becoming intermittently choked, the accumulation of gas beneath the crust caused the liquid "lava" to rise through any neighbouring holes as at e, f, giving rise to a ring crater. The pressure of the accumulated gas now drove out the obstruction in a, when the liquid lava receded in e as at g. This intermittent action went on till the crater i was built up-entirely by "rise and fall" (as of a tide), no gas escaping at this hole.

In the case of the moon the rise and fall would be caused by the tidal motion of the still liquid interior. The solid crust would resist the periodic rise of the liquid interior, and the liquid would well through the crust and recede again as the wave passed.

When the crust was thin, and the lava very liquid, the large ring structures would be formed, as the lava would flow far; but

FIG. 2.

as the crust got thicker and the lava more viscid, the more striking craters like Copernicus would be built up. When the vent was very small, or the lava very viscid, the exuded lava would build up mountain ranges, or peaks like Pico, as it could not flow far, and would be cooled too much to allow of its flow. ing back with the ebb tide.

The existence of the cause proposed by Messrs. Nasmyth and Carpenter, viz., expansion on solidification, is very doubtful. The proof they adduced was that a piece of solid slag would float on liquid slag. But when slag solidifies it becomes filled with small cracks, which doubtless contain air, and so aid in the flotation. When I was working at this subject I had some slag poured into an iron mould kept cool by immersion in water. When the slag had cooled a distinct depression was seen on the upper free surface, showing that the slag had contracted during solidification. No doubt its contraction or expansion will depend upon its composition, and we do not know the composition of the moon's surface, but we need not depend upon a doubtful property for an explanation when a set of conditions have existed which must have yielded an ample force for the production of the observed results.

In the photograph marked Fig. 2, at a can be seen a crater

66

with a raised floor and a central cone, at b a crater filled to be lip like "Wargentin," while on the plain near b, and round the open crater c, will be seen numerous minute craters, as on tie moon's surface in the neighbourhood of "Aristotle" or Copernicus," while in other photographs are seen waled plains like the "Mare Crisium," so that all the importan features of lunar topography are reproduced in this slag, and there are many minor points of agreement which cannot be gone into in the limits of a letter.

Although I have always considered the tides the cause of the wonderful lunar configuration, I was not satisfied that that cause alone was of sufficient magnitude, till the work of Mr. Darwin placed the matter in such a clear light that I now venture to submit the idea to your readers as a feasible explanation of the familiar lunar features. J. B. HANNAY.

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On the Need of a New Geometrical Term-"Conjugate Angles."

IN geometrical discussions, such as arise out of a grea variety of physical problems, it is frequently necessary to refer to an acute or obtuse angle A as being equal to another acute or obtuse angle B, because contained by two straight lines which are respectively perpendicular to those containing the angle B. Such a statement of the reason of the equality is, however, cumbrous. Sometimes, indeed, such angles when acute might be described as equal because they are the complements of equal (because vertically opposite) angles; but it will often happen that the figure does not show the vertically opposite angles that would be referred to.

I should be glad to know whether there is any term expressing the relation in question in use among either English or foreign writers, and, in default of such, would suggest that such angles be called conjugate, or if greater precision is required, rectangularly conjugate, the general term conjugate to be used when we wish to refer to an angle A as equal to an angle B because contained by sides whose directions are the directions of the sides of B, after each has experienced an equal and similar rotation in the plane of the diagram, whether the rotation is through a right angle or not.

The shorter inclusive term conjugate could always be used for the less general but longer term rectangularly conjugate, when brevity was aimed at. A. M. WORTHINGTON.

R. N.E. College, Devonport, October 30.

Printing Mathematics.

THE main features of mathematical work that give trouble in printing are three: the expressing of (1) fractions, (2) powers, (3) roots.

(1) To simplify the expression of fractions we have the solidus suggested by Sir G. Stokes. But the solidus has been hitherto much less used than it might be, on account of the uncertainty as to how far its influence reaches in any expression more complicated than the simplest fractions. This uncertainty can easily be removed, and the usefulness of the solidus greatly extended by defining more definitely its exact meaning. This is done in the simple conventions proposed below.

(2) To express the process of involution, the sign, suggested by Mr. C. T. Mitchell in the Electrician, is more concise and clearer than that mentioned by Prof. S. P. Thompson in NATURE. And Mr. Mitchell's sign, if defined by conventions similar to those applied below to the solidus, is capable of a like extensive application.

(3) To express roots we have the sign. But, when accom panied by a horizontal line above to show the extent of its influence, this sign also requires special spacing. But it can be brought into line with the rest by the use of the same conver tions. Taking then for

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"Sunshine."

IN acknowledging the courteous criticism and the kind remarks which "C. V. B." has been pleased to make about my little book, may I be permitted to comment on one or two points, which I think he has imperfectly understood from the text. We all know that when "C. V. B." undertakes to review a book, he does his work in a thorough and searching manner, and from his critique it is evident that "Sunshine" has been well read. Notwithstanding this, in one or two of the instances selected for criticism the meaning, at once simple and obvious to a little child, who neither knows nor suspects any other, seems to have missed him, presumably because he knows all the bearings of the subject. Thus it is sometimes a disadvantage to be learned. Of this I propose presently to give an instance in the order which

it occurs.

After poking fun at me, because, the "Sunshine" course being ended, Tommy meets King Sol face to face and "has it out with him," my critic proceeds to discuss the limits within which the imagination may be appealed to as a factor in scientific education, and while I agree with him in the main, I am tempted in passing to remind him of what Tyndall terms "the scientific use of the imagination," to which the clearness and (to me) the charm of his own lectures is largely due. Be that as it may, in one of "Nature's Story Books I feel fully justified in employing, within the limits of scientific accuracy, any or all of the powers of the mind, which shall help children and others to realize the relation they bear to their surroundings, assured that in a course based upon some hundreds of experiments synthetically worked out and deductions made-a course whose main object is to lead children to go direct to Nature, via experiment, for their knowledge, there is little danger that the imagination be cultivated at the expense of the reasoning faculties. The experience of the writer is that the children attending the lectures became extremely critical-a state of mind which, although of inestimable value in acquiring knowledge, is not one of the happiest in other respects. Therefore it was thought desirable to provide them with some necessary ballast, and this is my defence of the hypnotic visit to the moon, and the other two chapters to which the critic alludes.

Natural science apart, it seems to me that the tendency of the school-teaching of to-day is calculated rather to make children hard and matter of fact. For this reason I have endeavoured in these Sunshine Stories to interest children in the poetry of their common lives, myself playing somewhat the role of an optical instrument, presenting images sometimes real, sometimes virtual of those physical beauties which touch them at every point. The fact that "C. V. B." recognizes in "Sunshine" the realism which the "picturesque language" was intended to convey, disposes of the case of my Cape Town reviewer, who mildly insinuates that I have been guilty of some fraud upon little children in calling "Sunshine" a story-book. Therefore I am the more glad that "C. V. B. " agrees with me that the mathematical side of these questions should not be obtruded. There are so many excellent text-books which supply that information for older pupils. I need not say that I shall be most happy to add the exception in the case of the rainbow. I thank him also for pointing out a passage in the notes where an additional clause is necessary, owing to the transposition of a paragraph. But I take exception to the statement about the top, for it is evident that the

In some cases lines of differing thickness might be advisable; experiment is not made under the same conditions as that which

for instance

= |6\1/2 | /c\d+e\31. c(d + e)3

There are many other ways in which this notation might be used; but the above will suffice to illustrate the advantages of it. And these advantages are substantial. It enables the work to be printed in the same space as ordinary letterpress, and thus avoids the special spacing, from which nine-tenths of the troubles in mathematical printing arise. It requires no new types, except, perhaps, and each of the signs used is suggestive of the original mode of writing for which it is a substitute. It can be used without confusion in conjunction with all ordinary brackets. How far this notation would suit very complicated expressions, is a point that would have to be determined by experience; but for printing mathematics of ordinary complexity it would be useful in economizing space and diminishing the risk of printers' errors without any sacrifice of clearness. Cambridge, October 27. W. CASSIE.

"C. V. B." has in mind, because my boys get green and he gets (he says) white, or nearly white. The home experiment reads: "I am giving each of you squares of coloured paper to take home... then you may have the papers to put on your tops-e.g., cover half blue and half yellow, spin the top and you will see green." A note on page 341 refers to the kind of paper. Now it seems to me from the expression "painted disc," which "C. V. B." has made use of, that possibly he may have had Clerk Maxwell's top in mind when he wrote.

When I say to a boy, "Here are two squares of paper, one blue and one yellow; when you've done so and so, you can have the paper to keep-cover your top, half yellow, half blue, &c.," the lad understands me, and when I am not there he takes out his halfpenny whip-top, tears a piece of the blue paper, and rendering it slightly adhesive hammers it down on the top with his right fist; he tears a similar piece and treats it in the same way, and so on until he has covered half. Then he takes the yellow paper and covers the other half with irregular patches of yellow. He spins the top and sees green.

How different is this from Clerk Maxwell's top. Clerk Maxwell selected for his top the purest of paper and pigments. He endeavoured to match the spectral colours (considerably diluted). He selected a scarlet red with a tinge of orange like orange-red vermilion, lying in the spectrum one-third the way towards D, between the lines C and D. His green was one-fourth the distance from E, between E and F, and resembled emerald green. He also selected a blue violet midway between F and G, which was imitated by that purest of colours-ultramarine. Now let us try the given experiment under the favourable conditions guaranteed by Maxwell's discs, viz., the purest of colours painted on Whatman's paper. Taking up a disc of ultramarine and another of pale (not orange) chrome yellow, and concealing half of one disc behind the other, on rotating the compound disc so that the eye shall receive simultaneously blue and yellow light, the result is not white or even practically white, but a grey, tinged with yellow. By a careful adjustment, hiding more of the yellow and exposing more of the blue (thereby altering the proportions of the text), it is possible to get rid of this yellowness and to obtain an absolutely neutral grey which it might be possible to persuade some grown-up people represented white, but which on analysis yields 71 per cent. black to 28 per cent. white. This may be proved by revolving a disc of black and white sectors in the above proportions, the results in each case being identical. But even this result, unsatisfactory as it is, does not apply to the passage quoted in the text, in which no special conditions are observed. tain what is easily proved by experiment in less time than it takes to write it, that when ordinary colours, e.g., gamboge and Prussian blue, are used, the residual light is green. 1

I main

I fear that already this letter is too long, and since I do not wish to monopolize the space kindly placed at the disposal of your correspondents, I must defer the consideration of the annotations on soap films. The other points are dealt with in the preface. AMY JOHNSON.

52 Lower Sloane Street, S. W., October 12

I Do not think that the observations on my review of "Sunshine" require more than a very short answer.

I considered that the authoress had not by any means cleared the confusion which usually exists as to the meaning of the expression "mixing of colours." It is applied both to the case where two or more colours are seen superposed, e.g. by spinning coloured paper where the resultant tint is due to the sum of the separate colours in the constituents, and to the case of mixed pigments where the resultant tint is that which is common to the constituents. Now as the common paint box" rule says that blue and yellow make green, that is that blue and yellow pigments mixed produce a green pigment, it seems to me very misleading to say "Cover half (of your top) blue and half yellow and you will see green." Of course it may happen that the slight departure from white which will be observed may be in a greenish direction, but it may also be inclined towards pink, or, for anything I know, towards any other colour. The one thing it will not do, however, is to make a green such as is obtained by mixing the pigments, and such as I fancy from the context any one would expect. C. V. B.

The Photography of an Image by Reflection. THE great utility of spark photography for obtaining time records of quickly-moving objects must be apparent to all who know the experiments of Mr. C. Bell, Prof. Boys, and Lord Rayleigh. By means of spark photography the shadow of any object such as a jet of water, a flying bullet, or a broken soap film can be produced with perfect definition. The shadow of the moving object illuminated by an electric spark is thrown on to a sensitive plate in a dark room, and the plate is developed in the usual manner. The process of spark shadow photography will be found, I believe, of great service in physiological research. With a view to try this I attached a long sensitive plate to the traversing carriage of a chronograph; the moving carriage closed and opened the primary circuit of an induction coil at pre

1 The purport of the experiment will be best understood if I state that it rollows a series of chapters on colour, viz: the rainbow, the spectrum, its ecomposition by refraction and by reflection; while the last chapter discusses and explains, with experiments, the question of spectral lights versus pigments. The common surface papers, which the children are daily in the habit of using, are then analysed by the prism, and found to be anything but monochromatic.

arranged equal intervals of time. In front of the moving plate a frog's heart was placed in a slit on a screen; at each break a shadow of the heart was thrown on to the plate by means of the induced spark. By this means thirty positions of the heart were registered; the pictures were all sharp and clear. I have also used the same method for photographing the movements of in

sects.

Since these experiments which I showed during the University Extension Meeting in Oxford this year, I have made several attempts to get spark photographs of the front view of objects (not their shadows). In my first experiments the objects were illuminated by an electric spark, the image being received on plate in an ordinary camera. I found that so much useful ligh was shut off by the lenses that only a dim picture could be produced. A quartz lens was next tried and the results wer rather better. I then determined to use no lens, but in its place a silvered mirror. A concave reflector made by silvering a cocave lens of about 10 c.m. diameter was so placed that it reflected the image of a white paper star 7 c. m. diameter, revolving abcu 60 times in a second, on to an ordinary photographic plate, the total length traversed by the light being 80 c.m. The star wa illuminated with a spark exactly similar to that used in the previous experiment; on development a good picture of the star came out. The reflector was neither well made nor well silvered. The idea was suggested by observing some spark photograph: I obtained of waves on the surface of mercury reflecting light. When a steady light is used a photograph of any object is readily obtained by reflection from a suitable mirror. Prob ably a steel surface would be best. The mirror and plate were placed in a long box provided with a hole at one end through which the light reflected from the object passed. A few experiments made on living objects to test the time of exposure in Reflection Photography showed that in order to avoid over-exposure, a very rapid shutter must be used. FREDERICK J. SMITH.

Trinity College, Oxford, October 25.

Induction and Deduction.

As your correspondent invites discussion on this subject I hope you will allow me to repeat in a new form the views I expressed upon it in your columns some months ago. I quite agree with Mr. Russel in maintaining that "true induction is utterly unable to yield us any conclusion that is more than probable and approximate," understanding by induction inference from one or more special cases to a more general rule. But on the other hand it appears to me that Miss Jones's criticism is quite destructive of Mr. Russel's interpretation of geometrical reasoning. The point which both have missed I believe to be this, that a proposition stated in given words, such as the enunciation of Euclid's pons asinorum does not always and to every one convey the same information; and if it is meant in one sense its degree of reliability, and the method by which it must be proved, will be quite different from what they would be if it were meant in another. There are at least three different kinds of interpretation which may thus be put upon the proposition. It may mean (1) the triangle used to illustrate this proposition has equal sides; therefore it has equal angles; or (2) I have conceived a triangle which has equal sides, therefore I have conceived one which has equa! angies; or (3) the connotation ascribed by the adjective isosceles" implies the connotation "having equal sides."

It is not necessary for me here to dwell upon the distinction between the first two interpretations; but the difference between either of them and the third is that this latter gives us Do information about any real thing or concept, but only about what is implied by using certain terms. And this latter kind of information clearly does not require to be based upon any rea knowledge of things, but may be based solely on definitions of words. Arguments with propositions interpreted only in this sense are what I call symbolic arguments; and symbolic conclusions therefore give no real information unless they can be interpreted by the aid of real assertions, such as "I can conceive," or "There actually exist, things possessing the connotations ascribed to these terms by their definitions."

If this distinction has not before been recognized, it is because in most logical discussions we can in this way give a real meaning to our arguments. In elementary geometry, for example. we can with more or less effort-conceive things, or ever actually draw them, which answer to our definitions with sufficient accuracy. And, indeed, the reason why "Euclid'

and "Newton" are generally considered to yield a more valuable mental training than such subjects as analytical geometry is that the older authors, perhaps because they were a bit afraid of purely symbolic argument, tried constantly to keep real pictures and ideas before the minds of their readers. But even so our conviction of the truth of any but the simplest theorems of geometry depends chiefly on the symbolic argument, not on the realization in succession of the actuality of the relations and operations discussed in the course of the proof. This is perhaps sufficiently obvious in the higher branches of even Euclidian geometry, but

I had carried them on a three months' tour in the Mediterranean in 1888, and had taken no special care of them since. They proved in every way as good as new, both in sensitiveness, and perfection and evenness of film. ARTHUR E. BROWN.

THE GENUS SPHENOPHYLLUM.

it becomes absolutely indisputable when we reach such theorems NOTWITHSTANDING the small size and compara

as "Any two conics in one plane intersect in four points." Not only may some of the e points be at an infinite distance, but some, or all, may be what is called, on the lucus a non lucendo

tive scarcity of the plants belonging to this Palæozoic genus, they have long attracted a rather unusual amount of attention. This has been partly due to their

principle, “imaginary"; that is, they may be such that they peculiar external forms, which suggested even to the

cannot be imagined by anybody, much less actually drawn.

Accordingly I cannot admit that the theorems of geometry are established by induction at all. If they are interpreted in either of the first two ways I have described, they are only particular propositions, and the inference from them to a general proposition would no more yield a "mathematical certainty" in this case than in any other. And though the third way of looking at the proposition may be paraphrased into a form which appears general (e.g., anything which may fairly be called "an isosceles triangle" may also be said "to have two equal angles"), it is really only a particular proposition about the words" isosceles triangle," and so on. Its wide applicability and usefulness depends on the fact that we can, and do, often find things which can fairly be called isosceles triangles; but it must be admitted that the assertion that, on any given occasion, we have found such a thing,-is not a mathematical certainty. If the triangle in question is an objective one, we can only say that it is probably, or approximately, isosceles; and though perhaps we may subjectively conceive erfectly isosceles triangles, and so regard the pons asinorum as a subjective necessary truth, it must be doubtful whether we could do so in the case of a more

complex proposition such as Pascal's Theorem, and it is quite

certain that we could not do so in the case of such theorems as that about the intersections of two conics.

It is to be hoped, therefore, that logicians will come to recognize the importance of symbolic reasoning, as mathematicians have already done. And when they do so we may hope for this further advantage, that they in turn will teach mathematicians and others not to confuse a purely symbolic with a real conclusion-not to assume that, because they have correctly proved a conclusion symbolically, that it therefore necessarily gives any information about real things, or even real concepts. EDWARD T. DIXON.

Trin. Coll., Cambs., October 22.

Bell's Idea of a new Anatomy of the Brain.

IN NATURE of October 27 the writer of the review of Mr. Horsley's "Structure and Functions of the Brain," speaking of the rarity of the above book, states that he only knows of one copy in London, viz., that in the British Museum. It may be useful to some of your readers to know that there is a very interesting copy in the library of the Royal College of Surgeons. It is the presentation copy to Dr. Roget "from Mr. C. Bell, 34, Soho Square" by Dr. Roget it was given to Lady Bell, who presented it to the Royal College of Surgeons through Mr. Alexander Shaw.

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earliest observers the idea of resemblances to the Marsiliæ; but the interest they have excited has been further increased of late years by discoveries respecting the peculiar organizations of their stems. In 1822 Adolph Brongniart assigned to them the name of "Spenophyllites," and in 1823 Sternberg figured some of them under the generic title of "Rotularia." Sternberg's figures appeared in his "Versuch einer GeognostischBotanischen Darstellung der Flora der Vorwelt," which work is now best known through the French translation of it by Comte de Bray. To the first of his specimens figured (loc. cit., tab. xxvi., figs. 4a and b), Sternberg gave the name of Rotularia pusilla, and the example so designated is very characteristic of the simpler type of the group, in which we have a somewhat branched stem, with verticils of wedge-shaped leaves at each node. A second form was figured on a later plate of the same work. It is interesting to note that Sternberg associated with these figures the observation, "Plantæ organisatione foliorum Marsileis, forma caulis Hippuri Maritimæ." The generic name thus given by this author represents the rotate arrangements of the leaves in each verticil, as the wedge-shaped contour of each separate leaf is further indicated by Brongniart's generic term, "Sphenophyllites." In 1820 Von Schlotheim had also included similar examples in his too comprehensive genus, "Palmacites." "

In 1828 Brongniart published his classic "Prodrome d'une Histoire des Végétaux Fossiles," in which work we find the generic name of these plants changed to Sphenophyllum, which name they have retained to the present time. In this work Brongniart examines in some detail the probable affinities of these plants, which even in 1822 he inclined to regard as having some affinities with the Marsileæ. He defines them as having six, eight, ten, or twelve leaves in each nodal verticil, each leaf being wedge-shaped; sometimes entire, truncated at its apex, which is denticulate. In some others these leaves are bilobed, and in other species they are not only profoundly bifid, but each of these lobes is either divided into two, or their ends are laciniated. Lastly, in some cases the lobes become narrow and linear. Brongniart here compares these leaves with those of Ceratophyllum and Marsilea, concluding with the statement, "We cannot for the moment decide between these two rela

tionships." At this date the fructification was wholly

unknown.

In his introduction to the "Natural System of Botany," p. 37, Brongniart again reverts to the idea that Sphenophyllum had Marsileaceous affinities.

In 1831 the authors of the "Fossil Flora of Great Britain" commenced their publication of that work, and in one of its early numbers they figured and described under the name of Spenophyllum erosum what appears to be identical with the first figure published by Sternberg. When discussing the relationships of this plant, Lindley and Hutton

1 These figures were preceded in 1703 by a still earlier one by Scheuchzer

in his "Herbarium D.luv.anum." (Coemans and Kickz, "Monographie des

As an illustration of my experience I may mention that in April this year I opened a box of plates (plate Extra Rapid) Sphenophyllum d'Europe "'). which I bought in July 1886.

2 Die Petrefactenkunde auf ihrem jetzigen Standpuncte,"

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