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igneous rocks. It summarises the characters of the chief rock-forming minerals, and of the origin and classification of rocks, and is illustrated by an admirable series of photographs and diagrams showing the field relations of igneous rocks. The author makes a useful protest against the appropriation by geologists of popular rock names in new and technical meanings. The term granite, for example, is used in the stone trade in its correct historical and etymological sense, which is entirely different from its use in geology. This system is as inconvenient, as Prof. Pirsson points out, as if botanists had re-defined the terms bush, tree, and shrub, limiting each to a particular species. Prof. Pirsson's protest is justified, and though some American geologists are using the familiar terms in their popular meanings, this reform has probably been proposed too late.

(2) Mr. Brenton Symons's "Genesis of Metallic Ores and the Rocks which Enclose Them" is also intended to appeal to the general elementary student, and is an attempt to explain the formation of ore deposits free from unnecessary technicalities. It is a book, however, of very different standard from Prof. Pirsson's; it is written by a practical engineer, who is keenly interested in the theoretical study of mining geology, but whose knowledge of the subject is a little unequal.

The book begins with a general introduction on geological principles, followed by a section on rock metamorphism; the third part of the book deals with the ore deposits. Though the author avoids so far as possible technical scientific terms, his text is often repellent by the abundant use of such Americanisms as cavations for spaces, such reformed spellings as "lentiles" for "lenticles," and vegetal for vegetable, and mining terms of only local value. The most valuable part of the book is its collection of diagrams of ore occurrences; the instances drawn from Cornwall are the most satisfactory, for some of his diagrams and views regarding ores in other parts of the world are a little out of date. Mr. Symons takes, moreover, an extreme position as to the genesis of ores. He has a great belief in the agency of geosynclinals, by which sediments are carried down to depths where they are melted, and then forced to re-ascend as igneous rocks into overlying strata; and though he describes many ores as plutonic, he appears to regard the vast majority of ores as having been derived from the destruction of Archæan rocks and

precipitated in the sea. He says, on p. 381, "It has been already observed that nearly all the ores that can come within the reach of man have been derived from the Archean strata"; from these rocks, according to Mr. Symons, the metals are removed in solution and "precipitated on the bottom of the sea by chemical reactions that were principally set up by organic matter." He has no doubt, for example, that the gold in the reefs of Nova Scotia and the copper ores of Mansfeld were deposited in the rocks of those mining fields during their deposition in the sea. His view of the origin of crystalline rocks of most ores is shown by the following quotation.

"The presence of such minute proportions in all formations is natural, since the crystalline rocks, as

far as known, were originally deposited as marine strata, and, consequently, retain some part of the minerals that were precipitated during sedimentation from the oceanic waters. The proportion of these metals appears to be just the same, whether districts are metalliferous or not (p. 363).

This extract shows that the author adopts such an extreme position in regard to the genesis of ores that his book must be read with caution.

ZOOLOGICAL PRIMERS.

(1) Die Säugetiere Deutschlands. By Dr. C. Hennings. Pp. 174. (Leipzig: Quelle und Meyer, 1909.) Price 1.25 marks.

(2) Korallen und andere gesteinsbildende Tiere. By Dr. Walther May. Pp. iii+122. (Leipzig: B. G. Teubner, 1909.) Price 1.25 marks.

(3) Die Fortpflanzung der Tiere. By Dr. R. Goldschmidt. Pp. iv+124. (Leipzig: B. G. Teubner, 1909.) Price 1.25 marks.

Haustiere. By (4) Die Stammesgeschichte unserer Prof. Dr. T. Keller. Pp. iii+114. (Leipzig: B. G. Teubner, 1909.) Price 1.25 marks.

(5) Biology. By Prof. R. J. Harvey Gibson. Pp. viii +120. (London: J. M. Dent and Co., 1909.) Price Is. net.

(1) THE HE most useful portion of this sketch of the mammalia of Germany lies in the synoptic tables placed at the head of each order; but these can hardly be considered as complete, since they do. not include any account of the subspecies, which are of the greatest interest.

A complete list prefixed to this book would have. made comparisons with the fauna of other countries a much easier matter. As it is, one has to search. through the index in order to discover what forms are included in this work.

(2) Dr. May is a well-known writer on the anatomy of corals, and in this little work he brings together' descriptions of heterogeneous assemblage of animals, the common feature amongst which is the property of producing a hard exoskeleton, or of contributing otherwise by their remains to the formation

of strata.

The question inevitably arising out of this treatment is, What determines the difference between, say, a soft anemone and an encrusted coral? To this Dr. May has, so far as we can see, no answer. Nevertheless, his book contains a good sketch or the various hypotheses accounting for the origin and formation of coral-reefs, and for this, if for nothing else, it is welcome. The corals and lamellibranchs appear to us the best parts of the work.

(3) Dr. Goldschmidt has undertaken to compress into a hundred small pages an account of the methods of animal reproduction, with especial reference to the number of the young, their state on hatching, their habits and adaptations. The work cannot be considered as really up to date, but the treatment is interesting, and the subject is one of such importance that we regret more space could not have been allotted to it. The illustrations are better than those of any other booklet of this series we have so far seen. (4) In an earlier and larger work, published some

three years ago, Dr. Keller advanced his views on the origin of domesticated animals. The present little work is an abstract of the larger one, and gives only the most meagre outline of the evidence on this difficult subject. The time has not yet arrived when such a work can be successfully written. We know far too little to establish conclusions on the origin of most of our familiar animals, and we can only recommend this work on a most interesting subject with considerable reserve. Prof. Ewart's work on horses appears to be unknown to the author. The book has no index.

(5) The general scheme of this primer is excellently devised. Beginning with a sketch of function, the author passes on to differentiation. The values, transformations, and elaboration of food-stuffs are next dealt with, and a special section is given to "sensitivity." The adaptations of organisms are briefly considered, and a short account of reproduction is given. The primer concludes with a sketch of the theory of natural selection. Such a concise statement of the general principles of animal and plant life should be of considerable use to teachers of elementary

science.

The value of the book would have been increased

by better illustrations. Many of those employed (for example, Nos. 8, 9, 18, 19, 37, 40, and 47) are so incompletely described as to lose much of their value. The figure of Padina (Fig. 2) is extremely vague. The text as a whole is what we should expect from such an experienced teacher as Prof. Harvey Gibson, and it has had the benefit of revision from his col leagues. The account of the destruction of life as illustrated by a dinner (p. 114) is perhaps open to criticism. The benefits of cultivation in increasing the number and variety of edible organisms are not pointed out. Moreover, in contrast to wild species, the individuals of cultivated ones have surely not remained " fairly constant" in numbers. Demand has in this case created supply. So far from illustrating natural selection, such an example seems to typify artificial selection. The statement about green Hydra on p. 43 goes beyond our present knowledge.

SOME NEW ELECTRICAL BOOKS. (1) The Bell Telephone. The Deposition of A. G. Bell in the Suit brought by the United States to annul the Bell Patents. Pp. iv+469. (Boston: The American Bell Telephone Co., 1908.) (2) How Telegraphs and Telephones Work. Explained in non-technical language by C. R. Gibson. Pp. vi+156. (London: Seeley and Co., Ltd., 1909.) Price Is. 6d. net.

(3) Technical Electricity. By H. T. Davidge and R. W. Hutchinson. Second edition. Pp. xi+539. (Cambridge University Tutorial Press, Ltd., 1909.) Price 4s. 6d.

the American Bell Telephone Co. has performed a useful service in the publication of this book. To any who may still be interested in the legal aspects of the case the book should also prove valuable. But for the general reader, even when specially interested in telephony, the verbatim report of a legal examination and cross-examination is a very unsatisfactory medium for conveying information. The constant repetitions, the frequent insistence on what must be regarded from the broader point of view as wholly irrelevant details, and, above all, the clumsiness of a dialogue devoid of literary merit, make very poor reading, and one is liable to be overcome with ennuï before any salient points have been gleaned.

By judicious, if comprehensive, skipping, however, many facts of both scientific and general interest may be obtained from this volume, and to many the detailed descriptions of the earlier struggles and difficulties leading to an invention of enormous utility and importance will have a particular fascination. It is only to be regretted that the book was not written in consecutive narrative form, though possibly some of its value as a record might have been sacrificed thereby.

(2) That Mr. Gibson has an aptitude for the de scription in non-technical language of the achievements of modern technology has been amply proved by his earlier books which have been reviewed in these columns. The present small volume shares the merits of its predecessors. The very large degree to which the telegraph and telephone enter into the daily life of the community should make this book particularly useful, and it should find a large circle of readers. The book is more or less an amplification of the chapters dealing with this branch in earlier more general books. The subjects covered are telegraphy and telephony, both with wires and without; there is a short chapter on lightning, the reason for the inclusion of which "by request does not seem clear, and three concluding chapters of a more general character on electrical units and theory. The volume is well printed and illustrated.

(3) This text-book was originally published in 1906, and the present is the third impression. Advantage has been taken of the new edition to bring some parts of the book more up to date, but the revision has not been very thorough, as reference to the chapter on lamps (in which there has been very marked progress since 1906) will show. The tungsten lamp is allotted seven lines of small print, but the osmium lamp, almost if not quite defunct, remains in possession of what we presume was its original position in the main text. The whole chapter on lamps seems to us poor; the drawing of an arc in Fig. 128 is purely imaginary, and the authors would do well to refer to Mrs. Ayrton's book before they issue their next edition; the section on flame arcs and the reference to the Bremer arc lamp

(1) THE printing of the full deposition made by lead us to the conclusion that the authors have no

Mr. Bell in the suit brought by the United States to annul the Bell telephone patents doubtless furnishes a valuable historical record of the experiments which led to the invention of the telephone, and, since the deposition was never officially printed,

correct idea of the real difference between the flame and the ordinary arc.

It is perhaps somewhat unkind to take exception to such errors in what is only one chapter amongst four-and-twenty. But it is deplorable that a text

book should give incorrect or misleading information; the authors' aim "at spanning the gulf which too often divides pure theory and practical engineering" will not be realised if the student is obliged to unlearn much that they teach him when he becomes a practical engineer. We do not profess to be experts in the whole subject of electrical engineering, and cannot criticise the whole book, therefore, on the same lines as we have criticised the section

on lamps; but the authors, by writing such a book, lay claim-at least so far as fundamentals are concerned to be such experts, and if we find them at fault at one part we are led to suspect the whole.

The book covers the whole electrical field; the arrangement is that usually adopted, opening with electrostatics and magnetism, and passing on to electric currents. The diagrams and illustrations are for the most part good, but the process blocks (fortunately few) come out badly on the class of paper used. There are numerous exercises for the student to work out at the end of each chapter. M. S.

OUR BOOK SHELF. Gas-engine Theory and Design. By A. C. Mehrtens. Pp. v+256. (New York: John Wiley and Sons; London: Chapman and Hall, Ltd., 1909.) Price Ios. 6d. net.

THE writer of this book is an instructor in mechanical engineering in the Michigan Agricultural College. His aim, he tells us, has been to prepare a book for all who are interested in gas engines, whether students, draughtsmen, engineers, or engine operators.

This is an ambitious aim, and we may well doubt the possibility of its being carried out in such a small compass; but there can be no doubt that the cardinal virtues of simplicity and conciseness of language which any such intention must require are here presented in no usual degree. The reviewer does not remember any book hitherto written on the gas engine which presents its subject with such lucidity.

The chief entry to be made on the debit side of the account is that the extent of the field covered is far too great. It will be found, on perusing the volume, that it not only deals with the history and present position of gas-engine invention, and with the properties of the gases and fuels used, but also with such a big subject as the design of engine details and the dimensions of parts. Students usually learn their physics and machine design independently of the steam or gas engine, and a book on the gas engine which includes a great deal of what has already been studied separately is wasting space. The result in so small a book as this is that the truth and applicability of a great number of formulæ are taken for granted, which may account for the poor compliment paid to them by the author on p. 123,

where he remarks :

"A number of formulas will be given in the following paragraphs, but machinery cannot be designed by formulas alone. The author has frequently found that empirical, and other, formulas would sometimes come within 500 per cent. of the correct result."

There are also the inevitable slips of a "first edition," but they are not numerous. The author should, however, make a point in the next edition of correcting his description (on p. 33) of carbon monoxide as an unstable compound; his omission on p. 39,

in the discussion of the apparent suppression of heat on explosion, of any reference to the increase of specific heats admitted on p. 25; the error in saying (on p. 44) in an engine which is to run on kerosene, and he that it is usual to increase the compression pressure should also correct the general confusion of the table on p. 167. It is difficult to understand what the author means in his description (on p. 52) of the working of the gas producer by the remark:-"The limit of the ratio of steam to coal by weight is about 1 to 40." tempted to get too much into so small a volume, it Although, as has been stated, the author has atmust be acknowledged that he has produced a book at once interesting in treatment and clear in language. La materia radiante e i raggi magnetici.

By Prof. A. Righi. Pp. vii+308. (Bologna: N. Zanichelli, 1909.) Price 8 lire.

IN a recent number of NATURE a brief account was given of Righi's "magnetic rays," this being the name applied to a peculiar luminosity near the kathode of a vacuum tube, when the latter is placed in a longitudinal magnetic field. Righi supposes that this luminous column is due to electrically neutral doublets, which are not in sufficiently stable equilibrium to be looked upon as atoms or molecules, which owe, in fact, such stability as they possess to the action of the magnetic field. Several papers on this subject have been published by the author, and the main object of the present small volume is to give a connected account of the whole research. About one-third of the book is devoted to an extremely lucid and interesting summary of our present knowledge concerning the corpuscular theory of matter, written in a style which, as far as possible, is free from technical terms. The remainder, except for three short mathematical appendices, deals with the evidence for and against the existence of neutral doublets or magnetic rays. Here, while very suggestive, the experiments are not altogether convincing-this is evidently the opinion of Prof. Righi himself-but this is due in great measure to the difficult experimental conditions. While no one experiment can be said to have demonstrated the existence of magnetic rays, the results as a whole certainly tend to support the author's view. One point might have been treated more fully, viz., the conditions under which a magnetic field lowers the potential difference at the terminals of the discharge tube. Experiments are described, in some of which an increase, in others a decrease, of potential is brought about by the magnetic field, but it is not clear to what difference in the conditions this is due. R. S. W.

Brassolidae. By Dr. H. Stichel. (Das Tierreich, 25 Lieferung.) Pp. xiv+244. (Berlin: R. Friedländer und Sohn, 1909.) Price 15 marks. THIS is a very elaborate monograph of a comparatively small group of butterflies found only in Tropical America. They form a subfamily of the great family Nymphalidæ, and are most nearly allied to the great blue Morphidæ, but differ from them by their stouter bodies, darker colours, and the closed cell of the hind wings, which are generally ornamented with three large eye-spots on the undersurface. Their flight is crepuscular, while that of the Morphida (which are represented in the East Indies as well as in Tropical America), is diurnal.

In 1823, Latreille and Godart, in the second part of "Papillons" in the "Encyclopédie méthodique,' were acquainted with only twenty-three species now referred to the Brassolidæ. Of these, twenty-one formed the bulk of the second section of the genus Morpho, while the remaining two species were

H

placed in Brassolis. In Kirby's Catalogue of Diurnal Lepidoptera and Supplement (1871 and 1877) we find eight genera of Brassolidæ and fifty-four species, while Dr. Stichel now enumerates eleven genera and seventy-five species, in addition to a very considerable number of forms treated for the present as subspecies.

Dr. Stichel describes the species at great length, adding tables of the genera, species, and subspecies. The synonymy of the genera and species is very fully given, and the excellent text-illustrations include the neuration of one species of each genus, and also the markings of the wings of a large number of species, both surfaces being usually figured. Descriptions are also given of the eggs, larvæ and pupa of the insects, as far as known at present, and the range of each species is also indicated. On pp. 3 and 4 we find general information on the habits of the butterflies, and should have liked more detail under the various species; but we presume that there was either no room, or the available information on the subject was too meagre to be worth giving, except in a general manner. W. F. K.

The Volcanic Origin of Coal and Modern Geological Theories: a Plea for Lessening Demands on Geological Time; and for Further Separating the Life Histories of the Aqueous and Volcanic Formations. Ry Col. A. T. Fraser (late R.E.). Pp. 21. (London: R. Banks and Sons, 1909.)

THз old Wernerians used to account for volcanic action by the supposed combustion of coal within the earth's crust, but the author of this pamphlet turns the tables upon them by making the volcanoes produce the coal! The way in which this feat is performed is as follows:-first by pointing out that in the sides of the active volcano Gedeh in Java the tuffs are seen to be well stratified, and look, at a distance, like old red sandstone; then the mud deposits ejected by the eruption of Tarawera in New Zealand are also stratified. Next, we have somewhat of a leap in the advance of the argument. The Java experience showed, though coal was absent, another way in which it (coal) might originate; namely, being rained down in a shower of bitumen alternately with sandstones, shales, &c. In support of this view we are told that a visit to "the quarries of Carrara and Parnassus" show that "marble is a volcanic rock," "ejected, accompanied by high-pressure steam, from a fissure and showered down.' We must leave our author with the coal and marble, and not attempt to follow his leading among geological theories, old and new. We fear, judging from books advertised on a fly-leaf at the end of the one before us, that the author has been so much occupied with psychical research, occult powers of Eastern nations and the religions of the world, that he has not found time for even a very little elementary chemistry.

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Cassell's Nature" Copies (Wild Flowers). Aids to Nature Study, Brushwork, and Drawing. In twelve packets. (London: Cassell and Co., Ltd., n.d.) Price 6d. net per packet.

EACH of these packets of drawing copies contains ten examples of pictures of wild flowers executed in colours on stout plate paper. Though the best plan is to have wild flowers drawn from actual specimens, these copies may serve a useful purpose in town schools, where it is very difficult or impossible to procure the plants themselves; in any case they will add variety to the art work, and familiarise children with the beauty of common wild flowers.

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.]

August Meteoric Shower.

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I HAVE Summarised in a form which may be convenient for comparison some of the results of Perseid observations this year. The differences in some cases are remarkable, and sufficiently prove that to arrive at definite conclusions respecting the character of a shower a large number of materials should be consulted and averaged. Weather conditions are dissimilar, the places of observation are equally well situated (certain positions in towns are much affected by artificial light), and there are other causes which must introduce discordances. Though comparatively few Perseids were observed at Bristol and Meltham on August 10, they were fairly numerous at Blaina and Antwerp, and on the night of August 12, when a rich display of brilliant meteors was remarked at Bristol, there no striking exhibition witnessed at several other places.

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Results of Perseid Observations, 1909. h. m. h. m. h. m.

Aug.

C. B. Pennington, Notts. II Mrs. H. P. Hawkins, Brockham, Surrey

Miss Irene Warner, Bristol!!! John Hicks, Westonsuper-Mare.

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The Ringing of House-bells without Apparent Cause. UNTIL I read the two letters in NATURE of July 22 and August 12 I had no idea that the ringing of house-bells without apparent cause was so fascinating a subject, as my own experience of it has been rather prosaic. One of my bells occasionally rings when no one is in the room, but it is entirely due to bad workmanship. The strength of the spring which draws the wire back after it has been pulled is only about equal to the friction of the wires, and the result is that, though it generally draws the wire back immediately after it has been pulled, yet it sometimes fails to do so at the time; but after some time, it may be hours, owing to some change in the conditions, it succeeds in drawing back the wire, when the bell again rings when no one is touching it. The bell thus rings once when it is pulled, and a second time when the spring succeeds in drawing back the wire.

The electrical explanation of any mysterious ring

ings seems hopeless in any conditions, save possibly in a thunderstorm, when we remember that all the bells and wires are in good electric contact with each other, and in more or less indifferent contact at many places with pipes, walls, &c. Further, only the bell at the end of a row could be rung by electrical attraction to the opposite wall, because the bells swing parallel to the wall on which they are fixed, and considerable force is required to make them move in a direction at right angles to their free swing.

In the case referred to by Mr. C. L. Tweedale, it might have been worth while to see if the wire attached to the

lively bell he mentions did not come in contact with any other wires at any part of its length. What makes me suggest this is that in one of my rooms I can tell when the front-door bell is rung by a sympathetic movement of the bell-pull in the room, due to the wires rubbing against each other at some part and the wire to the door bell pulling the wire to the room.

When one considers the class of workmanship put into bell-hanging, one need not be surprised at the vagaries of the bells. Like plumber work, it is mostly out of sight, and as the work has often to be done in very imperfect light and under cramped conditions, anything that will work is considered good enough. JOHN AITKEN. Ardenlea, Falkirk, August 21.

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FLYING ANIMALS AND FLYING MACHINES. UNTIL quite recently human flight was considered by the mass of mankind as so impracticable that "I can no more do that than fly was a phrase used to denote something not to be accomplished. It is no wonder, then, that the fact that several people (probably some dozens at the present moment) have actually flown should appeal to the popular imagination, and the appeal is especially strong in such a case as M. Blériot's flight over the English Channel, although there is nothing really more formidable in a flight over water than over land. It may be of some interest to show briefly how it is that what was formerly looked on as a typical impossibility has now become a matter of everyday occurrence.

It will be a help to take first the case of such animals as have wings, and to see why it is that no creature the height of which approaches even onequarter that of a man has been able to fly either in present or former times. In order that the wings may support the body, their movement must generate a downward current of air of which the momentum per unit of time is equivalent to the downward momentum which the body and wings would acquire in the same time under the influence of gravity. This does not necessarily involve a large expenditure of work. For instance, when a weight is attached to a parachute and is dropped from a height the speed of descent soon becomes constant, and the work done in the air by the parachute is then just equal to the product of the weight into the distance fallen. The resistance of the parachute is proportional to its area, and the speed of descent can be made as small as we please if the area is made large enough. The work, therefore, expended in a given time, that is, the power delivered to the air, is diminished in the same proportion.

Suppose now that instead of an inanimate weight an animal is suspended from the parachute by a long rope ladder. When the speed of descent is slow enough, the animal will have no difficulty in climbing the ladder at such a rate that the centre of gravity of the "system" may remain stationary in the air, and this by an expenditure of work which can be diminished indefinitely by increasing the area of the parachute.

This case is analogous to the hovering of a bird in

the air without horizontal velocity during the downstroke of the wings, and as no means are here provided for restoring the wing to its primitive position the time of support is limited. The illustration suffices, however, to show that the work required in order to maintain a stationary position in the air by means of wings is equal to the work required to raise the total weight involved at the same rate as that at which it would fall were no work to be expended.

Of the total weight supported, namely, the animal and the parachute, the animal only is a source of power. Thus, while in " dynamically similar" combinations the total weight varies as the cube of the linear dimensions, the supporting area varies as the square, and the living power available varies, not as the total weight, but as the total weight less the weight of the supporting wing. It will be readily seen that if the animal can only deliver a certain amount of power per unit weight of body these conditions lead to an absolute limit to the weight of an animal which can sustain itself stationary in the air. For, suppose the total weight is w=wa+w (the weights, namely, of the animal and the parachute of area s), w, must vary as s, and if the downward velocity is to be constant s must be proportional to w. From this it can be shown that the greatest weight given speed) can have is 2b3/3c2, where b=w's' and an animal (incapable of climbing faster than some c=ws, w, and being known values of wing weight and wing area fulfilling the condition of falling with the required velocity when the total weight is w'. If we take ww/n, the expression 2b3/3c becomes 3w'n2.

As an example, suppose that 30 feet per minute is the limiting velocity at which an animal can continue to climb, and that the area of the parachute which will drop at the appropriate speed when the total weight of parachute and load is 1 lb. is 100 square feet, and also that the weight of the parachute alone islb., then it appears that no animal could maintain itself stationary in the air by means of a parachute the weight of which exceeded (4)2 (or about 10 lb.), and the area required for this weight would be more than 1600 square feet. Thus, if no more favourable way of supporting a weight was available than the down stroke of a wing in still air, flight would be impossible for all except the very smallest animals.

As is well known, however, the vertical reaction on a slightly inclined plane moving rapidly in a horizontal direction enormously exceeds that which it would experience in dropping through still air, and although the proportionalities between the weights and the supporting area still remain, viz. saw and was, the actual weight which can be supported by a given area increases indefinitely as the horizontal speed in

creases.

If there were no such thing as air friction, the work expended in supporting a given load might also be reduced indefinitely, for the resistance to the horizontal motion (which, when the inclination of the plane is small, may be regarded as the horizontal component of the normal force) could be diminished indefinitely by decreasing the inclination.

Air friction, however, fixes a limit beyond which the inclination of the plane to the direction of motion cannot be advantageously reduced. Experiments have shown that this inclination is about 5°, and that then the ratio of the supporting force to the resistance lies between 5 and 7 (depending partly on the shape of the plane). A knowledge of the best angle of inclination and the ratio of the resistance to the force on the plane at right angles to its path afford means of determining the possible efficiency (see "Experiments on

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