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There are expressions, such as "gingival fold," "ergastoplasmic venogen," "sanguinolent serosity,' "laccate,' 66 chloridate, asporogenous," to which even the hardest-mouthed jargonmonger will object.

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THE SCOTTISH LAKE SURVEY.

misses, in a book meant for medical men and travellers, are good, plain descriptions and diagrams giving the names and explaining the relations of all those parts of the snake's skeleton and integument that are of applied value in classification. Here there are descriptions and figures, but they do not explain all the terms employed in the specific and generic Bathymetrical Survey of the Fresh-water Lochs of diagnoses; moreover, some of the terms used are not those commonly current, and some do not correspond in text and figure. Thus the well-known quadrate bone is referred to as the tympanic; and the shields which in the text are called, in accordance with the authorised British version, internasal, prefrontal, frontal, and parietal, appear in the figure under other names. Seeing that the differentiation of species, and even of genera, largely depends upon scale-characters, this is hardly a matter of little moment.

The second part, which treats of snake-venoms, describes the methods of collecting venom and the chemical composition of the secretion, and gives an account of the way in which in the laboratory the various constituents of the venom act upon the blood and tissues. The gross effects of cobra-bite and viperbite are also contrasted. The author naturally draws largely on his own experiments, but the work of other investigators is duly considered. It is rather surprising, however, not to find any mention whatever of D. D. Cunningham, who for many years was in India the observed of all observers in this field.

The third part brings us to the cream of the subject, namely, the acquisition of immunity against snakevenom and the use of the serum of immunised animals as a cure for snake-bite. This subject is so largely the author's own that criticism can only be offered with deference. But, considering merely the way in which the matter is represented in the book under review, the author appears to rely rather too much on his own large experience with cobra-venom, and also to be hardly consistent; for although he seems to adhere to the untenable opinion that neurotoxin is the essential toxic constituent of all venoms, whether colubrine or viperine, he allows that cobra-antivenin is of no avail against what, by a strain of language, he calls the "local" effects of viperine venom, and he concedes the practical point that an antivenin of general efficacy can only be obtained from an animal that has been immunised against both kinds of venom, colubrine and viperine.

The only other part of the book that requires notice is that concerned with the venoms of animals other than snakes. Here we find many interesting fragments of information about the venom of polyps, seaurchins, arthropods, molluscs, fishes, and amphibia. The venomous Mexican lizard, Heloderma, and the spur and femoral gland of Ornithorhynchus are also remembered, but, strange to tell, the dreadful stingrays, the notorious jelly-fishes, and the molluscan Toxiglossa are quite forgotten.

As to Mr. Austen's translation, it is as near as possible perfect, being wonderfully faithful to the original, and yet, so far as technical terms do not interfere, good English. In the case of some of the technical terms, however, Mr. Austen's unflinching fidelity sometimes goes near to make the reader wince.

Scotland. Under the Direction of Sir John Murray, K.C.B., F.R.S., and Laurence Pullar. Pp. viii+ 288; maps and plates. (London: Royal Geographical Society, and Edward Stanford, 1908.)

IN

N some countries it appears so natural that the national surveys should present a complete delineation of the solid surface of the land that the accident of certain hollows being filled with water does not excuse the surveyor from continuing his contour lines across the submerged slopes. With us, however, until the Survey Department was supplied with the necessary data by private investigators, no sub-lacustrine contour lines appeared even on maps of the largest scale, and large surfaces of paper remained blank save for the artistically graduated lines

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which indicated the difference between a water and a land surface. Most of the English lakes were surveyed in 1893 and 1894, and the contour lines appear on the later editions of the six-inch maps, with due acknowledgment of the whence they were derived. The volume now before us completes the preliminary publication of the survey of the lakes of Scotland undertaken by Sir John Murray and Mr. Pullar in 1896, and now brought very near completion. It represents an immense amount of work of national importance carried out at the personal cost of the authors, and its very magnitude makes it impossible to give any serviceable summary here of the additions to limnology it contains. Eighteen papers appeared in the Geographical Journal between 1900 and 1908, illustrated by bathymetrical maps of 213 fresh-water lochs, and this volume, published separately by the Royal Geographical Society, gives particulars and bathymetrical maps of a further series of 349 lochs, making a total of 562 surveyed and described. The number is so great that we cannot help regretting that it has not been made complete, but the rule appears to have been that no steps were taken to survey those lochs on which a boat was not available. In this way some sheets of water of considerable size and great interest have been left unsounded, a fact the more regrettable because difficulties due to sporting rights in some of the nearly inaccessible valleys in the heart of the great deer forests may prove insuperable to less known investigators in the future, while the high distinction of Sir John Murray's name might possibly have smoothed a way in the course of his great survey.

Apart from this, the record of the Loch Survey is one that Sir John Murray, Mr. Pullar and their numerous assistants may well be proud of. How great a body of work it represents may in part be gathered from the complete index, which includes all lakes described here and in the articles which have appeared in the Geographical Journal; but a mass of additional

material bearing on the physics and biology of the the fact that the contributors are also mostly wellwaters has still to be published. known

The bathymetry of the lake-basins was determined by series of close soundings in lines transverse to the long axis, and the scale of the maps is sufficiently large (3 inches to 1 mile) to allow of all the soundings being represented in figures as well as by contour lines. We think that a longitudinal line of soundings along the axis of maximum depth would have been a useful addition in all cases, and a valuable check on the transverse series. Supplementary soundings would also have been useful in many places where the exceptional run of the contours suggests some unusual configuration. Such additional lines have been run on some of the lochs, and the maps of these inspire a more complete confidence as to detail than do the others. We should have liked to see some larger-scale surveys of such individual features as the sub-lacustrine slopes of delta fans, screes, steep rocky shores, and the transition belt between the steep sides and flat floors of many of the basins.

authorities in the mathematical teaching world. Messrs. Jackson and Roberts have fully justi fied the existence of their book by the amount of freshness and originality they have put into it, and particularly by the extent they have treated the subject from a common-sense, practical point of view. As the authors point out in the preface, there have been in the past two classes of book in which the rela tions between force, matter, and motion are dealt with. There has been, first, the book on applied mechanics, in which the principal object has perhaps been to describe machines, and there has next been the academic" book, in which dynamics might perhaps better be described as "dogmatics," the most prominent feature of which has been a collection of exercises in algebra.

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It has been the object of the present authors to make the principles of dynamics the prominent feature of their book, and to illustrate them by applications to phenomena of everyday life rather than by algebraic drill. In this they have been very successful, so far as can be judged without an extended trial of the

The main crux in writing a book on dynamics is the question of units. Shall the author use poundals and please one class of teachers, or shall he use slugs and be commended by another section? It seems to have been generally forgotten that there is a third alternative which still allows those who wish to do so to replace Newton's "proportional " by "equal" in the laws of motion. That alternative is to take the gee (g) as unit of acceleration, and write force in lbs. wt. =mass in pounds and acceleration in gees; and if any writer chose to champion the claims of the gee, he could point to the fact that the foot, if defined by the length of the seconds pendulum, is really a gravitation unit of length.

The sounding of the large area of fresh water which fell between the two stools of the Admiralty and the Ordnance surveys is a splendid example of public-book in the class-room. spirited private enterprise undertaking and carrying through work which should have been included in the routine of a Government department. It is, happily, not the only case in which the collective shortcomings of the nation in matters affecting the advancement of scientific knowledge have been made good by individual effort and at private expense. When the right men are at the head of such an investigation, and their labours are not trammelled by the want of means, we are of opinion that better work can be done at a smaller outlay than if the operations were conducted by an official department or under the auspices of a committee of many specialists on different subjects; but when the right men are not to be found the lack of Government interest in the completion of our knowledge of our own land and its resources may lead to unhappy consequences. It is fortunate, indeed, that Sir John Murray and Mr.

Pullar have had both the will and the power to carry out the work, which, when completed by the publication of the additional material already collected, will form a noble monument to the memory of the late Mr. Fred Pullar, to whose energetic assistance the early stages of the research were so much indebted.

H. R. M.

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Messrs. Jackson and Roberts, while discussing the two generally recognised systems, adopt the more rational plan of basing their treatment on the proportion :

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force acceleration weight g

It has been popularly supposed that this plan is theoretically good, but how would the equations of motion of complicated systems be written? Now in Mr. Jackson's hands the equations all look delightfully simple; not only is there no more difficulty than occurs somewhere in every system, but it is very easy to see if the results written down are correct in their dimensions. The suppression of constant multipliers in physical equations does not always conduce to simplicity; it more often causes confusion, especially in connection with electrostatic and electromagnetic units, and also in hydrodynamics, where problems of discontinuous motion are solved for jets of one particular breadth (generally) with one particular velocity, and the solution appears inapplicable to other jets differing in size and velocity. A little doubt may occur as to whether momentum should be defined as Wv/g, as Mr. Jackson does, or simply as Wv; but this is a matter in which experience will indicate the wisest choice.

The subject-matter treated includes such applications as the instantaneous centre of a connecting rod, twospeed gears, and the elements of dynamics of rotation. There are many reasons why the latter subject should be included in an elementary treatise; indeed, the authors claim that, "frankly, unless a student means to know, in broad outline, about as much of the principles of mechanics as we have given, he may with advantage allot more time to some other subject."

have been done. The separate formulæ for the resultant at angles of 30°, 45°, and 60° might surely be struck out now, although the present reviewer pleads guilty of having perpetrated the same bar- . barisms (under protest) when he was younger and was informed that certain classes of students required them. On the other hand, the addition of sections on harmonic motion, bending moment, and shearing force (under graphical statics), and the chapter on energy of rotating bodies are valuable additions. In the latter chapter the moments of inertia of simple figures are stated without proof. Perhaps this is the best way, in view of the fact that integral calculus is now usually taught at an early stage; had this not been the case, the use of the geometric progression formula for making the necessary summations would have been recommended.

A student might do worse than use Prof. Jessop's book for algebraical drill, supplementing it by a course of experimental mechanics, or by Mr. Jackson's book; and whatever else may be said, no exception can be taken to the general appearance of the book, or the diagrams, which fully maintain the high standard that characterises Messrs. Bell's text-books.

In certain details the book leaves something to be desired. It would surely be better, for example, to give the rule for composition of relative velocities after, instead of before, the construction for the relative displacement and velocity of two moving bodies. The present order is a survival of the old idea that because the parallelogram of forces is the fundamental proposition in statics, the parallelogram of velocities. ought to be the fundamental proposition in kinematics. In the proof of the relations between angular and linear velocity, a 60 is introduced unnecessarily and then cancelled by considering the space described in a minute instead of in the unit of time (a second) assumed in the definitions. In several places where uncertainty exists as to how much should be included in the text and what should be omitted, the final result suggests that the authors were not given sufficient facilities for making alterations when the proofs were in type. The paragraphs are unnumbered, and this is a great drawback, but the worst feature is the illustrations, which are badly reproduced, with coarse, unsightly lettering. In one of them, on p. 177, a capital V looks like a Greek 7. If books of this class are to hold their own in the field of competition, not only should the figures be above reproach, but a large amount of time and thought must be devoted to minor alterations and emendations such as only suggest themselves when the text has been seen industrial, health and the gratification of his æsthetic print.

(2) If novelty and originality is one of Mr. Jackson's strong points, this cannot be said of Prof. Jessop and Dr. Havelock's book. It brings back to memory days of long ago, with its "forces of 1, 2, and 3 lbs.," its Roman and Danish steelyard, its three classes of lever, the oar being included in the second regardless of the man's thrust on the rowlock, its mechanical advantage instead of the more modern velocity ratio and efficiency, its systems of pulleys which only lift a weight a small fraction of the height of the supporting beam-and perhaps do not lift it at all if the ropes are extensible, and its Attwood's machine neglecting inertia of pulley, in the first instance, although this is now taken into account at the end of the book. But Jessop's "Elements of Applied

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OUR BOOK SHELF.

The State and the Farmer. By Prof. L. H. Bailey.
Pp. xii+177. (New York: The Macmillan Co.;
London: Macmillan and Co., Ltd., 1908.) Price
5s.

LESS than a generation ago farming and farmers
made very small figures in the public eye; men of
affairs, when they gave the subject a thought, regarded
British agriculture as a dying craft, something that
had ceased to pay and might be left to extinguish
itself quietly, leaving the country for the recreation
of the town-dweller, to provide sport for the rich in
tastes for the employee. Business men paused some-
times to make pharisaical remarks about the wasteful-
ness of the farmer; men of science scolded him for
sticking to his old ways, not adventuring his substance
on the crude generalisations which were put forward
to represent the infinitely complex life of animals and
whose vote he knew was safe in the landlords' pockets;
plants; the politician had no use for the agriculturist,
and the journalist saw little but comic copy to be got
out of Hodge and its ways. As Sir Horace Plunkett
said in his British Association address, modern
civilisation has joined the rural exodus.

But latterly there have been signs of change; the triumphal march of industrial progress, with its concomitants of vaster factories and ever extending suburbs of mean streets, has proved less satisfying than its prophets had promised; the nation has begun to awake to the essential instability of such a system, and to the need of keeping up agriculture as the soundest basis of the State and the only means of creating wealth, whether of men or things.

To some men the necessity of drawing men back to country life seems little less than a holy cause into the service of which they are ready to put their whole strength, and among such men Prof. L. H. Bailey, of Cornell, is perhaps most prominent on the other side of the Atlantic. In the little book before us Prof. Bailey pleads for the better organisation of rural life with eloquence and conviction; rural life, not merely because it pays, but because it is the life best worth living, most calculated to raise a sober and

strenuous race of men. The author's particular text is the function of the State in fostering agriculture; left to himself, the farmer is normally a strong individualist, who readily becomes isolated and hidebound. His sole chance of success in modern life is collective action, and Prof. Bailey discusses in successive chapters the extent to which the State can profitably intervene in the organisation of rural life by education and by starting various forms of cooperative work which will lead the farming community to act together. Different as the agricultural conditions are in this country and in America, the problems are the same in both places, and Prof. Bailey's discussion of the subject gains a special interest for us at this moment, when the Chancellor of the Exchequer has just set aside a development grant" to be devoted to the promotion of all agencies for encouraging rural life.

The Problem of the Feeble-minded. An Abstract of the Report of the Royal Commission on the Care and Control of the Feeble-minded. With an introduction by Sir Edward Fry, G.C.B. Pp. x+113. (London: P. S. King and Son, 1909.) Price is. net. THE appearance of this abstract is most opportune. The small committee of persons interested in social problems which is responsible for its publication is anxious to bring before as large a section of the public as possible the urgency of the matters in question, and points out in the preface of the book that the Poor Law Commissioners have given it as their opinion that if the recommendations of the Commission on the Care of the Feeble-minded were carried into effect, a system of control over the feeble-minded would be initiated which would free the Poor Law administration from one of its greatest difficulties and, we may add, the country from a cause of enormous expenditure. In his introduction Sir Edward Fry quotes Bagehot's sad reflections upon the undue haste and benevolent thoughtlessness with which so much philanthropic effort is attended, and the terrible question which he poses as to whether the benevolence of mankind does not do more harm than good. Sir Edward Fry can, however, recommend the work of the Commission on the Feebleminded as one done with deliberation and not with "a wild passion for instant action." The various problems which came before the Commission, such as mental defect and drink, mental defect and crime, and mental defect and illegitimacy, are adequately epitomised, and the far-reaching recommendations of the Commission duly considered as to the essential points. The book also contains some special articles, of which that upon segregation, by Mr. Galton, we can especially recommend to our readers.

The Economy and Training of Memory. By Henry J. Watt. Pp. viii+128. (London: Edward Arnold, 1909.) Price is. 6d. net.

THE training of the memory is undoubtedly a part of any good education, and it has hitherto been too much the peculiar field of the faddist and of ingenious but ignorant a priori system-makers. This little book, which aims at making of practical value to student and teacher the results of scientific experiment into the subject, is therefore to be welcomed. It is true that some of its precepts appear obvious, but where there are so many conflicting truisms the selection of the right obvious is not unimportant; and much definite information is given on particular points where the merely empirical adviser is quite at a loss, e.g. the advantages and disadvantages of specific types of mental imagery, and the variations of method corresponding to differences in the material to be memor

ised. Moreover, if the book did no more than free the ordinary adult from that excessive distrust of his memory, which is so bad in effect, and is, perhaps, too optimistically believed by Mr. Watt to be quite ungrounded in fact, it would be abundantly justified. Mr. Watt considers the mechanical memory of association to be, in a sense, more fundamental than the intelligent memory based on connection of thought, since the association between word and "meaning is in itself mechanical. It seems doubtful if that ultimate "association" of meaning and imagery can be expressed so simply; but the point, though of great interest, is of minor importance in a confessedly prac tical book.

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.] Rate of Helium Production from the Complete Series of Uranium Products.

A KNOWLEDGE of this constant is essential to the estimation of the ages of minerals from their helium content. In a paper published in Proc. Roy. Soc., July 28, 1908, I gave the ages of some minerals provisionally on the assumption that the rate was 9.13X10- c.c. per gram U,O. per annum. This rate was calculated from Rutherford's indirect data. It has received much support from Sir J. Dewar's determination of the rate of production by radium. with its immediate products. I am now in a position to confirm it further by an experiment on the rate of growth of helium in a solution of pitchblende; I speak of a solution, but it has been found impracticable to take up all the constituents by one solvent.

necessary.

Two solutions were

The pitchblende solutions contained 115 grams of U2O., and yielded in sixty-one days a quantity of helium which was measured as 2 X 10- c.c. in the capillary of a McLeod gauge. This gives the rate as 10.4 X 10- c.c. per gram U,O, per annum. No stress can be laid on the close agreement with Rutherford's estimate in view of the very small gas volume measured. The experiment proves, however, that that estimate is of the right order of magnitude. Larger scale experiments are in progress, and these, in conjunction with similar experiments thorianite, will, it is hoped, enable data on the quantity of helium in minerals to be translated into estimates of time with full confidence. R. J. STRUTT. Imperial College of Science, South Kensington, July 27.

A Kinematic Illusion.

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PEOPLE are sometimes amazed by noticing that in a motor-car seen through railings the wheels appear to revolve the wrong way. As the eye follows the moving objects it is convenient to imagine that the car, which may be actually running to the right, is stationary, while a vertical rail is moving past it to the left with an equal velocity. The apparent intersection of this rail with the upper edge of the wheel is a point running round in a contrary direction to that of the rotation of the wheel. This moving point suggests rotation of the wheel. When oblique lines swing in front of vertical lines the movement of the intersections is curious to watch. It is true that the lower half of the wheel goes against our theory, but at a given moment its effect may be less noticeable, either from being hidden in dust or because the eye has a very small range of close attention. I have seen the appearance, and have had reports of it from others, but cannot speak with precision as to the condition of seeing it effectively.

It is common to rotate vacuum tubes while a discontinuous spark illumines them. A spark may pass at the instant of starting one revolution, and the illumination

may recur slightly before or after the beginning of a second round; in either case there is a false suggestion as to the rotation. The railings would make discontinuous vision of the spokes of the motor wheels, and a spoke might be seen upright in one gap but at slightly different angles at other gaps. I do not feel that the solution of the problem lies in this direction. Winchester College. W. B. CROFT.

Natural Selection and Plant Evolution. MANY readers of NATURE must have been browsing with delight in the goodly volume on "Darwin and Modern Science" which Prof. Seward, of Cambridge, has taken such admirable pains to collect. Of all its many chapters few are more significant than that on the palæontological plant record by Dr. D. H. Scott, because there, perhaps for the first time, the evidence of the fossils with regard to the influence of natural selection has been fairly tackled by competent hands.

Dr. D. H. Scott does not attempt to maintain that the record to-day is nearly so imperfect as it was when Darwin wrote his famous chapter thereanent, fifty years ago. Dr. Scott's namesake and collaborator from Princeton speaks even of the record as, in some parts, "crowded with embarrassing wealth of material "; and yet what about evidence of natural selection? The present writer ventured to say (Contemp. Rev., July, 1902, p. 83):-"Modern palæobotanists furnish us with next to no evidence at all of the work of Natural Selection in evolving new species." Prof. Seward vehemently challenged my statements next month; yet, seven years later, Dr. Scott feels constrained to tell us :-" As regards direct evidence for the derivation of one species from another there has probably been little advance since Darwin wrote."

To put it more plainly, Dr. Scott is forced to admit that he can adduce absolutely no satisfactory evidence at all. All he does is to affirm his own firm conviction (as it is Prof. Seward's too) that natural selection must have been the chief agent; and he instances two cases where he thinks the possible inference extremely plausible, viz. (1) the case of the pollen tube, quite absent in the Palæozoic seed-plants, found very short and imperfect in the living cycads and ginkgos, and fully developed in the angiosperms, but fossil proof of linking forms there seems none; (2) the embryo in the angiospermous seeds, whilst Palæozoic seeds contain none. It may, as he says, be impossible to some to resist the conclusion that the nursing of the embryo by the seed was a process of adaptation. But, at any rate, there is no fossil proof thereof; and yet, as Dr. Scott will scarcely deny, there surely ought to have been some hint and trace thereof, the record being so comparatively rich and full as it is. In the case of the Tertiary mammals the action of natural selection can be very clearly demonstrated in numberless cases. If natural selection was the factor in plant evolution too, why is the record so obstinately silent?

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Dr. Scott, like Prof. Seward, takes refuge in the thought that our plant record, for many purposes, begins far too late. "An immense proportion of the evolutionary history lies behind the lowest fossiliferous rocks." My chief object in writing this letter is to ask, Is there any valid proof of this in regard to land plants, the matter specially in hand? Their record begins, actually, in the Upper Silurian, and though it is very, very meagre and imperfect, the traces are too widespread to be denied. To deny the existence of known Upper Silurian plants is rankest scepticism, though Dr. Scott avoids all reference to them whatsoever. Why, even so very cautious an investigator as Mr. Robert Kidston tells us of "a plant showing woody structure,' a plant so high as that, in the Lanarkshire Ludlow beds (Summary of Progress of Geol. Survey for 1897, p. 74). The most important Upper Silurian plant-remains are probably those from the Tanne Greywacke of the Harz, a fairly numerous and well-developed series, of age a good deal lower than Wenlock. Drs. Scott and Seward ("Encyclop. Brit.," Supplement) wish to pronounce all these fern-like and other plants Devonian, because of their facies; but Sir Archibald Geikie ("Textbook of Geology," ii.. p. 976) tells us that these Tanne

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plants are found a long way below shales with graptolites, which surely is proof enough of Silurian age.

We have, then, fair evidence of land plants in the Upper Silurian. Our very first air-breather or land animal, a cockroach, comes from the top of the Lower Silurian; and the fossil record of the whole Silurian is rich, varied, widespread, without gap. Yet it yields no hint of conditions favourable to land life below the top of the Lower Silurian. Is it, then, scientific to postulate dogmatically land plants earlier than the Silurian, simply because a theory requires it? Dr. Scott admits quite freely that the known facts go the other way.

He tells us not only of the opposition of the mighty like Nägeli, he also tells us that, as regards the succession of species, there are no greater living authorities than Grand'Eury and Zeiller, and that, in their opinion, "the evidence from continuous deposits favours a somewhat sudden change from one specific form to another.' This is most certainly true of the palæontological record as a whole. The evidence is overwhelming here, if only our men of science would be brave enough to forget their theories for a little while. Why insist on exalting the a priori methods of the schoolmen on the fair field of modern science? Why insist on refusing all evidence that does not suit? Why? Surely it is not, and cannot be, to enjoy the pleasure of barring out all design from the world in which we dwell.

St. Andrew's Manse, Falkirk.

JAMES B. JOHNSTON.

Musical Sands,

64

I CANNOT call to mind the occasion upon which Dr. Irving suggested that grains of hyaline quartz might produce the notes from musical sands, but, as a matter of fact, the grains do not ring," or vibrate individually as sonorous bodies, and there is no apparent resonance or sensible continuance of the note after the plunger is withdrawn. I do not think any particular variety of silica is essential, because coral-sand is often musical, and my artificial musical sands are made up almost entirely of silicate of iron.

I have already shown that the natural sorting action of winds and waves is a requisite condition for the formation of musical patches on sea-beaches.

Mr. M. S. Gray's letter in NATURE of July 29 giving interesting particulars of his visit to the musical sandhill near Copiapo, in Chile, confirms the statements made by the inhabitants to Darwin in 1835. In his "Journal during the Voyage of H.M.S. Beagle "Darwin referred to this hill of sand as "El Bramador "-" the roarer or bellower," but he did not personally visit the spot.

The extraordinary sensations experienced by Mr. Gray were probably similar to those which have been described by the various writers who, from time to time, visited Rig-i-Rawán and Jebel Nakous, both of which were referred to at length in my paper on musical sands in 1888. Particulars of the artificial production of notes from certain sands were also given by me in NATURE of August 6, 1891. CECIL CARUS-WILSON.

A Question of Percentages.

IF a student obtains 37 out of 50 in one paper, 50 or full marks in a second, and 71 out of 100 in another, what is his percentage on the three taken together? If we add the marks as they stand we get 158 out of 200, or 79 per cent. If, on the other hand, we double the marks on the first two papers, we have 74 per cent., 100 per cent., and 71 per cent. If we add these we get 245 out of 300, or 813 per cent. Will any of your mathematical readers kindly tell me which of these two different results is the true percentage for the three papers taken together? The answer may be very obvious; I can that the two results must be different, but I cannot see which is the more correct method to use.

J. T. CUNNINGHAM. 60 Milton Park, Highgate, N., July 24.

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