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proposes to bring out triennially. The present two volumes Refractor shows (“ Pub. Ast. Soc. Pacific,” Vol. II. p. 164) form a continuation, and extend as far as $ 5 of the second that the circle of aberration of F light on the local plane for the chapter in the second book. The author proceeds on the

D line has a diameter which is in terms of the focal length same lines as formerly, and places before the reader

'COO0349. We may take this diameter as very nearly that of the

circle of aberration of D light on the focal plane for the F line. in a concise way all the new methods of development,

Thus if a star emits only D and F light, and the F light is measuring lenses, apparatus, &c., from the particulars

focussed, then the D light will fill a circle nearly 7" in diameter, of constitution which characterize developers down to

and the star will look like a planetary nebula with a stellar the latest form of kodak or tie camera. Not only is

nucleus. If the star ( mits light of wave lengths 500 and 575, each subject treated with the greatest care, but then interpolation based on Keeler's measurements shows that illustrations are numerously distributed. That which round a stellar nucleus in the focus for wave length 500 there will add great value to the work as a whole is the inser. must be a circle of aberration of nearly 4" diameter. tion of references, for what, after all, is more annoying Mr. Campbell sound lines of wave lengths 500 and 575 in the than having to wade through a great quantity of literature

spectrum of Nova Aurigæ with respective intensities 10 and 1. when the presence of one or two words would have

Mr. Barnard describes the appearance of nebulosity as “pretty eliminated all trouble?

bright and dense,” and as measuring 3" diameter. My own

inability to see either the circle of aberration for the yellow line The Reliquary: Quarterly Archæological Journal and

when the green was focussed, or the alleged nebulosity, may be Review. Vol. VI. (New Series). (London: Bemrose

explained in several ways (e.g. smaller aperture of object glass,

climatic conditions, &c.). The spectroscope could probably and Sons, 1892.)

decide the question at Mount Hamilton by showing whether This volume consists of the four numbers of The Reli the minimum length of any of the lines is that corresponding quary which have appeared during the present year. with 3" diameter on the slit. I have not been able to do more The contents include many things which do not quite

than observe that the yellow line is not visible when the 500 come within the scope of NATURE ; but it is satisfactory

line is focussed on the slit of a spectroscope having an effective to be able to note that the writers, speaking generally,

dispersion of two 60° prisms.

H. F. NEWALL. have done their work in a thoroughly scientific spirit.

Observatory, Cambridge, October 24. Mr. J. Lewis André contributes an interesting and wellillustrated paper on leather in the useful and ornamental

Formation of Lunar Volcanoes. arts, and a clear account is given by the editor of a part While we have, on the lunar surface, a series of markings of an early dial, bearing runes, which he was lucky enough so evidently volcanic that no one thinks of applying any other to find some months ago in the churchyard of Skelton, term to them, we have on the other hand no explanation of Cleveland. An illustration gives a good impression of their mode of formation which will stand examination. The the general character of the stone, the runes on which, explanation given by Messrs. Nasmyth and Carpenter in their according to Canon Browne, are “Danish." Among the splendid work on the moon, founded upon explosive expulsion other papers are two articles, by Mr. D. A. Walter, on of lava, fails to satisfy the mind when applied to wide craters ancient woodwork, and a discussion, by the Rev. A.

with a low wall such as Shickard or Grimaldi, of which there Donovan, of some of the probleins connected with the

are so many on the moon, and which look more like some dis

turbance in a semi-liquid career of Columbus.

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 LETTERS TO THE EDITOR.

experience, as the erupted material (unless light enough to be

driven by wind) invariably falls back into the neighbourhood of (The Editor does not hold himself responsible for opinions ex.

pressed by his correspondents. Veither can he undertake to returr, or to correspond with the writers of, rejected manuscripts intended for this or any other part of NATURE. No nolice is taken of anonymous communications.]

Nova Aurigæ. 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 sainter, but there was an obvious bright line in the yellow, which may be the line which Dr. Copeland estimated as 580'l on August 28 (NATURE, September 15), or may be that which has been measured several the vent, and we could not conceive of its being shot neatly imes at the Lick Observatory (Astrophysics, October, p. 717), out twenty-five miles on every side to form the familiar ring. nad appears to have a wave length of about 575. It had escaped | An explanation of the mode of formation sounded upon lunar Dy notice before, but I was induced to look most caresully in tidal motion occurred to me about seventeen years ago, from be yellow by considerations arising out of an attempt to recon. observations on a cooling slag ; but until the recent publication cile Mr. Barnard's observations of apparent nebulosiiy surround of Mr. Darwin's work on the history of the tides I was doubtful ng the Nova, as seen in the 36-inch refractor at Mount if that force were sufficient to account for observed results. Hamilton, with my own observations of September 14. Mr. I had noticed that the rise and fall of a sused slag through Barnard's “stellar nucleus " was the difficulty. There appears holes in its solidifying crust, formed craters exactly like those in

be no doubt that the Nova is emitting a spectrum similar to | the moon; and I enclose a photograph of a piece of that slag hat of a planetary nebula, but it seems to me necessary to have in which is reproduced all the salient features of the lunar urther spectroscopic evidence before it is established that surface. ebulous extension can be seen ; if it is to be seen with a simple The mode of formation was as follows:vepiece, it must be looked for in a reflecting telescope, as ihe. The sused liquid (wbich was polash "black ash" containing Sllowing considerations will show.

| a mixture of substances of very varied melting point) was still Prof. Keeler's study of the chromatic correction of the Lick 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 with a raised floor and a central cone, at b a crater filled to be intermittently choked, the accumulation of gas beneath the crust lip like “Wargentin,” while on the plain near b, and round the caused the liquid “lava” to rise through any neighbouring holes open crater c, will be seen numerous minute craters, as on the as at e, f, giving rise to a ring crater. The pressure of the ac moon's surface in the neighbourhood of "Aristotle" a cumulated gas now drove out the obstruction in a, when the “ Copernicus," while in other photographs are seen waled liquid lava receded in e as at g. This intermittent action went plains like the "Mare Crisium," so that all the importe! on till the crater i was built up - entirely by "rise and fall ” (as | features of lunar topography are reproduced in this slag, and of a tide), no gas escaping at this hole.

there are many minor points of agreement which cannot be gute In the case of the moon the rise and fall would be caused by into in the limits of a letter. the tidal motion of the still liquid interior. The solid crust Although I have always considered the tides the cause of the would resist the periodic rise of the liquid interior, and the wonderful lunar configuration, I was not satisfied that that cas liquid would well through the crust and recede again as the alone was of sufficient magnitude, till the work of Mr. Darvin wave passed.

placed the matter in such a clear light that I now venture to When the crust was thin, and the lava very liquid, the large submit the idea to your readers as a feasible explanation of the ring structures would be formed, as the lava would flow far ; but familiar lunar features.



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 oppo site angles that would be referred to.

I should be glad to know whether there is any term expresse ing the relation in question in use among either English a 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, wbea 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.

(I) To simplify the expression of fractions we have the solidas suggested by Sir G. Stokes. But the solidus has been hitherta 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 Fig. 2.

by defining more definitely its exact meaning. This is done in

the simple conventions proposed below. as the crust got thicker and the lava more viscid, the more (2) To express the process of involution, the sign \, suggested striking craters like Copernicus would be built up. When the by Mr. C. T. Mitchell in the Electrician, is more concise and vent was very small, or the lava very viscid, the exuded lava clearer than that mentioned by Prof. S. P. Thompson in would build up mountain ranges, or peaks like Pico, as it could NATURE. And Mr. Mitchell's sign, if defined by convention not flow far, and would be cooled too much to allow of its flow similar to those applied below to the solidus, is capable of a lit: ing back with the ebb tide.

extensive application. The existence of the cause proposed by Messrs. Nasmyth and (3) To express roots we have the sign . But, when accon Carpenter, viz., expansion on solidification, is very doubtful. panied by a horizontal line above to show the extent of a The proof they adduced was that a piece of solid slag would influence, this sign also requires special spacing. But it can be float on liquid slag. But when slag solidifies it becomes filled brought into line with the rest by the use of the same contes with small cracks, which doubtless contain air, and so aid in the tions. flotation. When I was working at this subject I had some slag Taking then for poured into an iron mould kept cool by immersion in water. When the slag had cooled a distinct depression was seen on the

a. the sign of division ... ... upper free surface, showing that the slag had contracted during

B. , „ involution solidification. No doubt its contraction or expansion will de

7. „ „ evolution ... pend upon its composition, and we do not know the composition of the moon's surface, but we need not depend upon a doubtsul we may use each of these signs in either of two ways: property for an explanation when a set of conditions have I. Simply as a sign of operation, in which case it can influers existed which must have yielded an ample force for the pro- only the quantities immediately adjacent to it. duction of the observed results,

II. In a double capacityIn the photograph marked Fig. 2, at a can be seen a crater 1 (1) As a sign of operation.

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(2) As one end of a bracket, of which the other end is 1.

“Sunshine.” This bracketing influence may be directed either forwards or IN acknowledging the courteous criticism and the kind rebackwards, or both ways at once.

marks which “C. V. B.” has been pleased to make about my Examples.

little book, may I be permitted to comment on one or two points,

which I think he has imperfectly understood from the text. We a. Division.

all know that when “C. V. B.” undertakes to review a book, a + b + d = a + b c + d,

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 a = 1 a + b/c + dl,

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 (b + c)(d + c) = arlo

education, and while I agree with him in the main, I am tempted

in passing to remind him of what Tyndall terms “the scientific sin = sin 0/n, sin o = | sin on.

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 Continued fractions also can readily be brought into one line one of “Nature's Story Books" I feel fully justified in employ. by this notation

ing, 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 T oin ' = a/b + clld + c) + fl8l,

course based upon some hundreds of experiments synthetically B. Involution.

worked out and deductions made-a course whose main object

is to lead children to go direct to Nature, via experiment, for a = a\b, a-= a \ - 6,

their knowledge, there is little danger that the imagination be (a + b) + d = 1 a +\c + d,

cultivated at the expense of the reasoning faculties. The ex. a + 3ctd = a + b c + dl,

perience of the writer is that the children attending the lectures

became extremely critical-a state of mind which, although of (a + b)^t« = la to\c+dl,

inestimable value in acquiring knowledge, is not one of the

happiest in other respects. Therefore it was thought desirable (a + b)ett = |a + 16+d/e+fl. to provide them with some necessary ballast, and this is my defence

of the hypnotic visit to the moon, and the o:her two chapters to \/c and a/0\c are ambiguous, but la 10/6= %, be which the critic alludes.

Natural science apart, it seems to me that the tendency of the cause I being unnecessary for \ in this case, can apply only school-teaching of to-day is calculated rather to make children

hard and matter of fact. For this reason I have endeavoured to/. dois a +6\/d, two vertical lines being required. 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 “Sunacd= a.

shine” the realism which the “picturesque language” was in

tended to convey, disposes of the case of my Cape Town 7. Evolution

reviewer, who mildly insinuates that I have been guilty of some Na + b + c = 1 n Ja + b + cl,

fraud upon little children in calling “Sunshine" a story-book.

Therefore I am the more glad that “ C. V. B." agrees with me * c+ d = 1 a ti ovc+d],

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 at"%c + d = 1 a + bnc + d,

that I shall be most happy to add the exception in the

case of the rainbow. I thank him also for pointing out a a + b. No + d = a + b c + d ),

passage in the notes where an additional clause is necessary, a + c + d = a + 1 b1c + d.

owing to the transposition of a paragraph. But I take excep

tion 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

C. V. B." has in mind, because my boys get green and he

gets (he says) white, or nearly white. The home experiment is = 10\1/21/11d +6\31.

reads : “I am giving each of you squares of coloured paper to

take home ... then you may have the papers to put on your There are many other ways in which this notation might be

tops-c.8., cover half blue and half yellow, spin the top and used ; but the above will suffice to illustrate the advantages of you will see green." A note on page 341 refers to the kind of it. And these advantages are substantial. It enables the work paper. Now it seems to me from the expression “painted to be printed in the same space as ordinary letterpress, and thus disc," which “C. V. B." has made use of, that possibly he may avoids the special spacing, from which nine-tenths of the troubles have had Clerk Maxwell's top in mind when he wrote. in mathematical printing arise. It requires no new types, except, When I say to a boy, “Here are two squares of paper, one blue perhaps, \, and each of the signs used is suggestive of the | and one yellow ; when you've done so and so, you can have the original mode of writing for which it is a substitute. It can be

paper to keep-cover your top, half yellow, half blue, &c.," the used without confusion in conjunction with all ordinary brackets. | lad understands me, and when I am not there he takes out his How far this notation would suit very complicated expressions, halspenny whip-top, tears a piece of the blue paper, and is a point that would have to be determined by experience; but | rendering it slightly adhesive hammers it down on the top with for printing mathematics of ordinary complexity it would be his right fist; he tears a similar piece and treats it in the same useful in economizing space and diminishing the risk of way, and so on until he has covered half. Then he takes the printers' errors without any sacrifice of clearness.

yellow paper and covers the other half with irregular patches of Cambridge, October 27.

W. CASSIE. yellow. He spins the top and sees green.


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How different is this from Clerk Maxwell's top. Clerk Max | arranged equal intervals of time. In front of the moving plate a well selected for his top the purest of paper and pigments. He frog's heart was placed in a slit on a screen ; at each break a endeavoured to match the spectral colours (considerably diluted). shadow of tbe heart was thrown on to the plate by means of the He selected a scarlet red with a tinge of orange like orange-red induced spark. By this means thirty positions of the heart were vermilion, lying in the spectrum one-third the way towards D, registered ; the pictures were all sharp and clear. I have also between the lines C and D. His green was one fourth the dis used the same method for photographing the movements of intance from E, between E and F, and resembled emerald green. sects. He also selected a blue violet midway between F and G, Since these experiments which I showed during the University which was imitated by that purest of colours-ultramarine. Now Extension Meeting in Oxford this year, I have made several let us try the given experiment under the favourable conditions attempts to get spark photographs of the front view of objects guaranteed hy Maxwell's discs, viz., the purest of colours (not their shadows). În my first experiments the objects were painted on Whatman's paper. Taking up a disc of ultramarine illuminated by an electric spark, the image being received on : and another of pale (not orange) chrome yellow, and conceal. plate in an ordinary camera. I found that so much useful ligh' ing hall of one disc behind the other, on rotating the compound was shut off by the lenses that only a dim picture could be disc so that the eye shall receive simultaneously blue and yellow produced. A quartz lens was next tried and the results were light, the result is not white or even practically white, but a rather better. I then determined to use no lens, but in its place grey, tingrd with yellow. By a careful adjustment, hiding more a silvered mirror. A concave reflector made by silvering a con of the yellow and exposing more of the blue (thereby altering cave lens of about 10 cm, diameter was so placed that it reflected the proportions of the text), it is possible to get rid of this the image of a white paper star 7 c.m. diameter, revolving about yellowness and to obtain an absolutely neutral grey which it 60 times in a second, on to an ordinary photographic plate, the might be possible to persuade some grown-up people repre- total length traversed by the light being so c.m. The star wa sented white, but which on analysis yields 711 per cent. black illuminated with a spark exactly similar to that used in the to 28, per cent. white. This may be proved by revolving a previous experiment; on development a good picture of the stur disc of black and white sectors in the above proportions, the came out. The reflector was neither well made nor well silverel. results in each case being identical. But even this result, un The idea was suggested by observing some spark photographs I satisfactory as it is, does not apply to the passage quoted in obtained of waves on the surface of mercury reflecting light. the text, in which no special conditions are observed. I main When a steady light is used a photograph of any object is tain what is easily proved by experiment in less time than it takes readily obtained by reflection from a suitable mirror. Prob

to write it, that when ordinary colours, e.g., gamboge and ably a steel surface would be best. The mirror and plate · Prussian blue, are used, the residual light is green. 1

were placed in a long box provided with a hole at one I fear that already this letter is too long, and since I do end through which the light reflected from the object passed. not wish to monopolize the space kindly placed at the dis. A few experiments made on living objects to test the time of posal of your correspondents, I must defer the consideration exposuie in Reflection Photography showed that in order to of the annotations on soap films. The other points are dealt avoid over-exposure, a very rapid shutter must be used. with in the prelace. AMY JOHNSON.

FREDERICK J. SMITH. 52 Lower Sloane Street, S. W., October 12

Trinity College, Oxford, October 25.

Induction and Deduction. I do not think that the observations on my review of " Sun

As your correspondent invites discussion on this subject I hope shine" require more than a very short answer.

you will allow me to repeat in a new form the views I expressed I considered that the authoress had not by any means cleared

upon it in your columns some months ago. I quite agree with the confusion which usually exists as to the meaning of the

Mr. Russel in maintaining that “true induction is utterly unexpression “mixing of colours." It is applied both to the case

able to yield us any conclusion that is more than probable and where two or more colours are seen superposed, e.g. by spin

approximate," understanding by induction inserence from one ning coloured paper where the resultant tint is due to the sum

or more special cases to a more general rule. But on the other of the separate colours in the constituents, and to the case of

hand it appears to me that Miss Jones's criticism is quite demixed pigments where the resultant tint is that which is com

structive of Mr. Russel's interpretation of geometrical reasoning. mon to the constituents. Now as the common “paint box”.

The point which both have missed I believe to be this, that a rule says that blue and yellow make green, that is that blue

proposition stated in given words, such as the enunciation of and yellow pigments mixed produce a green pigment, it seems

Euclid's pons asinorum does not always and to every one conto me very misleading to say “Cover half (of your top) blue

vey the same information ; and if it is meant in one sense its and half yellow and you will see green. Of course it may degree of reliability, and the method by which it must be happen that the slight departure from white which will be ob

proved, will be quite different from what they would be if it served may be in a greenish direction, but it may also be inclined

were meant in another. There are at least three different kinds towards pink, or, for anything I know, towards any other

of interpretation which may thus be put upon the proposition. colour. The one thing it will not do, however, is to make

It may mean (1) the triangle used to illustrate this proposition a green such as is obtained by mixing the pigments, and such

has equal sides; therefore it has equal angles; or (2) I have conas I fancy from the context any one would expect. C. V. B.

ceived a triangle which has equal sides, therefore I have con

ceived one which has equal angles; or (3) the connotation ascribed The Photography of an Image by Reflection.

by the adjective "isosceles” implies the connotation “having

equal sides." THE great utility of spark photography for obtaining time it is not necessary for me here to dwell upon the distinction records of quickly-moving objects must be apparent to all between the first two interpretations ; but the difference be. who know the experiments of Mr. C. Bell, Prof. Boys, and tween either of them and the third is that this latter gives us Do Lord Rayleigh. By means of spark photography the shadow of information about any real thing or concept, but only about any object such as a jet of water, a flying bullet, or a broken soap what is implied by using certain terms. And this latter kind of film can be produced with perfect definition. The shadow of information clearly does not require to be based upon any reai the moving object illuminated by an electric spark is thrown on knowledge of things, but may be based solely on definitions of to a sensitive plate in a dark room, and the plate is developed words. Arguments with propositions interpreted only in in the usual manner. The process of spark shadow photography | this sense are what I call symbolic arguments; and symbolic will be found, I believe, of great service in physiological research. conclusions therefore give no real information unless they can With a view to try this I attached a long sensitive plate to the be interpreted by the aid of real assertions, such as “I can traversing carriage of a chronograph; the moving carriage closed, conceive," or " There actually exist, things possessing the and opened the primary circuit of an induction coil at pre connotations ascribed to these terms by their definitions." • The purport of the experiment will be best understood if I state that it

If this distinction has not before been recognized, it is because rollows a series of chapters on colour, viz: : the rainbow, the spectrum, its

in most logical discussions we can in this way give a real meanecomposition by refraction and by reflection; while the last chapter dis ing to our arguments. In elementary geometry, for example, cusses and explains, with experiments, the question of spectral lights versus

we can-with more or less effort-conceive things, or ever 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

actually draw them, which answer to our definitions with monochromatic.

sufficient accuracy. And, indeed, the reason why “ Euclid

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and "Newton" are generally considered to yield a more valuable I had carried them on a three months' tour in the Meditermental training than such subjects as analytical geometry is that ranean in 1888, and had taken no special care of them since. the older authors, perhaps because they were a bit afraid of They proved in every way as good as new, both in sensitivepurely symbolic argument, tried constantly to keep real pictures ness, and perfection and evenness of film. and ideas before the minds of their readers. But even so our con

Arthur E. Brown. viction of the truth of any but the simplest theorems of geometry depends chiefly on the symbolic argument, not on the realization in succession of tbe actuality of the relations and operations discussed in the course of the proof. This is perhaps sufficiently

THE GENUS SPHENOPHYLLUM. obvious in the higher branches of even Euclidian geometry, but NOTWITHSTANDING the small size and comparait becomes absolutely indisputable when we reach such theorems

Y tive scarcity of the plants belonging to this Palæoas “ Any two conics in one plane intersect in four points." Not

zoic genus, they have long attracted a rather unusual only may some of the.e points be at an infinite distance, but some, or all, may be what is called, on the lusus a non lucendo

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.

earliest observers the idea of resemblances to the MarsiAccordingly I cannot admit that the theorems of geometry

liæ ; but the interest they have excited has been further are established by induction at all. If they are interpreted in

increased of late years by discoveries respecting the either of the first two ways I have described, they are only peculiar organizations of their stems. In 1822 Adolph particular propositions, and the inference from them to a general Brongniart assigned to them the name of “ Spenophyl. proposition would no more yield a “mathematical certainty” in lites," and in 1823 Sternberg figured some of them this case than in any other. And though the third way of under the generic title of "Rotularia."1 Sternberg's looking at the proposition may be paraphrased into a form figures appeared in his “ Versuch einer Geognostischwhich appears general (e.g., anything which may fairly be called Botanischen Darstellung der Flora der Vorwelt," "an isosceles triangle" may also be said "to have two equal which work is now best known through the French angles"), it is really only a particular proposition about the words " isosceles triangle," and so on.

translation of it by Comte de Bray. To the first of his

Its wide applicability and usefulness depends on the fact that we can, and do, often

specimens figured (loc. cit., tab. xxvi., figs. 49 and 6), find things which can fairly be called isosceles triangles; but it

Sternberg gave the name of Rotularia pusilla, and the must be admitted that the assertion that, on any given occasion,

example so designated is very characteristic of the we have found such a thing,-is not a mathematical certainty. If simpler type of the group, in which we have a somewhat the triangle in question is an objective one, we can only say that branched stem, with verticils of wedge-shaped leaves it is probably, or approximately, isosceles ; and though perhaps at each node. A second form was figured on a later plate we may subjectively conceive , erfectly isosceles triangles, and of the same work. It is interesting to note that Sternso regard the pons asinorum as a subjective necessary truth, it berg associated with these figures the observation, must be doubtful whether we could do so in the case of a more “Plantæ organisatione foliorum Marsileis, forma caulis complex proposition such as Pascal's Theorem, and it is quite Hippuri Maritimæ.” The generic name thus given by certain that we could not do so in the case of such theorems as

this author represents the rotate arrangements of the that about the intersections of two conics. It is to be hoped, therefore, that logicians will come to

leaves in each verticil, as the wedge-shaped contour of recognize the importance of symbolic reasoning, as mathe

each separate leaf is further indicated by Brongniart's maticians have already done. And when they do so we may

generic term, “Sphenophyllites." In 1820 Von Schlothope for this further advantage, that they in turn will teach

heim had also included similar examples in his too commathematicians and others not to confuse a purely symbolic with 'prehensive genus, " Palmacites." a real conclusion-not to assume that, because they have In 1828 Brongniart published his classic "Prodrome correctly proved a conclusion symbolically, that it therefore d'une Histoire des Végétaux Fossiles," in which work necessarily gives any information about real things, or even real we find the generic name of these plants changed to concepts.

EDWARD T. Dixon. Sphenophyllum, which name they have retained to the Trin. Coll., Cambs., October 22.

present time. In this work Brongniart examines in some

detail the probable affinities of these plants, which even Bell's Idea of a new Anatomy of the Brain.

in 1822 he inclined to regard as having some affinities IN NATURE of October 27 the writer of the review of Mr.

with the Marsileæ. He defines them as having six, Horsley's “Structure and Functions of the Brain," speaking of the

eight, ten, or twelve leaves in each nodal verticil, each rarity of the above book, states that he only knows of one copy

leaf being wedge-shaped ; sometimes entire, truncated at in London, viz., that in the British Museum. It may be useful

| its apex, which is denticulate. In some others these to some of your readers to know that there is a very interesting

leaves are bilobed, and in other species they are not only copy in the library of the Royal College of Surgeons. It is the profoundly bifid, but each of these lobes is either divided presentation copy to Dr. Roget“ from Mr. C. Bell, 34, Soho into two, or their ends are laciniated. Lastly, in some Square": by Dr. Roget it was given to Lady Bell, who pre. cases the lobes become narrow and linear. Brongniart sented it to the Royal College of Surgeons through Mr. Alex here compares these leaves with those of Ceratophyllum ander Shaw.

and Marsilea, concluding with the statement, “We Mr. Shaw has added in MS. a copy of the letter received cannot for the moment decide between these two relafrom the printers fixing the original date of publication, and also tionships." At this date the fructification was wholly the list of persons to whom presentation copies were sent. The

unknown. letter and the list are both published in Mr. Shaw's reprint of the Tract in the Journal of Anatomy, ol. iii., 1869.

In his introduction to the “Natural System of Botany," Jas. B. BAILEY,

p. 37, Brongniart again reverts to the idea that SpheOctober 27. Librarian Roy. Coll. Surgeons.

nophyllum had Marsileaceous affinities.

in 1831 the authors of the “ Fossil Flora of Great

Britain” commenced their publication of that work, Photographic Dry Plates.

and in one of its early numbers they figured and IN reference to "Prevention's" note on Photographic Dry described under the name of Spenophyllum crosum Plates, one cannot but agree with him that packets should be what appears to be identical with the first dated when issued from the factory.

figure published by Sternberg. When discussing I would venture, however, to suggest that good makers' plates the relationships of this plant, Lindley and Hutton do not deteriorate within a reasonable length of time.

As an illustration of my experience I may mention that in * These figures were preceded in 1709 by a still earlier one by Scheuchzer April this year I opened a box of plates (1 plate Extra Rapid) |

in his "Herbar um D.luv.anum." (Coe.nans and Kickx, "Monographie des

Sphenophyllum d'Europe'') which I bought in July 1886.

3"Die Betrefactenkunde auf ihren je zigen Standpuncte,"

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