148 



NA TURE 



[December 15, i{ 



attention is example 18, p. 229. Here the analysis really 

 solves the problem of finding when (o+ i)0+ i) . . . (X+ 1} 

 is a maximum subject to the condition that fl«^ . . . /* = N ; 

 a, ^, . . . /, N being given quantities. Hut the heading of 

 the article is, " How must the prime factors of a number 

 enter into it that it may have as many divisors as 

 possible? (Waring)," a question from which we have 

 vainly tried to extract any meaning whatever, and with 

 which, in any case, Prof. Smith's analysis cannot have 

 anything to do. ('.. B. M. 



OUR BOOK SHELF. 

 Die Optik der elektrischen Sclni.'ingungcn. (Experimental 

 Investigations on Electromagnetic Analogies of the 

 most important Optical I'henomena.) I5y Prof. .A. 

 Righi. Translated into ("■ernian, with additions by the 

 author, by 15. Dessau. I'p. xi + 267 ; with 40 illus- 

 trations and figures. (Leipzig : O. R. Reisland, 1898.) 

 Tho.sk to whom I'rof Righi's Italian edition of last 

 year was not accessible, will welcome this (German trans- 

 lation of his interesting book. The reproduction, by 

 means of electro-magnetic waves, of some of the more 

 complex optical phenomena, necessitates the use of an 

 oscillator which gives out a series of waves that do not 

 decrease too rapidly in intensity, and that arc consider- 

 ably shorter than those used by Hertz in his experiments. 

 Prof. Righi has carried on a number of investigations 

 with such oscillators which emitted waves ranging 

 upwards from 2'6 cms. in length, and the present volume 

 is devoted for the most part to an account of this work. 

 The first part deals with a detailed account of the con- 

 struction and use of his oscillators and resonators, and 

 with the secondary waves due to the presence of the 

 receiver and neighbouring bodies. These efiects are 

 studied first, in order that they may not lead to mis- 

 interpretations in the later results. 



In the second part the electro-magnetic analogies of 

 many optical phenomena are considered. 



The working details of the experiments are given, and 

 the difficulties attending them are pointed out, thus 

 enabling one to reproduce the effects with the least 

 amount of trouble. 



Two investigations which have appeared since the 

 publication of the Italian edition are then appended, and 

 the last part of the book consists of mathematical 

 additions on various topics connected with the subject 

 in hand. 



The book is written in an able manner, and conveys 

 to the reader a clear idea of the properties of electrical 

 waves, and Prof. Righi's method of manipulating them. 



J. Z. 

 Calculations in Hydraulic Engineering. By T. Claxton 

 Fidler, M.Inst.C.E., Professor of Engineering, Univer- 

 sity College, Dundee. Parti. Pp. xii-)-i55. (London: 

 Longmans, Green, and Co., 1898.) 

 This is the first part of an extended treatise, and it 

 discusses Fluid Pressure and the Calculation of its Effect 

 in Engineering .Structures. The treatment of the sub- 

 ject is refreshing and stimulating, by contrast with the 

 arid methods of our scholastic text-books. The illustra- 

 tions of the abstract theory are taken from actual 

 problems on a large scale, which appeal to the engineer- 

 mg student, to whom this treatise is addressed. A 

 striking novelty is the discussion in Chapters iv. and 

 vi. of the buckling tendency in straight pipes under 

 uniform fluid pressure. Although the material of the 

 pipe carries no longitudinal thrust, the conditions of 

 stability are exactly the same as in Euler s theory of the 

 bending of a column. This paradoxical fact is discussed 

 theoretically, and its experimental verification is de- 

 scribed in an Appendix. Chapter v. is on Fluid Arches, 



NO. 1520, VOL. 59] 



and shows how the pressure in a main, forming a tubular 

 arch, can be used to assist the stability. We are re- 

 minded of Prof. Fitzgerald's suggestions of inflated 

 structures and columns, and the pneumatic system of 

 architecture, in which the strength is kept up by com- 

 pressed air, pumped in at intervals as required, as in iIk 

 tires of our bicycles. .\ short account of Prof Fitzgerald's 

 theory will be found in the recent edition of Pern-'s 

 ".Applied .Mechanics.' Chapters viii. and ix. treat of the 

 equilibrium and stability and bending stresses of floating 

 bodies, not from the point of view of the Naval Architect, 

 but as rec|uircd by the Civil Engineer in the design of 

 pontoons, bridge-caissons, and gas-holders. 



The diagrams are carefully drawn to represent some 

 real actual construction, and the illustrative examples 

 are worked out to their numerical conclusions, an essential 

 part of the theory for the engineering student, although 

 so completely ignored in our academic treatises. G. 



Birds of the British Isles. By John Duncan. Pp. x\i 

 4-448 ; illustrated. (London and Newcastle : Walter 

 -Scott, Ltd., 1898.) 

 Thi; excellent illustrations and brief descriptions of 

 British birds published in the Nca>castlc Weekly Chronicle 

 met with such a favourable reception, that the author has 

 considered it advisable to reproduce them in book-form. 

 And in their new guise they form a volume which can 

 scarcely fail to be acceptable to readers with limited 

 purses, since, while every species is figured, the published 

 price of the work is only five shillings. Neither can it be 

 said that the volume is "cheap and nasty"; the type 

 being clear and good, and the illustrations for the most 

 part of high merit. Perhaps, indeed, they lack the pictorial 

 elegance of photogravures, but as good specimens of 

 wood-engraving they leave little to be desired ; and there 

 are many reasons why that style of illustration should not 

 disappear from works of natural history. In manv 

 respects Mr. Duncan appears to be a disciple of Bewick ; 

 and in the case of the cuckoo (p. 142) so closely has he 

 followed his master that his figure is merely a reversed 

 replica of the original cut, with some additional details 

 of surroundings. Generally, however, the figures are 

 original, and they are often in advance of those of Bewick. 

 Although brief, the descriptions appear sufficient to 

 identify the species. In the introduction, by Mr. C. 

 Dixon, criticism of the work from a literary standpoint is 

 deprecated ; but the author might have ascertained that 

 the British Isles form part of the Palaearctic region (p. 

 191), and also that the \\ox<\ palaios contains four vowels. 

 As a whole, the volume is a highly creditable and artistic 

 production. R. L. 



Railway '^ Block" Signalling. By James Pigg, A.I.E.E. 



Pp. 387. (London : Biggs and Co.) 

 This account of the development and details of the 

 " block " system of railway signalling brings together a 

 large amount of interesting information upon a method 

 of regulating railway traffic which has assisted very con- 

 siderably in bringing about the present stale of precision 

 and safety in railway work. The system has been in use 

 for about thirty years, and it now represents the most 

 extensive of all the adaptations of electricity to railway 

 work. Mr. Pigg describes clearly the principles of train 

 signalling and the apparatus employed ; he also includes 

 in his work the codes, regulations, and rules relating to 

 railway signals of various kinds. With regard to the 

 lines along which developments will probably be made 

 he remarks :— " Railway signalling appears to have now 

 reached a stage at which some departure from the pre- 

 sent methods seems probable. The lines upon which 

 changes will be made will, in all probability, result in a 

 greater degree of automatic control than obtains at 

 present." 



The volume is an instructive contribution to an im- 

 portant subject. 



