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rectilinear movement; but apart from this, the use of the word "rectilinear" here is a petitio principii of the grossest description. How can we say anything about the adaptation of the bones to rectilinear movement until we have the concept of what rectilinear motion is?

This leads us to the consideration of the more metaphysical parts of the book. Frankly, we disagree with the author on one or two fundamental points. He protests against the absolute as an illusion-even against what we may call the special absolute; we believe, on the other hand, with Bradley, that in a certain sense the absolute does "precede," or is involved by, the relative. At the same time, we may fully admit that concepts are formed by a psychological process, and that there is no realisation of an absolute, in the same sort of way that we cannot realise the arithmetical continuum as we can the numbers 2 and 3. Again, the author just touches on cases of illusion, insanity, and complete hallucinations; saying of the latter that "fortunately they seem quite rare." Doubtless this is fortunate, in one sense; but to ignore them without attempting to give a philosophical explanation of them is merely a. confession of failure. However, we must agree to differ on metaphysics for the present, and be thankful that so much has been done recently to clear away fallacies and quibbles, and bring the real problems of philosophy into view.

The translation reads well on the whole, and we have only found one misprint of importance: on p. 321 "vertical" should be "vortical." On p. 17 the account of Russell's "vicious circle " analysis is not clear; whether this is the fault of the author or that of the translator we cannot say. What Russell has pointed out is that we are talking nonsense when we ascribe to a class of classes a defining quality which characterises its members: for instance, to speak of "the number of all numbers" is as nonsensical as to say "the animal comprising all animals.' Similarly, there is no "class of all classes," and this is the most important example of the theorem. G. B. M.

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theoretical basis for the interpretation of the results obtained in the investigation of the vapour pressures and freezing points of solutions. It so far as dilute solutions are concerned, the problem of molecular complexity is partially solved by the application of osmotic methods, although the question of the association of solute and solvent in the same molecule does not lend itself to attack in this way. When we pass from dilute to concentrated solutions or liquid mixtures, the problem acquires an entirely different character. For such mixtures there is no general guiding and reconciling principle such as is afforded by the hypothesis of Avogadro. The same difficulty confronts us when we deal with pure liquids. methods available for the investigation of the molecular condition of pure liquid substances are entirely empirical, and the value to be attached to the various methods which have been proposec is at present largely a matter of personal opinion.

The

It is with the dependence of the complexity of the molecule on the nature of the constituent atoms, and on the forces which act on it, in so far as these forces are modified by changes in temperature, concentration, state of aggregation, and nature of the solvent, that the author's subjectmatter is concerned. One chapter is devoted to the molecular complexity of gases, two to the complexity of dissolved substances, and three to that of pure liquids.

The molecular condition of pure liquids has attracted a great deal of attention in recent years, and the literature of the subject has attained to such dimensions that a summary and critical survey of the methods involved is particularly opportune. Molecular association has been the theme of the author's own work for many years, and it is therefore quite intelligible that the monograph is not a mere compilation of facts and hypotheses, but represents an extensive, well-ordered, and closely reasoned discussion of the salient features of the subject.

In an appendix, which runs to forty-four pages, the author gives a tabular record of the results of the investigation of the molecular complexity of dissolved substances. As a table of reference this should be found extremely useful, and its compilation adds materially to the value of the work.

Comprehensive as the monograph appears to be, there are certain noteworthy omissions. For instance, the reviewer has looked in vain for any reference to the determination of the molecular complexity of dissolved substances by means of the lowering of transition temperatures. Such investigations afford information relative to the molecular condition of substances in concentrated salt solutions. Although limited in their appli

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THE FUNDAMENTALS OF THREE-COLOUR
PHOTOGRAPHY.

Three-Colour Photography: with Special Reference
to Three-Colour Printing and Similar Processes.
By Arthur Freiherrn von Hübl. Translated by
H. O. Klein. Pp. 138. (London: Percy Lund,
Humphries and Co., Ltd., 1915.) Price 7s. 6d.
HE
of this volume is much more
scope
limited than the title might be supposed
to indicate. The author deals with the theories

ΤΗ

it is more or less immaterial whether or not the photographic colour analysis is absolutely correct, and that "fine-etching or retouching is the greatest factor in solving the problem of threecolour process work." One may be rather sorry to see so high an authority take up such a posi| tion, but he justifies his opinion with regard to inks, by pointing out that the theoretical inks are so "very bright and fiery," that the colour scheme is very sensitive, and therefore the slightest error in the balance of the pigments makes it impossible to produce neutral greys or black under ordinary printing conditions. The use of a pure yellow, an almost blackish blue, and a very deep red allows of slight variations in their proportional intensities without greatly influencing the result, and are to be preferred, although they reduce, to a certain extent, the range of colours that can be reproduced. Moreover, artists use blackish (not pure) colours, and the "colour magnificence of a painting is not due to the use of brilliant pig

ments, but to the effects of colour contrast." The
pigments of modified colour have the further
advantage of being less liable to change on ex-
posure than those that more nearly approach the
theoretical requirements. In spite of this apparent
qualification of the indications of theory pure and
simple, the theory is and remains sound, and it
is only the uncertainties of practical work that
require a little concession.
C. J.

of light and colour so far as concerns the subject, and in a thoroughly practical way with the sensitising of plates, the making and choice of colour filters, and the choice of inks, but the actual printing processes themselves are barely mentioned. Screen-plate processes, such as the use of autochrome and similar plates, are not dealt with. We have therefore a treatise on the fundamentals of three-colour photography. We must first express our disappointments. At page 95 there are eight absorption spectra, showing the effect of each dye in two concentrations, but we cannot find any indication as to the dyes to which these (1) The Extra Pharmacopoeia of Martindale and

spectra refer. There are references to "Supplement IV.," a coloured plate which should contain some most interesting results, but the plate is not anywhere to be found. At page 80 we are told that "for accurate work it is necessary to measure the densities with the aid of Marten's polarisation photometer," as if this were the only instrument suitable for this purpose, or the only accurate photometer applicable. Of course, there are many forms of photometer available, and not everyone would prefer the Marten instrument.

Having said so much, we have nothing to express but a vivid appreciation of the value of the treatise. The formulæ given are not innumerable, but they are the select few chosen by one who is thoroughly conversant with the subject. It is interesting to note that the author is not one who struggles after theoretical perfection at any price, as some seem to do, perhaps because of their want of acquaintance with the practical side of the art. He says quite clearly that three-colour photography is based upon sound theoretical principles, and fully justified from a theoretical standpoint. But on the other hand,

MEDICINES AND THEIR MANIPULATION.

Westcott. Revised by Dr. W. H. Martindale
and W. W. Westcott. Sixteenth Edition.
Vol. i. Pp. xl+1113. Price 145. net.
Vol. ii.
Pp. viii+469. Price 7s. net. (London: H. K.
Lewis, 1915.)

(2) Squire's Pocket Companion to the British
Pharmacopoeia. By P. W. Squire. Second

edition. (London: J. and A. Churchill, 1915.) Price 10s. 6d. net.

(1)THE

(1)THE first volume of Martindale and Westcott's Extra Pharmacopoeia contains all matters relating to the chemical and therapeutic properties of those "extra-pharmacopoeial" chemicals and drugs which have attracted particular attention in the medical world. It includes details of their manufacture and modes of administration, their medicinal uses, pharmacy and solubilities, and references to current literature. This volume also contains, inter alia, a chapter on vaccines, supplying much new information, the section on organo-therapy, the supplementary list of drugs, and a list of the most potent antiseptics based on researches by the authors. Volume ii. contains the latest methods of assaying and testing

chemicals and drugs, and those employed in clinical and bacteriological diagnosis and analysis. We find a full account of Abderhalden's serum reaction, of a bacteriological examination of distilled and drinking waters, with a table of the analytical results obtained, and the conclusions founded on them, of the various methods for performing the Wassermann reaction for syphilis, and of the chief advances made in bacteriological technique. This volume will be found invaluable chemical, bacteriological, and pharmaceutical laboratory. Martindale's Extra Pharmacopoeia should find a place on the library shelf of every medical practitioner and pharmacist.

presentation of the best methods by means of which the problem of the nature of animal conduct is now being investigated. This problem is primarily one for the naturalist who knows very intimately the habits of the organisms that are to be studied. Yet experimental psychology is now a science with well-developed methods and criteria, and with a technique of its own, and one cannot consider the multitude of instances of apparently intelligent behaviour in the lower animals without feeling that much of the lack of critical examination of these cases is due to imperfect knowledge of this technique. The student of biology will find the author's short accounts of the experimental methods devised by Jennings, Yerkes, Thorndike, and others very serviceable, and the bibliography contains references to most of the important memoirs.

(2) In 1904, owing to the increasing size of Squire's Companion," it was decided to subdivide the work, and to publish it in two parts, "Squire's Pocket Companion" and "Squire's Companion." Squire's Pocket Companion" is the smaller volume, containing information on such matters as are commonly arising in the orinary course of prescribing and dispensing, and is written specially for the medical profession. This second edition of the work follows the lines of previous editions of the Companion, and is arranged in alphabetical order. The principal monographs are divided into distinctive headings, a description of the drug with its usual method of preparation, solubility, medicinal properties, dose, prescribing notes, incompatibles, official pre-in parations, not official preparations, and antidotes.

The solubilities of chemical substances have been completely revised and the medicinal properties brought thoroughly up to date, the latest references being included. The doses are given in both the imperial and metric systems, and are those generally employed. The prescribing notes have received particular attention, and the revision has been very thorough and complete.

The chapter on therapeutic agents of microbial origin has been almost completely re-written by Prof. Hewlett; it gives full information on antitoxins, serums, tuberculins, vaccines, etc. A list of British and foreign spas is included, also a therapeutical classification of remedies, with a list of those applicable for special ailments. A full general index enhances the value of the work, which will be found of the greatest service by the medical practitioner and pharmacist.

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The author avoids controversy and discussion as much as possible, and short statements of his own conclusions would have added to the value of the book. He relegates the theory of tropisms to a very subordinate place, refusing it that generality that has occasionally been claimed for it. Jennings's interpretation of the apparently random movements of certain protozoa as based upon a method of trial and error is accepted, but it is argued that rigid determinism is nevertheless involved, although plasticity of behaviour is implied Jennings's interpretation. The conclusion is not

very
clear. The book contains a fair account of
the admitted phenomena of "homing" among
birds and insects. There is a short summary of
the evidence in favour of ideation in animals other
than man; and in the last chapter the reader will
find too short a reference to the wonderful thinking
horse which in ten seconds found the fourth root
of the number 456976!
J. J.

OUR BOOKSHELF.

The Principles of Rural Credits as Applied in
Europe and as Suggested for America. By
J. B. Morman. Pp. xviii+ 296. (New York:
The Macmillan Co.; London: Macmillan and
Co., Ltd., 1915.) Price 5s. 6d. net.

ALTHOUGH this book is written primarily with the
idea of calling attention to the problems of credit
as they affect farmers in the United States and
Canada, it contains much of interest to any stu-
dent of rural economics. The whole subject has
been investigated recently by the United States
Commission on Rural Credits, and the present
volume is largely a condensed and popularised
version of the Commission's reports to Congress.
In this way the book falls naturally into two
parts: the first consists of the information col-
lected from an exhaustive study of the systems
of rural credit in operation in Europe; in the

second this information is used to suggest methods applicable to the special needs of American farmers. In 1913 the German farmer could borrow from his mutual credit association at 3 per cent., while his confrère in the Western States was paying from 6 to 10 per cent. for similar accommodation. The difference in the value of money in the two continents was, of course, partly responsible for this a difference which the present enormous waste of capital in Europe will certainly reduce-but the advantages of the old-world farmer were chiefly due to his superior organisation.

For the provision of personal or short-time credit, the combination of farmers into co-operative credit societies is recommended. Seventeen States have already passed laws to facilitate the formation of such societies, but the scattered population on the large farms of the West renders the Raiffeisen type of credit bank, so successful in Europe, much more difficult to organise in America. As regards long-time loans to the landowning farmer, the State should grant these at reasonable rates of interest, and on the amortisation plan of repayment, by which equal payments over the period covered by the loan both meets the interest and extinguishes the capital debt. The author has set out a mass of facts and figures with great clearness, and has further provided a very complete bibliography of the subject.

The Statesman's Year Book. Edited by Dr. J. Scott Keltie, assisted by Dr. M. Epstein. Fifty-second annual publication. Revised. Pp. xxxiv+1536. (London: Macmillan and Co., Ltd., 1915.) Price 10s. 6d. net. THE editors of the "Statesman's Year-Book," gravely incommoded as they have been by the effects of the war, have met the situation successfully. The statistics given for enemy countries and Belgium are for the most part of no more than historical interest, but they have been revised to the latest dates possible, and will be of value in the future for purposes of comparison. Special revision is stated to have been applied to the sections on Turkey, China, Greece, Spain, and the Panama Canal zone. The accounts of Chinese government and administration are very clear so far as they go, and the statistical tables for this country have been decidedly improved. To the introductory tables some pages have been added specifically dealing with the war. The dates of nineteen separate declarations of war between July 28, 1914, and May 23, 1915, are furnished. The list of principal events of the war might well have been fuller, but there is a useful catalogue of the principal official and unofficial war publica

tions.

The coloured maps are all pertinent to the war -an ethnographical map of Central Europe, an historical map of Prussia, and a map illustrating the three partitions of Poland (1772, 1793, and 1795), which is not very easy to follow. A map of the "World Colonial Powers concerned in War" is merely a map of the dominions of all the

great European colonising Powers, including the Dutch. Attention has clearly been paid to the bibliographies, many of which are substantially more valuable than formerly; perhaps the selection of works other than those quite recently published is still open in some instances to further revision.

Lessons and Experiments on Scientific Hygiene and School Temperance for Elementary Children. By Helen Coomber. Pp. xx+163. (London: Macmillan and Co., Ltd., 1914.) Price Is. net.

MANY people have an idea that it is impossible to learn physiology without the complex paraphernalia of the modern laboratory. Some go to the other extreme, and imagine it is possible to become acquainted with the subject from books alone. Both are obviously wrong, and Miss Coomber's manual will show how easy it is to teach the principles of elementary hygiene (applied physiology) with quite simple materials, such as a few bottles, a spirit lamp, a chemical reagent or two, and material such as any butcher can furnish. Whilst thoroughly agreeing with the underlying idea of the book-that such teaching, to be effective, must be practical-one is a little doubtful whether the system of question and answer, which is adopted throughout, though most suggestive to the teacher, is really the best for the learner. Some little summary of the main conclusions in each section should follow (or precede) the catechism and practical exercises. Indeed, the authoress oftens feels this herself, for some of the answers are prodigiously lengthy. Experience will, however, show whether some short connected accounts will be advisable in future editions. Any competent teacher could quite well supply the want if it is found necessary, and perhaps Miss Coomber thinks that this is the duty of the actual teacher rather than that of the writer of the present admirable little guide.

Making the Most of Life.

W. D. H.

By Prof. M. V. O'Shea and J. H. Kellogg. Pp. ix + 298. (New York: The Macmillan Co.; London: Macmillan and Co., Ltd., 1915.) Price 3s. 6d.

THIS is another of the many elementary manuals on physiology and hygiene which are being so prolifically produced in the United States. It is written clearly and to the point, and without any undue use of technical terms. How to live healthily and long is the ambition of most of us; this makes all the more astonishing the colossal ignorance which prevails, even amongst otherwise well-educated people, of the most elementary rules of health. One cannot praise sufficiently a nation which seeks to make knowledge on such a vital question part of the education of every citizen. Useful lessons are drawn from the lives of such men as Gladstone, Tolstoi, Cornaro, and others; but the most important section of the book appears to us to be that devoted to the history of our microscopic foes, and the means to combat their attacks upon us. W. D. H.

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.]

The Principle of Similitude.

DR. RIABOUCHINSKY directs attention concisely in NATURE (July 29, p. 591) to an important point, which must have arrested the notice of readers of Lord Rayleigh's weighty exposition and illustration of the scope of the method of dimensions, as an instrument of precision in the analysis of physical problems. The example under consideration was the cooling of a hot wire by a stream of air passing across it. The point is that temperature, although in ultimate analysis it must be expressible in terms of the three fundamental dynamical entities-mass, space, and time-can yet be in that problem considered effectively as a fourth independent entity, thus vastly increasing the information derivable from comparison of dimensions. In the formal analysis of mere diffusion or conduction this is clearly valid, for the dynamical aspect of temperature is not involved.

In so far as thermodynamic considerations, such as work of expansion, etc., are of secondary importance in the analysis of the convection from a hot wire (as is the case so long as only an adhering surface layer of the gas need be taken as operative 1), the same principle will apply approximately there. But in a problem the content of which is mainly thermodynamic, the relations will be far more complex. In fact there is nothing transcendental about dimensions; the ultimate principle is precisely expressible (in Newton's terminology) as one of similitude, exact or approximate, to be tested by the rule that mere change in the magnitudes of the ordered scheme of units of measurement that is employed must not affect sensibly the forms of the equations that are the adequate expression of the underlying relations of the problem. J. L.

Cambridge, July 31.

THE question raised by Dr. Riabouchinsky (NATURE, July 29, p. 591) belongs rather to the logic than to the use of the principle of similitude, with which I was mainly concerned (NATURE, March 18, p. 66). It would be well worthy of further discussion. The conclusion that I gave follows on the basis of the usual Fourier equations for conduction of heat, in which heat and temperature are regarded as sui generis. It would indeed be a paradox if the further knowledge of the nature of heat afforded by molecular theory put us in a worse position than before in dealing with a particular problem. The solution would seem to be that the Fourier equations embody something as to the nature of heat and temperature which is ignored in the alternative argument of Dr. Riabouchinsky. August 2. RAYLEIGH.

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p=yo sin +yR-1 sin whence, if σ is the standard error of the y's, it is easy to prove that o2/n is the standard error of the or q. This is also the standard error for any highe order term depending on the n observations.

σ

From the way in which p and q are obtained it is obvious they may be positive or negative; the sig depends, in fact, upon the origin chosen, and their mean value obtained from many samples would be zero. But even in the case of there being no period at all, and the y's being purely casual, it is very improbable that both p and q should be zero. In this special case the amplitude a is really zero, but it is almost certain, since it equals p2+q2, not to be given as zero. Its mean square is plainly equal to twice the mean square of por q, but this is not the square of the standard error, because it is not taken about the mean value.

To ascertain the general magnitude of the error the following plan has been adopted. From a sort of roulette board of 100 compartments, 500 pairs of numbers have been taken, the numbers on the board being arranged to have a standard deviation of 10, ard a distribution as nearly normal as the limit of 100 numbers permits. From these pairs, representing the p and q of the sine curve, 500 amplitudes have been found. The result gives a mean amplitude of 12-5, a standard deviation of 6.5, and a distribution such that 4 per cent. exceed the value 25.

Similar results from 500 other pairs, but with a genuine sine curve of amplitude 10 superadded, give a mean amplitude of 16.5, a standard deviation of 8c, and a distribution such that 8 per cent. are below 5, and 5 per cent. above 30.

From theoretical considerations it is apparent that as the periodic part of the variation becomes large compared with the casual part, the mean amplitude will still exceed, but will approximate to, the genuine amplitude, and the standard error will approximate towards that of p or q.

may

Suppose, then, that we have a set of n well-distributed observations, and that nothing is known about them in regard to their periodic variation. Let their standard deviation be σ. Now let the first three terms of the Fourier series be found in the usual way, and let the amplitudes be a, a, and a,, the question that arises is, to what extent do a,, a2, and a, represent genuine periodic variations? The standard deviation ☛ may be due entirely to the periodic variations, or be purely casual. In the former case it is easily proved that σ = = √ a12 + a22 + a‚2/√2, and if this relationship is approximately satisfied, the larger ampli tudes may be accepted as correct. But if the deviation of the observations is distinctly larger than that produced by the periodic part, the casual part of it will lead to error in the 4 a,, and a,, and unless an amplitude when com pared with o√√n is well outside the limits for the special values given above, it need not be significant.

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