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that with no further elaboration of the furnace than a short firebrick arch at the fore-part (illustrated in Fig. 15) they will perform their work very efficiently, and with practically no smoke when using a bituminous coal.

A chapter is devoted to the chemistry of the combustion process. In referring to the hydrogen in fuels, the statement occurs, "it is generally assumed to be present combined with carbon to form hydrocarbons. The most important of these for the fuel user are -methane, ethylene and acetylene." A small amount of at least the first may be present in coal, but are we to assume the authors to mean that these are the important hydrocarbons existing in the coal before it has been heated?

In view of Bone's work (mentioned in a short footnote) it is a pity the authors did not revise their theory to account for the formation of smoke, seeing that the book was not published until a twelvemonth after Bone and Wheeler's paper appeared in the Journal of the Chemical Society (August, 1903), and Armstrong's paper in the same number, in which it is definitely stated "neither hydrogen nor carbon being burnt preferentially." J. S. S. B.

SCHOOL MATHEMATICS.

New School Arithmetic. Part ii. By Charles Pendlebury, assisted by F. E. Robinson. Pp. vi+207 to 468+ xliv. (London: George Bell and Sons, 1904.) Price 2s. 6d.

New School Arithmetic. By Charles Pendlebury, assisted by F. E. Robinson. Pp. xvii +468+xliv. (London: George Bell and Sons, 1904.) Price 4s. 6d. New School Examples in Arithmetic. By C. Pendlebury, assisted by F. E. Robinson. Pp. xiii +223 + xliv. (London: George Bell and Sons, 1904.)

Price 38.

A School Geometry. Part vi. By H. S. Hall and F. H. Stevens. Pp. iv+347 to 442+ iv. (London: Macmillan and Co., Ltd., 1904.) Price 1s. 6d. Theoretical Geometry for Beginners. Part iv.

By C. H. Allcock. Pp. 224. (London: Macmillan and Co., Ltd., 1904.) Price 1s. 6d. Elementary Plane Geometry. By V. M. Turnbull. Pp. vi+136. (London: Blackie and Son, Ltd., 1904.) Price 28.

PART

Mathematical Problem Papers. By the Rev. E. M. Radford. Pp. vi+203. (Cambridge University Press, 1904.) Price 4s. 6d. net. DART II. of Messrs. Pendlebury and Robinson's "New School Arithmetic " has followed quickly on the publication of part i., and this excellent textbook is now complete. The second part is concerned mainly with the application of arithmetic to the transactions of commerce, dealing with such subjects as interest, discount, commission, stocks and shares, profit and loss, &c. Ratio and proportion find a place, and they are illustrated largely by this class of problem. The authors devote a little space to the training of youths in computations suitable to experimental work in the laboratory. Thus we find that algebraical symbols are freely introduced, and chapters are given

on averages, approximations, mensuration, and logarithms.

graphs, elementary This portion of the book might well have been extended even at the expense, if necessary, of some of the chapters relating to purely business matters. But the subjects treated are very numerous, affording considerable ground for selection, and many teachers will no doubt, and with advantage, omit some of the technical commercial chapters. At every stage examples are introduced in great abundance, the answers to which extend to nearly fifty pages. The book concludes with a collection of test papers, and a large number of miscellaneous problems. Parts i. and ii. are published separately, and also in one volume. The examples and answers may also be obtained without the other text. Altogether the book is one that deserves, and will no doubt obtain, an extended circulation.

With the issue of part vi. of Messrs. Hall and Stevens's "School Geometry," this popular text-book must now be nearing its completion. The present section corresponds, substantially, with Euclid, Book xi., 1–21, and it further deals with the mensuration of the simpler geometrical solids. In establishing the theorems of pure solid geometry, the authors follow Euclid rather closely, but there are some useful additions. Thus it is shown how a point in space is located by means of rectangular coordinates; but it is not shown how position and form may be exhibited graphically by means of projections. In dealing with areas and volumes, elementary trigonometry is used. The prismoidal formula is also introduced, but its value is scarcely made sufficiently manifest, and it is not shown how to deal approximately with irregularly shaped figures, by means of Simpson's or other rules. The book is printed in very distinct type, and the figures and diagrams are beautifully designed and executed. The subject-matter is presented and developed in the clear and attractive style which is always found in the authors' text-books, and is illustrated by well chosen examples.

Part iv. of Mr. Allcock's "Theoretical Geometry for Beginners " treats, in the first instance, of ratio and proportion, with geometrical applications. The propositions correspond roughly with Euclid, Book vi., but the style of proof is different. The reader is first introduced to the conception of ratio and proportion by means of numerical and algebraical examples, and his knowledge of arithmetic and algebra is drawn upon in establishing some preliminary theorems, which are subsequently used in demonstrating the various theorems. The latter half of the book is devoted to modern geometry, including chapters on harmonic pencils, the complete quadrilateral, poles and polars, centres of similitude, inversion, maxima and minima, and envelopes. Some numerical examples are given at intervals, but, as the title implies, the propositions and the exercises thereon are almost entirely confined to deductive geometry, and from this point of view the treatment is eminently satisfactory. The book is got up and printed in a way that leaves nothing to be desired.

The "Elementary Plane Geometry" by Mr. Turn

bull is intended for youths who have already had a course of experimental geometry, and is almost entirely devoted to demonstrative geometry. It is divided into four sections, dealing respectively with triangles and quadrilaterals, circles, areas, and with ratio, proportion, and similar figures. Most of the propositions contained in the volume belong to Euclid, but the author has allowed himself that freedom of treatment that is now happily prevalent. The book shows no conspicuous merits such as would render its general use either likely or desirable.

In the volume by the Rev. E. M. Radford, the author has compiled and arranged a hundred test or examination papers, each containing twelve problems; a large number of the latter are stated to be original, and many are taken by permission from published examination papers. The collection is "intended primarily for the use of candidates for mathematical entrance scholarships at Oxford and Cambridge," and the subjects on which problems are set comprise "pure geometry, algebra, trigonometry, analytical conics, and elementary mechanics," with the addition in the last fifty papers of elementary theory of equations and elementary differential calculus. The book will no doubt prove useful to the class of student for whom it is intended, but the problems show no sign whatever of having been influenced by the reform in the teaching of mathematics which is now in progress. The author hopes shortly to publish a volume of solutions, and this will be very acceptable to teachers who may use the work.

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By

Handbuch der Laubholzkunde. Charakteristik der in Mitteleuropa heimischen und im Freien angepflanzten angiospermen Gehölz-Arten und Formen mit Ausschluss der Bambuseen und Kakteen. Camillo Karl Schneider. Erste Lieferung, pp. 160; Zweite Lieferung, pp. 161-304. (Jena: Gustav Fischer, 1904.) Price 4 marks for each Lieferung. THESE two parts form the commencement of a work intended to render possible the identification of the hardy species of angiospermous trees and shrubs indigenous to, or cultivated in, Central Europe. Such a work invites comparison with Koehne's well known book on the same subject rather than with the more comprehensive descriptive works by Koch and Dippel. From the first named it differs in the vastly greater number of illustrations, and in the fuller details given regarding the characters of buds and twigs. These additional details contained in Schneider's book go far towards removing the uncertainty of diagnosis involved in the provisional identification by means of the dichotomous keys employed throughout the work. present Lieferungen, dealing with the Salicaceæ, Myricaceæ, Betulaceæ, Fagaceæ, Ulmaceæ, Moraceæ, Urticaceæ, Santalaceæ, Loranthaceæ, Aristolochiaceæ, Polygonaceæ, Chenopodiaceæ, Phytolaccaceæ, Caryophyllaceæ, Trochodendraceæ, Ranunculaceæ, Lardizabalaceæ, and some species of Berberis, nominally include 197 illustrations, but in reality contain quite 2000 figures of buds, twigs, leaves, inflorescences, flowers, fruits, and their parts. addition, the free use of abbreviations and of small print has rendered possible the condensation into small

The

In

compass of much information concerning not only diagnostic characters of species, varieties, and forms, but also concerning their nomenclature, distribution, and phenology. To illustrate the method of treatment adopted by the author, Populus alba may be selected from the twenty-three species of Populus considered in this work. Three varieties of this tree are sufficiently described as regards their distinctive features; figures are given of resting-buds, twigs and their transverse sections, four forms of leaves, flowers

seed, embryo, and seedling; information is tendered as to the times of flowering, of flushing of the vege tative buds, and of fruiting, also as to the germin ation, distribution, and age attained by this species; and finally hybrids including this species are noted. In so thorough a work it is exceedingly difficult to but the solitary one that the reviewer has observed is avoid making statements not universally applicable, to the effect that Carpinus Betulus has a trunk with a light grey coating of cork. The work may be strongly recommended to all engaged in the study of dicotyledonous woody plants growing in the open in this country. PERCY GROOM.

The Cancer Problem in a Nutshell. By Robert Bell, M.D. Pp. 39. (London: Baillière, Tindall and Cox, 1904.) Price is. net.

DR. BELL in this pamphlet ascribes the development of malignant disease to a withdrawal of some controlling influence exerted by the thyroid gland upon the cells of the body, caused by some toxic state of the blood. He therefore advocates the administration of thyroid gland or of its active principle in the treatment of the disease, and claims to have obtained successful results. Little or no evidence is given in support of these views, and since malignant disease occasionally, though unfortunately rarely, undergoes spontaneous cure, the apparent success of any form of medical treatment has to be carefully controlled before such a result can be admitted. Dr. Bell's suggestions for the prevention of malignant disease may be of some value. R. T. H.

Photography on Tour. Pp. 132. (London: Published for the Photogram, Ltd., by Dawbarn and Ward, Ltd., n.d.) Price 18. net.

IN these pages, the sizes of which are only 3 inches by 4 inches, we have a number of useful hints and instructions which are well worth an amateur's time to read. When the photographer is away from his base, and has to invent all sorts of makeshifts, he may find many a useful wrinkle given here for which he may later be very thankful. The author seems to have brought into a very small compass a great deal of information covering a wide field, and this pocket book for the touring photographer should serve a useful

purpose.

From the German of Illustrated by Paul (London: Duckworth and

The Story without an End.
Carové. By Sarah Austin.
Henry. Pp. vii + 77.
Co.) Price Is. 6d. net.

In this allegory a child is introduced to the beauties of plants, birds, insects, and other forms and aspects of nature. It pleases children to imagine themselves in close communion with inanimate nature, and they have no difficulty in endowing all the objects around them with human attributes. Poetic feelings, and sympathetic interest in plant and animal life, are appealed to by this daintily bound and gracefully illus trated contribution to literature.

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.]

On the Origin of Flagellate Monads and of Fungusgerms from Minute Masses of Zooglea. BACTERIAL SCums are exceedingly common in ditches and ponds, nature's laboratories, and it is a matter of much importance to know what goes on therein. Some light may be thrown upon this subject by making infusions or macerations from cut fragments of various plants, and then examining, at different periods, the scum or pellicle that forms on such fluids. What I have now to say will refer almost exclusively to infusions made from hay. The hay employed may be either fresh or old, but it does not do to substitute for hay mere unripe grasses. I have elsewhere shown how remarkably different are the products derivable from living unripe grasses and from ordinary hay.'

In making such an infusion I have been accustomed to cut the hay into short pieces, to place these in a little beaker, and then to add water so as well to cover the fragments. After maceration for three or four hours at a temperature of about 86° F. (30° C.), the infusion has been filtered through two or three layers of the finest Swedish filtering paper into another small beaker. In this way all but the smallest particles, 1/12,000 of an inch or thereabout, will be excluded. For observation of the changes now to be described it is best that the bacterial scum, which soon forms on the surface of the fluid, should be very thin, therefore the depth of the fluid ought not to be more than about one and a half inches-though if one is seeking to make out the origin of ciliated Infusoria infusions of greater depth should be employed in order that a fairly thick pellicle may

form.

When such an infusion is kept under a bell-jar (to exclude dust) at a temperature of about 65° F. (18° C.), the pale sherry-coloured fluid in less than twenty-four hours becomes lighter in colour and very turbid. Soon a scum, almost invisible, begins to form on the surface, composed of several different kinds of bacteria, and in about thirty-six hours small Zooglea masses of the most varied sizes and shapes begin to appear therein. In Fig. 1, A, a portion of such a scum is shown as it appeared at the end of the third day on a hay infusion in which the masses of Zooglea were exceptionally numerous. The portion of this scum here represented had been transferred on the tip of a sterilised scalpel to a drop of a dilute solution of eosin, which stained the surrounding bacteria a pale red tint, but left the Zooglea masses unstained, so that they were rendered very distinct. Had logwood been used the results would have been reversed-that is, the Zoogloa areas would have been more or less deeply stained, while the surrounding bacteria would have remained unstained.

Examination of one of these masses with a high power will show its constitution, and reveal the fact that we have to do with an aggregation of separate bacteria imbedded in a jelly-like material. This may be seen from Fig. 1, B, which shows a highly magnified portion of one of the Zoogla masses from the same pellicle after it had been immersed in a drop of a weak solution of Ehrlich's eosinophyle fluid, which stained the surrounding bacteria a yellow tint, while it left the Zooglea mass unstained. The slightly altered bacteria within the Zooglea mass are at this early stage plainly to be seen, though later on they become more or less obscured by reason of progressive molecular changes taking place in the mass during its subsequent transformation.

Some of these Zooglea masses are destined ultimately to be converted into numbers of flagellate Monads or of Amoeba, while others become resolved into heaps of Fungusgerms. I have found it impossible to tell from the mere microscopical appearance of the Zooglea masses whether they are destined ultimately to yield Monads or Fungusgerms. The latter transformation is undoubtedly by far the commoner of the two, and when I was working for many months at this subject during 1899 I was unable to 1 "Studies in Heterogenesis," p. 87 (1904).

find any good specimens, capable of being photographed, showing the conversion of Zooglea masses into Monads, although I many times saw and photographed Monads originating from the pellicle as discrete motionless corpuscles-especially when the infusions were kept at a temperature of about 72° F. (22° C.). But one day last month, on October 19, desiring to make certain observations, I made a weak infusion from a portion of a small handful of hay gathered in Norway more than two months. previously, which had since been kept in a small cardboard box. The infusion was prepared and filtered in the manner already indicated, and divided into two portions: one, which we may name A, being placed in a small open beaker and left beneath a bell-jar at the end of the mantelpiece in my study; while the other (a very small portion), which we may name B, was put into a small half-ounce earthenware pot, over which the cover was placed. The two specimens of the infusion, covered and uncovered, were then left side by side beneath the bell-jar, so that the temperature to which they were exposed might be as nearly as possible similar. Some of the changes in the scums that formed on the surface of these fluids are now to be described.

Origin of Flagellate Monads from Minute Masses of Zoo gloea.

A. When examined fifty-one hours after the time of filtration the scum on this infusion was found to be very thickly crowded with small masses of Zoogloea varying much in shape and actual size, as shown in Fig. 1, A.

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In the course of the fourth day very many of the smallest masses were seen to be undergoing segmentation into small motionless spherical bodies, while multitudes of active flagellate Monads of the same size were for the first time seen in the fluid and in the midst of the portion of the scum under examination. When a similar examination had been made twelve hours previously not a single Monad was seen; now there were swarms of them, and all were of about the same size.

In Fig. 2, A (x 500), some of these small masses are shown together with their contained bacteria; B (x375) shows a number of the small masses undergoing segmentation; while C (x700) shows one of these bodies more highly magnified, in which the segmentation into embryo Monads, still in a motionless condition, is almost complete. In the course of the next day the Monads were found in prodigious numbers. They were spherical or ovoidal in shape, and provided with a single flagellum about twice the length of the body. Under a high power a nucleus could be distinctly seen, generally surrounded by a circle of very minute granules. In addition, two or three larger granules were to be seen-one of them, larger and more highly refractive than the others, being often present in the 1 "Studies in Heterogenesis," pp. 69-73, Figs. 53-55

posterior half of the body of the organism, and there showing faint oscillations. Numbers of the Monads that were aggregated between three small contiguous air bubbles are shown in Fig. 2, D (x 125), as they appeared under a low power of the microscope. Many of them were in active

B. The closed pot was not opened until the end of the fifth day, and I then found the surface of the infusion covered with a very thin, scarcely perceptible film of bacteria, which on microscopical examination was seen to be densely crowded with very minute Zooglea masses such as are shown in Fig. 3, A (x 500). Not a single Monad was to be seen, but many of the masses were found to be about to segment as in B, or actually segmenting as in C, into a number of motionless spherical corpuscles.

During six subsequent days I uncovered the pot for a moment to take up on the tip of a sterilised scalpel a portion of the scum for examination, and on each occasion found the minute Zooglea masses presenting similar characters, except that day by day a rather larger number of them showed evidences of segmentation, though not a single active Monad was to be seen.

The Zooglea masses formed in the dark, and in a comparatively airless pot, were not only different in character from those formed in the open vessel, but it would seem that their process of change was slower and was in part arrested by the opening of the pot, since after eleven days there was still not a single active Monad to be seen, though in the open vessel swarms of them were found during the fourth day. This arrest of the process of change recalls the similar arrest which was always found to occur when the pot was opened in which Hydatina eggs were being transformed into ciliated Infusoria of the genus Otostoma. It so happened that on the very day that I first observed the segmentation of the small Zoogloea masses in A I had

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FIG. 2. A. Small Zooglea masses from the hay infusion (x 500); B, Other of these masses undergoing segmentation (x575); C, One such mass the segmentation of which is nearly complete (X700); D, Monads derived from products of segmentation (X125).

movement and are not shown, but those that were stationary were photographed by a very brief exposure. I found it impossible to photograph these particular Monads under a high power because they were mixed up with active bacteria, and were themselves very delicate in texture. The movements of these bacteria could not be arrested except by a

B

FIG 3.-A, Portion of pellicle taken from the pot (x 500); B, Small Zooglea masses about to segment (X 500); C, Small Zooglea masses which have undergone complete segmentation (X 500).

comparatively strong osmic acid solution, or by exposure to the vapour of a 1 per cent. solution for more than half a minute, and in either case the result was to make the Monads almost invisible, if it did not cause their complete diffluence.

FIG. 4.-A, Minute Zooglea masses in various stages of change (x 5co); B One of these masses in which segmentation has been nearly completed (X700).

on my work-table under a bell-jar a small petri dish in which a tuft of dead lichen had been soaking for a few days in distilled water. There was a very thin scum here and there on the surface of this water, and on examining a portion of it I was surprised to find that it also was crowded with small Zooglea masses, many of which were apparently in different stages of segmentation into Monads, though the majority of them showed no signs of segmentation. Being busy with what seemed at the time to be the more important A infusion, I did not examine this new scum again until after the expiration of two days, and then I found crowds of active Monads, and all the Zooglea masses now in different stages of segmentation such as are shown in Fig. 4, A (x 500). The only portion of an unaltered mass that I could find is seen on the left hand side of this figure, contiguous to the black speck. In the two days all the small Zooglea masses had either 1 Examinations of the scum taken from the pot have since been made at intervals during another week. and still, up to the eighteenth day, not a single Monad has been met with, though very many of the small Zooglea masses have been found segmenting into pale brown Fungus-germs. But nine days ago (in order to test the question whether the premature opening of the pot had caused an arrest of the formation of Monads) I made another similar infusion from the same hay, and placed some of it in another small half-ounce pot, which was opened for the first time to-day. In the first portion of the scum obtained from this second pot I found swarms of active Monads, and also heaps of the small brown Fungus-germs resulting from the segmentation of other of the Zooglea masses.-November 14. "Studies in Heterogenesis," pp. 49-51, and xiv.

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FIG. 5-A, Products of segmentation stained, and appearing as minute spherical nucleated cells (X900); B, Monads in a resting stage (X700). shown in Fig. 5, A (x900), after they had been lightly stained with Westphall's mastzellen fluid. In this embryonic condition the future Monads are seen as spherical nucleated cells, either single or in pairs. Some of the

FIG. 7.-A Zooglea mass undergoing change (375).

been unable to ascertain, though I know that in rare cases swarms of minute Amoeba rather than Monads appear in this way in hay infusions. The production of swarms of minute Amoeba is, however, the rule in the pellicle that forms on an emulsion made by pouring about eight ounces of water on a teaspoonful of mixed white and yolk of egg. Such Amoebæ, slightly stained with logwood, are shown in Fig. 6, B (x200), taken from a pellicle on the seventeenth day, while in C (x 125) they are seen, as I believe, originating in another egg and water emulsion on the eighteenth day, in the midst of irregular clumps of bacteria. These aggregates of bacteria had been noticed for several days, but when first observed not a single Amoeba had, up to this time, been seen either in them or in the surrounding

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FIG. 6.-A, Monads developed from Zoogloca masses in a hay infusion (x 500); B, Amoeba stained with logwood, from an egg and water emulsion (x200); C, Amoeba originating in the scum from an egg and water emulsion (x125).

Monads which were found a few days later in a motionless, resting condition, are shown in B (x700).

On other occasions I had been a little more successful in photographing Monads produced from Zoogloea areas in a hay infusion. Thus Fig. 6, A (x 500), shows some such

FIG. 8.-Portion of a Zooglea mass about to segment (X500).

fluid. Then there were appearances as though changes were taking place within the aggregates, followed in two or three days by the presence of swarms of minute sluggish Amabæ around, and issuing from, the bacterial aggregates, as shown in the figure under a low magnification.

In reference to the occurrence of these swarms of minute Amoebæ, I may say that I have never seen one of them multiply by fission, and certainly their vast numbers are not to be accounted for in this way. I make these remarks concerning Amoeba without pretending that what I have here said in regard to them is quite conclusive, or in any

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