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“TECHNICAL" SERIES of PHYSICAL APPARATUS.

Prof. HARTL'S

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• DIAL" BAROGRAPH,

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POLARISING APPARATUS,
covering all the important

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THURSDAY, AUGUST 9, 1906.

presentment. The well-known treatise of Watson we owe to America. Of other works, by far the most not

able is that of Oppolzer. Unfortunately, the second THE DETERMINATION OF ORBITS.

volume of this book is now out of print and has beDie Bahnbestimmung der Himmelskörper. By Julius come scarce.

Bauschinger. Pp. xv +653; mit 84 Figuren im In these circumstances a warm welcome must be

Text. (Leipzig: Wilhelm Engelmann, 1906.) extended to Dr. Bauschinger's treatise. His position Die Gauss-Gibbssche Methode der Bahnbestimmung as Director of the Recheninstitut in Berlin, the promicines Himmelskörpers aus drei Beobachtungen.

nent feature of the work of which is the surveillance of Mit einem Anhang zum “Grundriss der theo- the rapidly accumulating multitude of minor planets, retischen Astronomie." By Prof. Johannes Fris- | leads us to expect an eminently practical treatment, chauf.

(Leipzig: Wilhelm Engelmann, and we are not disappointed. No great originality 1903.)

will be found, nor was it to be looked for, so far as THE HE development of convenient and general regards the fundamental methods themselves. The methods for calculating the orbit of any body

aim of the author has evidently been to follow the around the run from a limited number of observations path which has been proved by experience, and any constitutes a classical problem in the annals of originality must be sought in the modes of presentaudronomy. Its history, which has yet to be ade-ation, which are always elegant, concise, and lucid. quately written, now covers a period of rather more A most important feature of a work of this kind is than two centuries, and during that time it has the choice of illustrative examples of actual computaattracted the attention of many famous mathematicians tions. In both the liberal selection and the arrangewhose successes and failures are alike remarkable. ment of these Dr. Bauschinger has done well. The At the time of Newton long records had made the prin- diagrams are neat and clear. The style of printing, a cipal features of the orbits of the known planets matter of which the importance in the case of a familiar, and no addition to their number was made mathematical work can hardly be exaggerated, will within the next hundred years.

Hence in the bear comparison with the best English examples of a righteenth entury efforts were mainly directed to the similar class. It is impossible that all errors should driermination of the parabolic orbits of comets.

Yet have been detected in the course of proof-reading, but the completely satisfactory solution was deferred until though two or three have certainly escaped notice, it 1747, stirs Obero's cek brated work appeared. Why is unlikely that there will be any necessity for a list of Olbers succeeded when far greater mathematicians, corrections such as that inserted in Oppolzer's second such as Eulis and Lagrange, had m. t with compara- volume. live failure is an interesting question. The fact is

Some time ago Dr. Bauschinger published a very that the determination of orbits is an art demanding useful collection of astronomical tables.

Frequent its such a sense of arithmetical technique and not reference is made to these in the present work, which meren an insight into the mathematical principles is thus relieved of a large amount of additional matter, insolved.

while the tables themselves are available in a handier In the nineteenth century, on the other hand, the dis- form than as an appendix to a bulky volume. As it is, covery of minor planets, which are now being found the author has covered the same ground as Oppolzer's at the average rate of on a week, has required " Bahnbestimmung," and even included some addigeneral methods of dealing with planetary orbits. The tions within the limits of a single volume. But it is deduction of an orbit from the incessary three observ- of necessity a large one, and can scarcely fail to sugistions has be: n based mainly on the methods of gest the question whether its size could not be reduced (sauss's " Theorid Motus." Even in matters of de- by omissions or compression without prejudice to its tail the variations which have been added have been utility. At first sight this would certainly seem to be for the most part slight and unimportant. In a less the case.

The first part, containing a discussion of degree ust has been made of the earlier method of astronomical coordinates, is occupied with matter Laplace, which has been generally regarded as inferior which ought to be accessible in general treatises on in practice. In reality the two solutions are essentially I practical astronomy. The chapter on the method of equivalent as regards their mathematical foundation, I least squares might be replaced by simple references a remarkable theorem due to Lambert standing as the to some work devoted to that subject, and what is formal connecting link. Again the difference is a given in the chapter on mechanical integration ought matter of technique rather than of principle.

to be found in treatises on the calculus of finite difThe determination of orbits, considered in a wide ferences. But apart from the fact that this supposes sense, forms a subject so complicated and so closely the existence of ideal books which have not yet been w.pendent on other branches of astronomy that com- written, it is a distinct advantage to be saved the prehensive treatises serving to bring together what ex- trouble of consulting a number of separate works, perience has shown to be the most practical methods even when these are at hand. The fuller treatment have rendered indispensable service. In England, must be justified by a severely concise and practical 04 ing, prthaps, to the too exclusive predominance of discussion of all subordinate topics, and in this respect the school of thought, little has been contributed to the little fault will be found with Dr. Bauschinger's development of the theory and nothing to its connected handling of his material. It is difficult to believe,

however, that some matters of elementary mathematics of subject, their inclusion is justified. But that on could not have been omitted without detriment. Thus satellites is certainly valuable, especially in view of the discussion, at the beginning of the second part, of recent discoveries. the equations of a conic, based on the definition of a a The source of the numerous theorems which are conic as the plane section of a right circular cone, met with in the work has generally been indicated, must be superfluous for a reader who is capable of but this is not always the case. Thus the theorems following the whole of the first part intelligently. But on p. 184 are due to M. Radau (Bull. Astr., X. p. 11) the fault is doubtless on the right side.

and to Mr. Shin Hirayama (Monthly Notices, R.A.S., The whole work consists of seven parts. The first lxii., p. 620). Such references add greatly to the indeals with those portions of general astronomy which terest, but of course it is always difficult to be sure are relevant to the main purpose. The chapters on that the sources are strictly original. For instance, time and on precession and nutation seem particularly the proposition attributed (p. 131) lo van der Kolk clear and good. That on aberration follows the tra- was, as has been recently pointed out, previously given ditional lines of Gauss and Bessel, and criticism would by Whewell. There is an index at the end of the be out of place here. Yet the exposition of Gauss, volume, but it is not so complete as it should have been. which seems to assume the apparent composition of the A full index of names is needed. velocities of light and of the earth as a matter of An outline of the method of Gibbs will be found in course, appears to be imperfect in view of the difficul- Dr. Bauschinger's work, but for fuller details th: ties in the physical theory. Is it not more logical to pamphlet of Dr. Frischauf may be consulted with consider the apparent composition as an inductive re- advantage. The method is based on the use of a par. sult instead of the explanation of the astronomical tícular expression for the ratio of a triangle to the corphenomena?

responding sector of an ellipse. The form is matheThe second part contains a discussion of undis- matically elegant and the degree of approximation is turbed heliocentric motion. Dr. Bauschinger asserts high, but it was thought to entail greater complexity (p. 170) that Lambert's equation is of little use in the in the computations, while, on the other hand, the case of ordinary elliptic orbits. This opinion may be method by itself gave little assistance when a still closer disputed. It is true that the development in series is approximation proved necessary. This defect was of little assistance owing to slow convergence, but in remedied by Prof. Harzer. The modified method is its original form the equation can be easily solved in described by Dr. Frischauf in a clear and interesting all ordinary cases. The natural expression of the for- manner; the practical value of his account would havr mulæ for motion in a hyperbola involves hyperbolic been enhanced by the addition of a fully worked 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 supplementary notes to the author's "Grundriss der as a rule accessible to the computer.

theoretischen Astronomie," a work of which a second The properties of the apparent or geocentric motion edition appeared in 1903 after an interval of thirtyare discussed in the third part. Here will be found two years from its first publication. H. C. P. 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

INDUCTION AND CONDUCTION JOTORS, measure of fame to which his unquestionable eminence

Moteurs a Collecteur a Courants alternatifs. B; as a mathematician entitles him.

Dr. F. Niethammer. Pp. 131. (Paris : L'Éclairage The longest part is the fourth, in which the various

Électrique, 1906.) methods of determining a preliminary orbit are de- THE

HE title leads one to believe that the author is scribed. An excellent feature is the compendious

going to deal with at least all the principal type arrangement of the working formulæ. This part is of modern alternate-current commutator motors, followed by that on the adjustment of an orbit by the

whereas the book is practically restricted to a conmethod of least squares.

In both sections numerical sideration of the series induction and conduction examples are fully and clearly worked out.

motors. Shunt induction motors of the commutator The sixth part contains the theory of special per- type are occasionally touched upon, but all remarks turbations. Three methods are given, according to

concerning these must be considered as quite which the perturbations can be calculated in the ele

Generally speaking, the number of misments, or in polar or in rectangular coordinates. takes is too great. In the preliminary chapter, on mechanical integration, In chapter i. the historic part does not deal with the usual German notation for interpolation formulæ the machines out of which those modern single-phase is employed. It is difficult to see the advantage of commutator motors have been directly evolved, which this over the ordinary notation of finite differences. are afterwards considered more closely. The last chapter of this section brings the reader to the liminary consideration of some of the types now in determination of the definitive orbit.

use is full of errors, and much prominence is given Here the work might have ended, but Dr. Bausch- to the least important of these types. The indisinger has added a final part, in which he investigates | criminate use of the expression “repulsion " motor the determination of the orbits of meteors, satellites, leads to the usual confusion. and double stars. These last chapters are necessarily In the second chapter, which is the most important brief, and it may be doubted whether, as regards unity in the whole book, we find the author trying to

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establish exact diagrams which will cover all types | been assumed by the author, so that Er is not nil as of motors. It may be possible to achieve this, but stated. No more is Ei 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 The writer's space is limited, and he must thereillustrates the action of the motor shown in Fig. 30, fore cut his remarks short. The fundamental the second (which is not referred to in the text) is diagrams of chapter ii. having been proved to be probably intended to illustrate the action of the motor wrong, the value of the whole chapter is naturally shown in Fig. 31. The E.M.F. (J.Wa) in Fig. 32 greatly discounted. The chapter, however, contains is responsible for the current Ja flowing in the short- a number of other mis-statements, some of which we circuited rotor; it must therefore be the resultant of will note in passing. all those E.M.F.'s which are effective so far as the On p. 34 it is stated that the transformer flux in short-circuiting brushes

concerned. These a short-circuited transformer is zero! On p. 42 that E. M.F.'s are Er, Ei, Er', Ei', and Ex'. When the the motor shown in Fig. 53 is compensated in the motor is standing, E, and Er' are nil, but they in

the Winter-Eichberg machine, crease in direct proportion with the speed, with the whereas compensation is due to the alteration brought result that J.W, must, according to the diagram, in- about in the phase of the motor field by the introcrease with the speed independently of the load! In duction into the exciting circuit of the auxiliary other words, the rotor current Ja must increase with E.M.F. derived from S. In diagram 43 the E.M.F. the speed, consequently also the stator current Is. (Er) is shown as being of opposite phase to the Seeing that the machine is one with a series character- E, of Fig. 32, although both diagrams refer to the istic, it is very obvious that the diagram in question

motor. The remarks commutation cannot be correct. In a machine of the kind the difficult to follow, because of the attempt to deal with tendency of the current is, of course, to diminish with the various types of motors at one and the same time. the speed. The fact of the matter is that the phase It is recommended that Aux Ku should be chosen of E, is shown incorrectly. If the direction of rota- low at starting for motors of the series induction tion is such that Er is in phase with the flux Ka, then type, whereas it is the flux K, which at that time Er must be of opposite phase to the Aux Kq, for should be small. Contrary to the author's statethese fluxes are not only at right angles to each ment, the commutation difficulties with polyphase other in space, but also nearly at right angles to commutator motors are just about of the same order each other in phase. The presence of this very serious as those met with in the series induction motor. In mistake evidently prevented the author from grasping dealing with the power factor (p. 59), the author the full meaning of the various vectors of his diagram. makes a statement in the last paragraph which re(E) must be considered as the working E.M.F.; veals a great confusion of ideas. This mistake prob(Er'; is then the back E.M.F., (E,+E;') represents ably arises ont of the confusion of the axes of K, ihe self-induction of the rotor circuit, whilst E, (and and Ke already pointed out in connection with not E,', as stated by the author on p. 32) must be Fig. 34; in addition, the notation is now suddenly looked upon as the compensating E.M.F. It is nearly changed. It is, however, evident that for the case opposed to (E.'+ E'), therefore tends to cancel the of the series conduction motor (Fig. 34) k, stands effect of the self-induction in the rotor and to bring for the field coaxial with the armature brushes and Je more and more into phase with Ei. Since E, in- due to the armature ampere turns; k, is perpencreases with the speed, it follows that with increasing dicular to K, and by neutralising k, as shown in speed the phase of Ja will approach that of Ei, and Fig. 37 or 39 the power factor is improved as that the power factor will rapidly improve.

stated. But in "repulsion" motor such The writer also fails to agree with the author's | Fig. 30, k, does not exist; it is neutralised ipso Fig. 33. Owing to a mistake similar to that present | facto because the energy is conveyed into the rotor in Fig. 32, we get the following curious and im- by induction, and not by conduction as in Fig. 34. possible result. It is obvious that Er, which appears Furthermore, if k, did exist, it would be coaxial at the brushes (aa), must be responsible for the flux with Ka. If k, is a misprint for K, then by Ky; it is generally admitted that a magnetic field neutralising it the torque of the motor would be lags by about go degrees behind the E.M.F. responsible destroyed, for K, is the motor field. As to speed for it, yet in Fig. 33 K, actually leads E, by nearly regulation, and contrary to the author's opinion, any that amount. The author also ignores the fact that so-called repulsion motor can be satisfactorily confor the arrangement of brushes shown in Fig. 31 we trolled by suitably influencing the rotor circuits. have two currents in the rotor, the one flowing from Chapter iii. only deals with motors full descrip(b) to (b), the other from (a) to (a), the former being tions of which have appeared from time to time in the working current, the latter producing K,

the technical Press. As to the notes on the preThe value of the next fundamental diagram (Fig. 35) determination of alternate-current commutator motors, is greatly reduced because the author mistakes, in these are very superficial, and mainly apply to the Fig. 34, the axis K, for the axis ką, thus making series conduction machine. a comparison between Fig. 34 and Figs. 30 and 31 On the whole, the book is more likely to bewilder quite impossible. In Fig. 34 the motor-field axis K, the reader than teach him anything; it ought to be is the vertical axis, and not the horizontal, as has very thoroughly revised and corrected before it can

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Thandlincomprehensive history of

be recommended. The author will find it easier and tunnel by filling the cavities left by the advancing more profitable to treat each type of motor separately, shield with grout. and then to point out the differences between the The system, however, as successfully carried out, in various types, than to try and establish diagrams and the absence of water, in the Tower Subway, was not formulæ which will meet all cases.

adapted for passing through water-bearing strata; VAL. A. FYNN.

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combined use of a shield, a cast-iron lining put 'HIS fine quarto volume furnishes a very valuable together under shelter of the shield, and compressed

air to exclude the water from the works in traversing

a system of tunnelling, especially under rivers and in water-bear- water-bearing strata, has enabled abandoned tunnels

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out under such unfavourable conditions as would have Isambard Brunel, as regards the employment of a

been considered impracticable by the methods preshield, in the celebrated Thames Tunnel between

viously in use. This combination of shield, cast-iron Rotherhithe and Wapping, commenced in 1825, but, lining, and compressed air, for carrying a tunne! owing to the inrush of the river into the works on two occasions through breaks in the stratum of clay, Greathead for the first time in 1887, in constructing

through water-bearing strata, was resorted to by Mr. and financial difficulties, only completed in 1843.

the City and South London Railway, the first of the The second important step in the development of metropolitan tube railways, where it passes through the system in a practical form was, curiously enough, the loose, water-logged gravel of the Thames basin, taken in constructing a second tunnel under the overlying the London Clay; and in 1889 it was adopted Thames rather higher up the river, crossing just for continuing the Hudson Tunnel in the silt underabove the Tower, which was commenced in February, lying the Hudson River separating New York from 1869, and completed in November the same year.

the mainland, when different systems of carrying forThis Tower Subway, originally proposed by Mr. Peter ward an iron lining by the aid of compressed air, under Barlow, but eventually executed by the late Mr. Great- the shelter of which a brick tunnel was constructed, head, whose name will always be prominently associ- proved increasingly difficult as the work advanced. ated with the system of tunnelling under consider- The shield for the continuation of the two singleation, was carried forward through the London Clay line Hudson tunnels was 109 feet long and 20 fre' under the shelter of a shield, similar in principle to, outside diameter; whilst the cast-iron lining has an though much smaller than, the Thames Tunnel shield. external diameter of 19. feet and 18 feet internal The shield in this instance consisted of a short

diameter, formed of rings it feet long, made up of wrought-iron cylinder laid horizontally, 4! feet long eleven segments and a key, put in place by a revolving and slightly more than 7 feet internal diameter, hydraulic erector. This work was stopped for want stiffened at its front cutting-edge, and provided in- of funds in 1891, but was resumed in 1903 and comside with a vertical plate diaphragm having a central pleted last year. Where the silt traversed was very opening, which could be readily closed, through which soft, the shield was kept closed and pushed forward the men passed for excavating the ground in front by sixteen hydraulic rams; and to avoid unequal preparatory to pushing forward the shield by a series

settlement of the tube under the weight of a train, it of screws. The novelty consisted in the lining of the has been supported at intervals on iron piles driven tunnel being formed of a series of cast-iron rings, down to a hard stratum underlying the silt. Comcomposed of segments boited together, which were

pressed air had been used successfully for many years crected under the shelter of the rear part of the in constructing foundations and piers of bridges under cylindrical portion of the shield as it was pushed for- water, or in water-bearing strata, before it was ward; and as the shield overlapped the lining of the applied to subaqueous tunnelling; but whereas in tunnel, and left a slight annular space between the bottomless, vertical caissons, the compressed air forces lining and the clay stratum, lime grout was injected out the water uniformly all over the bottom, the through holes provided in the casting, so as to fill pressure of the air at the open end of a horizontal up the vacancy left by the shield in its advance. This

tube meets with less opposition from the water at the subway traverses the London Clay throughout, at a top than at the bottom, where the head of water is minimum depth of 22 feet below the river-bed, no greater, in proportion to the diameter of the tube water having been encountered; and it indicates the Accordingly, in large tubes there is a liability in general method of constructing tunnels by this system. traversing loose soil for the air to escape through The shield serves to protect the completed end of the the stratum at the top, and for the water to rush in Tunnel from the fall of earth at the working face, and simultaneously at the bottom. To provide for the acts like timbering in supporting the superincumbent safety of the men in such a contingency, in addition mass and preventing settlement above during con- to two or three platforms at the back of the diaphragm struction, which is further insured over the completed I of the shield, with openings at each stage which can

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