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OUR BOOKSHELF.

A Manual of Oils, Resins, and Paints, for

Students and Practical Men. By Dr. H. Ingle. Vol. I., Analysis and Valuation, by the author and J. A. L. Sutcliffe. Pp. 129. Pp. 129. (London: C. Griffin and Co., Ltd., 1915.) 35. 6d. net. THIS small volume is intended for students, analysts, and works chemists who are familiar with general chemistry but have had little or no practical experience in analysing oils, or preparations which contain oils. It includes much of what one would put in a good notebook intended for personal use in the laboratory. A short introduction serves to refresh the reader's memory upon points in organic chemistry specially relevant to oils and fats, after which the authors give short accounts of the most approved chemical and physical methods used in examining these bodies. Theoretical explanations are included as well as practical details. For example, the chemical reactions concerned in the absorption of iodine by oils are described more fully than usual-though

it is true that we have to look in more than one

place for them. A chapter on technological analysis deals not only with oils, fats, and waxes as such, but with articles such as paints, pigments, and varnishes which may contain oil as an ingredient, and with allied substances, such as turpentine and gum-resins.

The correct interpretation of the results obtained would often require much more knowledge than could be obtained from the descriptions given. Information as to the origin and methods of preparation of the various oils is not within the scope of the work. It is understood, however, that further volumes are to follow, dealing with these matters. The book is a useful introduction to laboratory work in the subject. Potting, for Artists, Craftsmen, and Teachers. By G. J. Cox. Pp. ix + 200. (New York: The Macmillan Co.; London: Macmillan and Co., Ltd., 1914.) Price 5s. 6d. net.

THE book will prove a distinct help to an artist craftsman who wishes to "do something" with clay. The author is right in saying: "Too much stress cannot be laid upon the importance of close study of the best work, both ancient and modern, for it is a truism that however handily a craftsman may work, his output will be worthless if he has not, with his increasing powers of technique, developed a sound judgment and refined taste."

The description of the various simple processes of pottery work is very exact, and the illustrations are admirable.

The book, indeed, is a simple, though thorough and concise, first tutor to an artist craftsman, and should, to use the author's words, "set one or two sincere students to the making of some of the many beautiful objects of utility and art with which the craft abounds."

The list of pottery terms is useful, though there are a few which are not employed in this country in the sense given by the author, for example,

clammings in England means the doors of the

kiln, and not simply the sand or siftings applied to the cracks in them; pug in this country is used to mean the mechanical wedging of clay; galena is classed by the author as highly poisonous, and lead as poisonous, whereas galena is practically safe to use, but there may be considerable danger in using white lead carelessly. BERNARD Moore.

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.

neglect among physicists of the principle of similitude WHEN Lord Rayleigh directs attention to the (NATURE, March 18), he has perhaps forgotten the excellent paragraph in which Tait deals with the question in his "Properties of Matter." Curiously enough, one of Lord Rayleigh's first illustrations is also Tait's, namely, the fact that the velocity of waves on deep water is as the square root of their lengths, to which Tait adds the corresponding fact that the velocity of ripples is inversely in the same proportion. The principle is of great use in biology, as Herbert Spencer was the first to show. By its help we understand how there is a limit set to the possible growth in magnitude of terrestrial animals; how, on the other hand, the whale gains in activity and speed the bigger it grows; why the ostrich is unable to fly; why the bee's wing vibrates so much quicker than a bird's; and why the flea can jump well-nigh as high as a man. And not less does the principle deserve to be borne in mind when we consider what must be the conditions of life in the most minute organisms: especially if there be any so small as that Micrococcus of the rabbit, the diameter of which is given in the books as only o00015 mm., or not far from the limits of microscopic vision.

D'ARCY W. THOMPSON.

It is rather curious that Prof. D'Arcy Thompson should refer to Tait's Properties of Matter," for I fancy I might claim some part of the credit for the paragraph in question. In a review of the first edition (NATURE, vol. xxxii., p. 314, 1885) I wrote:"There is one matter suitable to an elementary work which I should be glad to see included in a future edition, viz., the principle of dynamical similarity, or the influence of scale upon dynamical and physical phenomena. It often happens that simple reasoning founded upon this principle tells us nearly all that is to be learned from even a successful mathematical investigation, and in the numerous cases where such an investigation is beyond our powers, the principle gives us information of the utmost importance."

And, after an example or two: "I feel sure that in Prof. Tait's hands this very important and fundamental principle might be made intelligible to the great mass of physical students." Though I believe I was in correspondence with him at the time, I do not remember to have seen Tait's second (or later) edition,

and I can only wonder that it has not had a more marked effect in popularising the general principle. Prof. Thompson's illustrations from biology (attributed in part to Spencer) are, of course, of first-rate importance. RAYLEIGH.

The Age of the Earth.

SOME fifty years ago Kelvin announced that the temperature of the earth could not have been anything like its present value for more than some 20-30 million years. This estimate was based upon three independent considerations, namely, the temperature gradient inside the earth's crust, the amount of tidal friction, and the total amount of energy radiated by the sun.

The first of these arguments has been invalidated completely by the discovery of the radio-active elements. The other two arguments are scarcely affected by this event.

The geologists always found some difficulty in compressing the history of the earth, more especially of the sedimentary strata, into the period allowed them by Kelvin. Prof. Harker's presidential address before the Yorkshire Geological Society, reprinted in your issue of March 25, seems to show that there is a general impression abroad that Kelvin's estimates have been superseded, and that the discoveries in radio-activity allow one to assume a period of the order of thousands of millions of years since the earth has reached a constant state as regards climate. I should like to be allowed to state as succinctly as possible what difficulties this view entails.

The mean temperature of the earth is about 280° absolute. It therefore radiates about 17 x 1024 ergs per second into space.

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cal Assuming the latest value 192 for the solar cm.2 min. constant, the earth receives 1-72 x 1024 ergs per second from the sun. Therefore the radiation from the sun just compensates the amount lost by the earth; in other words, the temperature of the earth is determined by the temperature of the sun. The possibility that the earth's temperature might have been maintained by radio-active processes before the sun incandescent, and that the radio-active substances have died off since then need scarcely be discussed seriously. For quite apart from the well-known sterilising effects of the rays, any radio-active substances with a sufficiently long life to keep up the temperature of the earth for any considerable length of time would not disappear quickly. Uranium, for instance, only diminishes at the rate of about 15 per cent. in 100 million years.

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One may conclude, therefore, that the time during which the earth can have existed in its present state cannot be greater than the time since which the effective temperature of the sun has been about 6000°, its present value. This time cannot exceed about thirty million years. For the sun loses energy at the rate of about 3.8 × 1033 and the total energy to be gained by a mass of 1.97 x 1033 gm., contracting to a radius 6'96 x 1010 cm., is 2.2 × 1048 ergs, assuming approximate homogeneity. (Taking the increase in density towards the centre into account does not alter these figures much.) Now even if one assumes that the whole of this energy was radiated at a rate of about 38 × 1033 erg, i.e., at the present rate, it will only

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last 18.3 million years. But any other supposition, namely, that the sun at one time emitted more or less

energy per second, leads to a shorter period for the earth in its present state.

To explain a greater age it was necessary to find other sources of energy, and since neither the heat of chemical combination nor any possible increase in the specific heat was anything like large enough, the heat of radio-active transformations was invoked. This was perhaps excusable in the early days before very much was known about the laws governing these processes, but it seems quite inadmissible to-day.

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It has been suggested that at the enormous pressure and temperature inside the sun radio-active processes might be modified, and even that ordinary elements might break up. A consideration of the quantitative relations involved shows that this is most unlikely. Though one can scarcely apply ordinary thermodynamics to radio-active processes one can certainly apply the general rule, which may also be developed from the quantum theory if desired, namely, that a reaction the energy of which is A ergs per molecule is affected chiefly by the collisions of atoms of energy of the order A. Now A is of the order 10-5 ergs in radio-active processes, and one can therefore only expect the temperature to affect those if an appreciable number of atoms have an amount of energy of this order. The average energy of an atom would be 10-5 ergs at about 5.1010 degrees. Therefore even at 500 million degrees only one atom amongst 101o would be moving fast enough to influence a reaction which liberates 10- ergs. Obviously 500 million degrees is quite beyond the bounds of possibility in any part of the sun. One must conclude, therefore, that any process which liberates anything like the requisite energy is unaffected by solar conditions, and takes place at the same rate on the sun as on the earth. Thus one must fall back upon the ordinary radio-active materials, and as Sir Ernest Rutherford has pointed out, one would only gain a paltry five million years even if the whole sun were composed of uranium. The only way out would seem to be to suppose that the sun was created some 10° or 100 years ago out of special radio-active material which produces an enormous amount of energy, and that it has been breaking up ever since. This material does not exist on the earth though, so the earth would have to be the object of a special creation. Such an assumption, of course, can neither be controverted nor even discussed. But unless some such hypothesis is introduced, i.e., unless the presumably radio-active solar material which liberates a quantity of energy sufficient to keep up the sun's heat for the desired 10 or 1010 years, is supposed to have been created by some inconceivable force at the epoch at which the sun is supposed to have begun to radiate, this material would have disintegrated long ago. It might be objected that the same holds good of uranium, that the fact that uranium exists in measurable quantities proves that it has not existed for a time great in comparison to 5.10 years.

This is doubtless true, but there is no real difficulty about assuming uranium or other radio-active substances to have been produced if one supposes the solar system to have been formed by the collision of two stars.

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material might be formed at such a temperature if some helium were present.

But of course the heat used up in forming these substances would cool the rest of the mass: any energy gained in radio-active form would be lost in the form of heat. It could never avail to explain a solar constant such as has been measured for longer than Kelvin's 20 million years. In other words, radioactive substances produced would act only as accumulators of energy, not as primary batteries.

To recapitulate: As Kelvin showed, gravitational energy can only account for 18.3 million years of sunshine at the present rate. Invoking radio-activity as a source of energy implies the assumption that unknown radio-active materials liberating considerably more energy than uranium were created by some unknown agency within a measurable period of time, and that these are now breaking up. This assumption is not necessary to account for the existence of uranium, as it is quite conceivable that a certain amount of radio-active matter might be produced afresh during every stellar collision. The energy of substances formed in this way would not be available to explain a greater amount of energy on the sun as their energy is abstracted from the gravitational energy, and has already been taken into F. A. LINDEMANN.

account.

Sidholme, Sidmouth, April 5.

Harmonic Analysis.

IN a paper which I read to the Physical Society last January (see NATURE, February 11, p. 662) I suggested that the best way of analysing a wave, the graph of which was given, was to apply the rules for the mechanical quadrature of integrals which are given in treatises in the calculus of finite differences. I am convinced that these methods when applied intelligently are much simpler and ever so much more accurate than most, if not all, of the methods in everyday use.

In the paper referred to above I applied a wellknown method of mechanical quadrature (Weddle's rule) to the case of a semicircular alternating wave, the equation to the positive half of which is y = √x−x2. I chose this wave because I found that the evaluation of the Fourier integrals for it by analysis was laborious. Prof. A. E. Kennelly, of Harvard University, has kindly written to me to point out that the equation to the curve can be readily put in the form

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or measure the lengths of 8, 13, 18, and 23 ordinates respectively. Doing this, we find that b1=0-0942, b=0.0423, and that b, and b, are given correctly. It will be seen that from the practical point of view the simplicity and accuracy of the method in this case leave little to be desired. It has the great advantage that the amplitude of each harmonic can be computed independently of the others.

When the wave passes smoothly through the extremities of the ordinates we measure, we can apply the rule with confidence. Jagged or very distorted waves must be treated more carefully. For example, if we apply the rule to a rectangular alternating wave of height unity we find from the formula given above that Iob, 11+√3, and so b1 = 1.27321 approx. The true value is 4/, i.e., 1.27324_• and hence the error is less than 1 in 40,000. For a triangular alternating wave of height unity, however, if we apply the rule intelligently we get b1 =0.88... instead of 0.81057... The error in this case arises from applying Weddle's rule through a point of discontinuity. If we apply it over one-quarter of the wave, it being necessary to measure six ordinates instead of three, we find that b1=0·81056 . .

ALEXANDER RUSSELL. Faraday House, Southampton Row, W.C., April 12.

A Mistaken Butterfly.

REFERRING to Prof. Barnard's letter so titled in NATURE of April 15, which describes the apparent mistake of a butterfly in visiting a peacock's feather as if expecting to “extract food," I think it probable that there are no animals that do not make mistakes

at times. I observed an analogous mistake made by a species of Pieride-Appias nero-in Sumatra, as I have recorded in "A Naturalist's Wanderings," p. 130" In the open paths I netted scarlet Pierida ... often flying in flocks of over a score, exactly matching in colour the fallen [withered] leaves, which it was amusing to observe how often they mistook for one of their own fellows at rest, and to watch the futile attentions of an amorous male towards such a leaf moving in the wind."

Redcliffe, Beaconsfield, Bucks, April 17.

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HENRY O. FORBES.

The "Green Ray" at Sunset.

PROF. A. W. PORTER, in NATURE of February 18 (vol. xciv., p. 672), seems to think that the green ray" is more of a subjective phenomenon than anything else, or at least often is so; but the fact that it is seen at sunrise also shows that in this case at least it is not a result of complementary colours. Besides, if it were a subjective phenomenon, one would expect to see it on every occasion when the sun set behind a clear horizon, whereas the sight is somewhat rarer. I once saw a lovely blue flash, and I read a description recently of a sunset in Palestine where the writer speaks of the sun vanishing like a blue spark. If you hold a lens almost edgeways on between your eye and a light and move it until it is quite edgeways on a few discs of light will be seen, and at last these vanish in a green or blue flash, the effect of dispersion.

35 Roeland Street, Cape Town, March 17.

HEALTHY ATMOSPHERES. HYSIOLOGICAL research has proved that the cause of discomfort felt in close, illventilated rooms is due to the physical, and not to the chemical, properties of the atmosphere. We exclude gross contamination by products of imperfectly combusted coal gas, e.g. from defective gas fires imperfectly flued. These chemical products irritate the nose and throat, and one of them-carbon monoxide-is a poison. We exclude too, those mines and factories wherein certain poisonous products of industry may pollute the atmosphere. We are writing of rooms crowded with human beings, of over-heated, windless rooms. The percentage of oxygen in such crowded rooms is never reduced by more than Io per cent., and at any of the mountain health resorts the concentration of oxygen is reduced considerably more owing to the attenuity of the air. Similarly the percentage of carbonic acid is never raised in crowded rooms to such a level that

it has the least toxic effect. Within the lungs a constant concentration of carbonic acid of about 5 per cent. of an atmosphere is maintained. The acidity of the blood regulates the action of the breathing mechanism, so that both it and the concentration of carbonic acid in the lung are kept constant. The only result of breathing an atmosphere containing o'5-10 per cent. of carbonic acid-the most crowded room does not contain more-is a slight deepening of the respiration by which the concentration in the lung is kept at the normal figure. It becomes difficult to maintain the normal concentration in the lung when the concentration in the atmosphere rises above 3'0 per cent.; the breathing of even a resting man then becomes over-laboured. The crew of a submerged submarine feels the need for fresh air when the CO2 concentration rises above this level.

Exact experiment, made by many competent researchers, wholly fails to confirm the assertion, so confidently made in all popular books of hygiene, that the expired air contains a subtle organic poison. The air of a crowded room smells offensive to one coming in from the fresh ar, and it may, and often does, infect us with the living germs of disease, sprayed out from the mouth, or nose, of those who cough, sneeze, or speak, but it contains no organic chemical poison, and the fatigue and headache felt by the more sensitive occupants is certainly not due to such. These effects are produced by the physical properties of the atmosphere acting upon the nose and skin, on that enormous field of sensory nerves which supplies the surface of the body, contributes so greatly to our feelings of well-being, and regulates the metabolism of our bodies. The cutaneous and nasal sense-organs are influenced by the temperature, movement, and vapour pressure of the air, and the physical qualities of the atmosphere, which control the loss of body heat by convection or evaporation. Out of doors we are ceaselessly stimulated by the play of wind; cloud, and sunshine, cold and heat, wet and dry alternate; monotony, the curse of the nervous system,

is repelled. Cool, moving air braces us up; we are made active, eat more, and breathe more to keep up our body furnace. The daily turnover of the body is thus enlarged, the appetite is stimulated, and the food eaten is completely utilised and does not become dross and waste, the generator of bacterial decomposition in the bowel. The blood is refined out of a larger choice of foodstuffs, and the organs receive from it an ampler supply of the more precious and rarer building stones; the muscular exercise which we are compelled to take to keep warm, occasions the blood to circulate in ampler and quicker streams, and deepens the breathing, thus ensuring the proper expansion of the lungs, and the natural massage of the organs of the belly.

We are built to be active, and keep ourselves warm by muscular action. By over-clothing our bodies and over-heating our rooms we weaken our vigour, expose ourselves to nutritive disorders, and debilitate the natural mechanism of defence against infective disease. against infective disease. Moreover, in these heated, stagnant atmospheres we expose ourselves to massive infection by those carriers of disease who have in their respiratory tract some strain of microbe exalted in virulence, and thus spread "colds" or influenza, pneumonia, or phthisis. Mere exposure to cold does not cause these ills. Arctic explorers and shipwrecked people who suffer the extremes of exposure do not suffer in consequence from such illness. Excessive cold may cause local death and gangrene, or kill by cooling the whole body below a viable temperature, but our power to withstand cold is enormous, innate, the result of a million years of an evolution spent in struggling against the forces of nature. The inclement and dark wintry weather impels people to shut up windows, crowd into close, over-heated rooms, and thus expose themselves to massive infection.

The sedentary worker in heated, windless atmospheres runs his metabolism at a low level, and if he over-indulges in the pleasures of the table, easily becomes the sufferer from digestive and metabolic ailments. It is not the bad weather that causes the ill-health prevalent in the winter, but the excessive precautions most of us take to avoid exposure to cold. Only the very old and feeble, in whom the lamp of life burns low, want such protection. The young and the able-bodied require the stimulus of exposure to the weather; the discomfort arising therefrom soon results in vigorous health, and ceases to be felt. The soldiers of our new armies taken from shop, desk, or factory, and exposed in trench or camp, have been singularly free from disease which is supposed to result from chill, in spite of the hardship of cold, wet, and mud. Adequately fed, clothed, and rested, the open-air life has made the clerk, shop, or clubman twice the men they were, given them a healthy hunger, steady nerves, a clear, ruddy complexion, and increased weight, and yet for days together their clothes may have been damp.

The fear of cold and damp instilled in the

sinuses, resulting in obstruction of the nasal airway, feelings of stuffiness in the head, and increased liability to infection by the germs of

nursery often checks the physical development of the young, and leads to a lessening of national vigour and health. The open-air school works wonders on the badly nourished, defective chil-"colds" and influenza. A system more contrary dren, and should become the school of every child in the community. The camps of to-day placed in the wind-swept open spaces of the land are founded on the emergency of war, but should become the week-end playgrounds of the nation in times of peace. Our cities have been built so as to satisfy regulations based on the chemical theories of ventilation and the nursery-bred fear of cold. They should be re-planned so as to allow the maximum of sunlight and wind, affording baths and exercise grounds for all. The conditions of life at present wage a deadly war against

us.

We listen for the whirr of the Zeppelins, and take little heed of the silent sowing of the germs of preventible disease.

To secure these healthier conditions we require instruments which will measure the physical conditions of the atmosphere and make manifest the differences between confined and open air. The thermometer registers the average temperature of the surroundings; it gives us no information as to the rate of heat loss from the surface of the human body. It is the rate of heat loss which matters to us. Out of doors, on ideal spring days, the ground is warm and the wind scarcely moves at footlevel, while our heads are blown upon by a variable cooling breeze; the sun warms one side of us while the other is cool. The clouds chasing each other across the blue sky give us shade alternating with sun. Our feet are kept warm, our heads cooled, and our cutaneous nerves are continually excited by the ever-varying rate of cooling. There is no monotony, but an agreeable energising of our nervous system. When the heating and ventilating engineer gives us a uniform summer temperature of 63° F. by means of steam coil (so called) radiators, he secures us a warm atmosphere above and a cold floor below, cold feet and warm heads, and a deadly monotony of conditions. The right system of heating and ventilation would give us a warm floor and a variable, gentle, cool breeze moving round our heads.

FIG. 1.-The Wet and Dry

Katathermometer. The Dry instrument is shown enclosed in a wire cage, which was used for taking observations in investigations on clothing.

In the House of Commons the engineer forces air, heated to 63° F., through a perforated floor, and thus, cooling the Members' feet, gives them conditions which lead to congestion of the mucous membrane of the nose and its air

to the outdoor ideal conditions could not have been invented. To measure the physical conditions outdoors and indoors we require an instrument which will measure the rate of cooling by radiation, convection, and evaporation, and will tell us whether the atmosphere is monotonous or not. The present writer has introduced the katathermometer for making these measurements, and with Mr. O. W. Griffith has introduced an electrical instrument, the caleometer, for the purpose of recording not only rate of cooling, but indicating whether the atmosphere is monotonous or lively.

The katathermometer (Fig. 1) is a large-bulbed spirit thermometer, made (by Mr. J. Hicks, 8 Hatton Garden) as nearly as possible of a standard size. Each instrument is tested against a standard one, and a constant obtained by which the rate of heat loss can be deduced in calories per sq. cm. of surface. The katathermometer is heated in warm water until the spirit just rises into the top bulb, and the column is free from bubbles. The instrument is then wiped dry and suspended in the atmosphere, and the time observed taken by the meniscus in falling from 100° F. to 95° F. This gives the rate of heat loss by convection and radiation, the instrument being approximately at body temperature. muslin finger-stall is then drawn over the bulb and the operation repeated after heating the instrument and jerking the excess of water off the muslin cover. The time taken in this case gives us the heat loss by radiation, convection, and evaporation. The difference between the dry and wet readings gives us the heat loss by evaporation only, and from this, when the readings are taken in still air, the vapour pressure can be determined.

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The value of rate of heat-loss measurements are seen by the following examples :-(1) Inside a cottage room on the East Coast and outside on the cliff edge the summer temperature was the same, but outside the katathermometer cooled much faster. It registers just as the human body feels the bracing effect of the moving air. It acts as an anemometer, sensitive not only to currents in one direction, but to every eddy which the ordinary anemometer fails to register. The instrument shows the vast difference between the conditions of the indoor and outdoor worker. (2) In the debating chamber of the House of Commons the thermometer registers a temperature of 63° at foot and head level, but the katathermometer shows the rate of cooling is 50 to 100 per cent. greater at foot level than at head level. When the conditions were experimentally altered in one part of the House so that all floor inlets were closed, and the air introduced at the gallery level, the rate of cooling became slower at foot level than at head level. Then the congestion of the nose was relieved as the feet became warm and comfort was secured. (3) In a room heated

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