however, that some matters of elementary mathematics could not have been omitted without detriment. Thus the discussion, at the beginning of the second part, of the equations of a conic, based on the definition of a conic as the plane section of a right circular cone, must be superfluous for a reader who is capable of following the whole of the first part intelligently. But the fault is doubtless on the right side. The whole work consists of seven parts. The first deals with those portions of general astronomy which are relevant to the main purpose. The chapters on time and on precession and nutation seem particularly clear and good. That on aberration follows the traditional lines of Gauss and Bessel, and criticism would be out of place here. Yet the exposition of Gauss, which seems to assume the apparent composition of the velocities of light and of the earth as a matter of course, appears to be imperfect in view of the difficulties in the physical theory. Is it not more logical to consider the apparent composition as an inductive result instead of the explanation of the astronomical phenomena? of subject, their inclusion is justified. But that on satellites is certainly valuable, especially in view of recent discoveries. The source of the numerous theorems which are met with in the work has generally been indicated. but this is not always the case. Thus the theorems on p. 184 are due to M. Radau (Bull. Astr., x. p. 11) and to Mr. Shin Hirayama (Monthly Notices, R.A.S., Ixii., p. 620). Such references add greatly to the interest, but of course it is always difficult to be sure that the sources are strictly original. For instance, the proposition attributed (p. 131) to van der Kolk was, as has been recently pointed out, previously given by Whewell. There is an index at the end of the volume, but it is not so complete as it should have been. A full index of names is needed. An outline of the method of Gibbs will be found in Dr. Bauschinger's work, but for fuller details th pamphlet of Dr. Frischauf may be consulted with advantage. The method is based on the use of a particular expression for the ratio of a triangle to the corresponding sector of an ellipse. The form is mathematically elegant and the degree of approximation is high, but it was thought to entail greater complexity in the computations, while, on the other hand, the method by itself gave little assistance when a still closer approximation proved necessary. This defect was remedied by Prof. Harzer. The modified method is described by Dr. Frischauf in a clear and interesting manner; the practical value of his account would have been enhanced by the addition of a fully worked The second part contains a discussion of undisturbed heliocentric motion. Dr. Bauschinger asserts (p. 170) that Lambert's equation is of little use in the case of ordinary elliptic orbits. This opinion may be disputed. It is true that the development in series is of little assistance owing to slow convergence, but in its original form the equation can be easily solved in all ordinary cases. The natural expression of the formulæ for motion in a hyperbola involves hyperbolic functions. The use of these is entirely avoided, pre-example. The pamphlet also contains a number of sumably because tables of hyperbolic functions are not as a rule accessible to the computer. The properties of the apparent or geocentric motion are discussed in the third part. Here will be found Bruns' elegant proof of the theorem of Lambert on the curvature of the apparent orbit. Incidentally it may be remarked that Lambert seems to have missed that measure of fame to which his unquestionable eminence as a mathematician entitles him. The longest part is the fourth, in which the various methods of determining a preliminary orbit are described. An excellent feature is the compendious arrangement of the working formulæ. This part is followed by that on the adjustment of an orbit by the method of least squares. In both sections numerical examples are fully and clearly worked out. The sixth part contains the theory of special perturbations. Three methods are given, according to which the perturbations can be calculated in the elements, or in polar or in rectangular coordinates. In the preliminary chapter, on mechanical integration, the usual German notation for interpolation formulæ is employed. It is difficult to see the advantage of this over the ordinary notation of finite differences. The last chapter of this section brings the reader to the determination of the definitive orbit. Here the work might have ended, but Dr. Bauschinger has added a final part, in which he investigates the determination of the orbits of meteors, satellites, and double stars. These last chapters are necessarily brief, and it may be doubted whether, as regards unity supplementary notes to the author's "Grundriss der theoretischen Astronomie," a work of which a second edition appeared in 1903 after an interval of thirtytwo years from its first publication. H. C. P. INDUCTION AND CONDUCTION MOTORS Moteurs a Collecteur a Courants alternatifs. By Dr. F. Niethammer. Pp. 131. (Paris: L'Éclairage Électrique, 1906.) THE title leads one to believe that the author is going to deal with at least all the principal types of modern alternate-current commutator motors. whereas the book is practically restricted to a consideration of the series induction and conduction motors. Shunt induction motors of the commutator type are occasionally touched upon, but all remarks concerning these must be considered as quite erroneous. Generally speaking, the number of mistakes is too great. In chapter i. the historic part does not deal with the machines out of which those modern single-phase commutator motors have been directly evolved, which are afterwards considered more closely. The pre liminary consideration of some of the types now in use is full of errors, and much prominence is give to the least important of these types. The indis criminate use of the expression "repulsion" motor leads to the usual confusion. In the second chapter, which is the most important in the whole book, we find the author trying to The writer's space is limited, and he must therefore cut his remarks short. The fundamental diagrams of chapter ii. having been proved to be wrong, the value of the whole chapter is naturally greatly discounted. The chapter, however, contains a number of other mis-statements, some of which we will note in passing. establish exact diagrams which will cover all types | been assumed by the author, so that E,' is not nil as of motors. It may be possible to achieve this, but stated. No more is E, nil, although it is now imthe task is not an easy one, and the solution offered pressed on the rotor by conduction, and not by inby the author can certainly not be accepted. Take duction, as in Figs. 30 and 31. the two simple diagrams Figs. 32 and 33; the first illustrates the action of the motor shown in Fig. 30, the second (which is not referred to in the text) is probably intended to illustrate the action of the motor shown in Fig. 31. The E.M.F. (JW) in Fig. 32 is responsible for the current Ja flowing in the shortcircuited rotor; it must therefore be the resultant of all those E.M.F.'s which are effective so far as the short-circuiting brushes are concerned. These E.M.F.'s are E, E., E., E, and E.. When the motor is standing, E, and E, are nil, but they increase in direct proportion with the speed, with the result that JW, must, according to the diagram, increase with the speed independently of the load! In other words, the rotor current J, must increase with the speed, consequently also the stator current J. Seeing that the machine is one with a series characteristic, it is very obvious that the diagram in question cannot be correct. In a machine of the kind the tendency of the current is, of course, to diminish with the speed. The fact of the matter is that the phase of E, is shown incorrectly. If the direction of rotation is such that E, is in phase with the flux Ka, then E, must be of opposite phase to the flux K, for these fluxes are not only at right angles to each other in space, but also nearly at right angles to each other in phase. The presence of this very serious mistake evidently prevented the author from grasping the full meaning of the various vectors of his diagram. (E) must be considered as the working E.M.F.; (E) is then the back E.M.F., (E,'+E) represents the self-induction of the rotor circuit, whilst E, (and not E, as stated by the author on p. 32) must be looked upon as the compensating E.M.F. It is nearly opposed to (E,+E), therefore tends to cancel the effect of the self-induction in the rotor and to bring J. more and more into phase with E. Since E, increases with the speed, it follows that with increasing speed the phase of Ja will approach that of E, and that the power factor will rapidly improve. The writer also fails to agree with the author's Fig. 33. Owing to a mistake similar to that present in Fig. 32, we get the following curious and impossible result. It is obvious that E,, which appears at the brushes (aa), must be responsible for the flux K; it is generally admitted that a magnetic field lags by about 90 degrees behind the E. M. F. responsible for it, yet in Fig. 33 K actually leads E, by nearly that amount. The author also ignores the fact that for the arrangement of brushes shown in Fig. 31 we have two currents in the rotor, the one flowing from (b) to (b), the other from (a) to (a), the former being the working current, the latter producing Ka The value of the next fundamental diagram (Fig. 35) is greatly reduced because the author mistakes, in Fig. 34, the axis Ka for the axis K,, thus making a comparison between Fig. 34 and Figs. 30 and 31 quite impossible. In Fig. 34 the motor-field axis K, is the vertical axis, and not the horizontal, as has On p. 34 it is stated that the transformer flux in a short-circuited transformer is zero! On p. 42 that the motor shown in Fig. 53 is compensated in the same manner as the Winter-Eichberg machine, whereas compensation is due to the alteration brought about in the phase of the motor field by the introduction into the exciting circuit of the auxiliary E.M.F. derived from S1. In diagram 43 the E.M.F. (E,') is shown as being of opposite phase to the E, of Fig. 32, although both diagrams refer to the same motor. The remarks on commutation are difficult to follow, because of the attempt to deal with the various types of motors at one and the same time. It is recommended that flux Ka should be chosen low at starting for motors of the series induction type, whereas it is the flux K, which at that time should be small. Contrary to the author's statement, the commutation difficulties with polyphase commutator motors are just about of the same order as those met with in the series induction motor. In dealing with the power factor (p. 59), the author makes a statement in the last paragraph which reveals a great confusion of ideas. This mistake probably arises out of the confusion of the axes of Ką and Ka already pointed out in connection with Fig. 34; in addition, the notation is now suddenly changed. It is, however, evident that for the case of the series conduction motor (Fig. 34) k, stands for the field coaxial with the armature brushes and due to the armature ampere turns; k is perpendicular to K, and by neutralising k, as shown in Fig. 37 or 39 the power factor is improved as stated. But in a "repulsion" motor such as Fig. 30, k, does not exist; it is neutralised ipso facto because the energy is conveyed into the rotor by induction, and not by conduction as in Fig. 34. Furthermore, if k, did exist, it would be coaxial with Ka If k, is a misprint for K, then by neutralising it the torque of the motor would be destroyed, for K, is the motor field. As to speed regulation, and contrary to the author's opinion, any so-called repulsion motor can be satisfactorily controlled by suitably influencing the rotor circuits. Chapter iii. only deals with motors full descriptions of which have appeared from time to time in the technical Press. As to the notes on the predetermination of alternate-current commutator motors, these are very superficial, and mainly apply to the series conduction machine. On the whole, the book is more likely to bewilder the reader than teach him anything; it ought to be very thoroughly revised and corrected before it can be recommended. The author will find it easier and more profitable to treat each type of motor separately, and then to point out the differences between the various types, than to try and establish diagrams and formulæ which will meet all cases. VAL. A. FYNN. SUBAQUEOUS TUNNELLING. Tunnel Shields, and the Use of Compressed Air in Subaqueous Works. By W. C. Copperthwaite. Pp. xv+390. (London: Archibald Constable and Co., Ltd., 1906.) Price 31s. 6d. net. THIS tunnel by filling the cavities left by the advancing shield with grout. The system, however, as successfully carried out, in the absence of water, in the Tower Subway, was not adapted for passing through water-bearing strata; and a third step, consisting in the introduction of compressed air, was essential to enable this system to cope effectually with the conditions liable to be encountered in tunnelling under rivers, or at a considerable depth below the surface, in loose ground. The completion of this system of tunnelling, by the combined use of a shield, a cast-iron lining put together under shelter of the shield, and compressed air to exclude the water from the works in traversing 'HIS fine quarto volume furnishes a very valuable and comprehensive history of a system of tunnelling, especially under rivers and in water-bear-water-bearing strata, has enabled abandoned tunnels ing strata, which was inaugurated by Sir Marc Isambard Brunel, as regards the employment of a shield, in the celebrated Thames Tunnel between Rotherhithe and Wapping, commenced in 1825, but, owing to the inrush of the river into the works on two occasions through breaks in the stratum of clay, and financial difficulties, only completed in 1843. The second important step in the development of the system in a practical form was, curiously enough, taken in constructing a second tunnel under the Thames rather higher up the river, crossing just above the Tower, which was commenced in February, 1869, and completed in November the same year. This Tower Subway, originally proposed by Mr. Peter Barlow, but eventually executed by the late Mr. Greathead, whose name will always be prominently associated with the system of tunnelling under consideration, was carried forward through the London Clay under the shelter of a shield, similar in principle to, though much smaller than, the Thames Tunnel shield. The shield in this instance consisted of a short wrought-iron cylinder laid horizontally, 4 feet long and slightly more than 7 feet internal diameter, stiffened at its front cutting-edge, and provided inside with a vertical plate diaphragm having a central opening, which could be readily closed, through which the men passed for excavating the ground in front preparatory to pushing forward the shield by a series of screws. The novelty consisted in the lining of the tunnel being formed of a series of cast-iron rings, composed of segments bolted together, which were erected under the shelter of the rear part of the cylindrical portion of the shield as it was pushed forward; and as the shield overlapped the lining of the tunnel, and left a slight annular space between the lining and the clay stratum, lime grout was injected through holes provided in the casting, so as to fill up the vacancy left by the shield in its advance. This subway traverses the London Clay throughout, at a minimum depth of 22 feet below the river-bed, no water having been encountered; and it indicates the general method of constructing tunnels by this system. The shield serves to protect the completed end of the tunnel from the fall of earth at the working face, and acts like timbering in supporting the superincumbent mass and preventing settlement above during construction, which is further insured over the completed to be completed, and tunnels to be successfully carried out under such unfavourable conditions as would have been considered impracticable by the methods previously in use. This combination of shield, cast-iron lining, and compressed air, for carrying a tunnel Greathead for the first time in 1887, in constructing through water-bearing strata, was resorted to by Mr. the City and South London Railway, the first of the metropolitan tube railways, where it passes through the loose, water-logged gravel of the Thames basin, overlying the London Clay; and in 1889 it was adopted for continuing the Hudson Tunnel in the silt underlying the Hudson River separating New York from the mainland, when different systems of carrying forward an iron lining by the aid of compressed air, under the shelter of which a brick tunnel was constructed. proved increasingly difficult as the work advanced. The shield for the continuation of the two singleline Hudson tunnels was 10 feet long and 20 fee outside diameter; whilst the cast-iron lining has an external diameter of 19 feet and 18 feet internal diameter, formed of rings 13 feet long, made up of eleven segments and a key, put in place by a revolving hydraulic erector. This work was stopped for want of funds in 1891, but was resumed in 1903 and completed last year. Where the silt traversed was very soft, the shield was kept closed and pushed forward by sixteen hydraulic rams; and to avoid unequal settlement of the tube under the weight of a train, it has been supported at intervals on iron piles driven down to a hard stratum underlying the silt. Compressed air had been used successfully for many years in constructing foundations and piers of bridges under water, or in water-bearing strata, before it was applied to subaqueous tunnelling; but whereas in bottomless, vertical caissons, the compressed air forces out the water uniformly all over the bottom, the pressure of the air at the open end of a horizontai tube meets with less opposition from the water at the top than at the bottom, where the head of water is greater, in proportion to the diameter of the tube. Accordingly, in large tubes there is a liability in traversing loose soil for the air to escape through the stratum at the top, and for the water to rush in simultaneously at the bottom. To provide for the safety of the men in such a contingency, in addition to two or three platforms at the back of the diaphragm of the shield, with openings at each stage which can be readily closed, a metal screen is hung down the upper half of the tube at the back to provide an air space at the top, to which the men can escape by an air-lock through the screen on the occurrence of an inrush of water, and pass out through an emergency air-lock in the bulkhead behind. The author has collected together a large quantity of information from a variety of publications, so as to present a fairly complete record of the numerous subaqueous tunnels carried out by means of a shield, and more particularly those where compressed air has been also resorted to, of which there are several interesting examples in Great Britain, France, and the United States, all constructed within the last twenty years. The clear descriptions are very well illustrated by numerous drawings; and the book deserves a cordial welcome from all persons who are concerned or interested in the latest developments of subaqueous tunnelling. PROBLEMS IN METABOLISM. Problems in Animal Metabolism. By J. B. Leathes. Pp. viii+205. (London: John Murray, 1906.) Price 75. 6d. net. THIS HIS volume is the latest of the series that Mr. Murray is issuing in connection with the work of the physiological laboratory of the London University. The subject Dr. Leathes took for his lectures is perhaps the most important one in the whole of chemical physiology. In a study of metabolism one seeks to understand the innermost workings of the living cells, and thus to comprehend the sum total of the chemistry of life. In order, however, to pave the way for such complete knowledge it is necessary to study individual chemical reactions, the items that go to form the final sum; and so in the interesting book Dr. Leathes has produced he is mainly concerned with a separate consideration of the way in which the carbohydrates, fats, and proteids are utilised, and finally catabolised. The author has taken infinite pains to get his facts correct, and has presented the subject in an extremely clear way. He is able to point out quite lucidly how far present knowledge carries us, and where speculation steps in to fill up the gaps. One becomes conscious of the width of these gaps when one realises that any exact knowledge of how simple substances like sugar are ultimately converted into water and carbon dioxide in the body is at present lacking. In the case of the more complex materials, such as the proteids, hypotheses are still more numerous, because our facts are still scantier. The whole work is full of pregnant suggestions, and the writing is so attractive that one can confidently recommend it to all those who desire a picture of exactly where physiology stands at the present day in relation to these important matters. The spirit of the physiological chemist should not be to make this branch of science an offshoot of chemistry, but to use organic chemistry as the means to an end. This is the correct attitude that Dr. Leathes assumes throughout. In the remote past so-called physiology was largely anatomy. When all that anatomy could contribute had been learnt, it was found that the real work of the physiologist was only beginning. So, too, as Dr. Leathes points out, we look forward to a future in which chemistry will have contributed its share, and the workers will discover that physiology has still problems before it which cannot be learnt from pure chemistry, any more than the whole of physiology can be learnt by dissections. The subject of proteid metabolism is in the air just now, so it is specially interesting to ascertain what views Dr. Leathes holds in relation to it. He accepts the view which is daily gaining greater credence, that in digestion the albuminous molecule is broken up into quite simple substances, mainly of the aminoacid variety. He believes that these are absorbed as such, and that the work of proteid synthesis is carried out by the living cells of the tissues from these crystallisable products transported to them by the blood and lymph. He admits this hypothesis is in the unproven condition, but has himself been successful in showing that the nitrogen of the blood, combined in amino-acids and molecules of that order, is increased during absorption. To identify the individual amino-acids is a matter of much greater difficulty, and a simple calculation shows how greatly even the most abundant of them must be diluted by the whole mass of the blood even during the progress of the absorption of a considerable meal. His views on the catabolism that proteids undergo The very largely coincide with those of Folin. nitrogen of ingested albumin is readily split off with comparatively little loss of energy and discharged via the liver as urea. The non-nitrogenous residue is therefore available as a source of heat and energy in much the same way as fat and carbohydrates are. Until, therefore, we know how the cells dispose of such simple organic compounds as fat, our knowledge regarding the fate of the fat-like moiety of proteids must be in abeyance. Dr. Leathes puts this much more fully, but very clearly, which makes one wonder why, in another part of the book, all his arguments are against the possible origin of fat from proteid intra-cellularly. Is it, then, advisable to limit our proteid intake to the low level advocated so forcibly by Chittenden? Should we take only sufficient to balance the small amount of proteid waste that is associated with tissue activity? In his answer to this question Dr. Leathes has taken an independent and original line. He admits that the necessary minimum is much less than the conventional dietary of 100 grams daily, but he thinks it does not necessarily follow that it is unphysiological to take more than the minimum, any more than it is unphysiological to take any food which yields more than the minimum of fæcal refuse. In the infant, the dietary provided by nature in the amount of milk it takes is, even after making due allowance for growth, at least ten times greater than the minimum. The minimum can therefore hardly be normal for the adult; and a possible reason for this is that there may be a few members of the amino acid group which are required in large amounts for cell repair, and that it is only the commoner aminoacids which are not required in the amount usually taken, and which are consequently so rapidly discharged from the body. This example of the manner in which the puzzles of metabolism are grappled with will be sufficient to show the character of the book, and one hopes that those interested in these fundamental questions will themselves study' in full what a reviewer is only able to state imperfectly in barest outline or in samples. W. D. H. siderations of the orbits of comets, and was finally discredited by the law of gravitation. What may be regarded as the modern era of scientific cosmogony, in which serious attempts were made to explain what is seen on the background of space, opened about a century and a half ago with Wright's "cloven disc " theory of the Milky Way and Lambert's view of it as a sidereal ecliptic. These considerations of the nature of the universe are related to those of its origin adumbrated by Swedenborg and Kant as the nebular hypothesis, and afterwards worked out in mathematical detail by Laplace. During the past few years several objections of a mathematical and physical nature have been raised to this hypothesis, which has proved to be vulnerable at many points. In Miss Clerke's words, "It has, OUR BOOK SHELF. indeed, become abundantly clear that the series of Poverty and Hereditary Genius; a Criticism of Mr. operations described by Laplace could scarcely, under Francis Galton's Theory of Hereditary Genius. the most favourable circumstances, have been accomBy F. C. Constable. Pp. xyi+ 149. (London: plished, and in a thin nebulous medium would have Arthur C. Fifield, 1905.) Price 2s. net. been entirely impossible. The nebular cosmogony THE criticism which Mr. Constable brings forward has not, then, stood Foursquare to all the winds in this book is that reputation is not a test of ability, that blew.' Its towers and battlements have crumbled and as Galton's theory of hereditary genius is based before the storms of adverse criticism. It survives on this assumption, it has to be discarded. The statis only as a wreck, its distinctive features obliterated, tical evidence given in " Hereditary Genius" has to although with the old flag still flying on the keep." be explained away, and Mr. Constable attempts to Tidal evolution, the meteoritic hypothesis, and other do this by what he calls the "swamping effect of views developed in recent years to satisfy the depoverty." We quite agree with Mr. Constable that mand for a cosmogony consistent with existing knowit is harder for a poor man with uninfluential parents ledge of the heavens, particularly with spectroscopic to achieve success as a judge than for a rich one with observations, are described by Miss Clerke. While influence, but this does not seem to us to justify Mr. we cannot subscribe to all her judgments and interConstable in discarding the conclusions of "Heredi-pretations, her work contains a large amount of tary Genius," for if the social conditions of both material, both observational and speculative, and parents and offspring are relatively about the same, it general readers will find much to interest them in it. seems as if the omission of the ability in povertystricken parents and their children is rather like leaving out of account the addition of numbers to both the numerator and denominator of a fraction. The omission may therefore not affect the result at all, and whether fuller statistical evidence should modify Mr. Galton's conclusions is a matter which can only be decided by statistics other than those which Mr. Constable discusses. He appears, however, to have overlooked altogether in his argument that other statistics exist and tend to show that psychical and physical characteristics are inherited in the same way, a point which seems to us to upset a good deal of Mr. Constable's criticism. Mr. Constable does not refer to Mr. Galton's other books, and apparently quotes from the 1869 edition of "Hereditary Genius." It is a pity that Mr. Constable does not always succeed in expressing himself very clearly, and his habit of putting his arguments in the form of questions becomes somewhat tiresome, and makes the book seem a rather disjointed composition. net. Modern Cosmogonies. By Agnes M. Clerke. Pp. vi+287. (London: A. and C. Black.) Price 3s. 6d. THIS popular account of the structure of the universe, so far as it can be understood with the means of inquiry now at the disposal of astronomers, should serve a useful purpose in directing attention to the position of the most difficult problem of celestial science. To early philosophers it was sufficient to regard the heavens as a solid and crystalline firmament in which the stars are fixed; facts of observation were not considered essential for the metaphysical foundation upon which the great minds of antiquity sought to support their universe. The ingenious framework of solid concentric spheres and epicyclic motions was shown to be a baseless fabric by Tycho Brahe's con R. A. G. The Geometry of the Screw Propeller. By W. J. The writer is a lecturer en mechanical engineering in Paisley Technical College, and possesses a good knowledge of workshop practice in addition to ject. He does not attempt any discussion of the thorough familiarity with the geometry of his subdesign of a screw propeller most suitable for a new ship, but restricts attention to the preparation of drawings, patterns, and moulds required in the manufacture of propellers for which the dimensions and forms have been determined. This is a wise discretion, for while the geometry of screw propellers admits of exact treatment, the selection of the most efficient propeller for an individual steamship is even now a matter not admitting of exact scientific treatment when precedent has to be departed from; experi ments alone can be trusted. Mr. Goudie describes in clear and simple language the methods by which helical surfaces of uniform or variable pitch may be constructed, and illustrates in detail the practical methods of moulding the blades in the foundry. For the benefit of students who may not have the opportunity of actual work in the foundry the author indicates how, with the aid of a few simple tools and materials, skeleton models of the various |