May 1 8, 1905J 



NA rURE 



51 



figured, one hundred and fifty in number, seem to 

 have been well selected, and the plates in which 

 they are represented by Mr. Keulemans are in the 

 stvle which has won him so much reputation as 

 an ornithological artist. But all these merits pale 

 before the admiration which the bold conception and 

 patient execution of this grand undertaking excites. 

 There is no English work on natural history com- 

 parable in these respects with the " Biologia Centrali- 

 .\mericana," and the only foreign one which it calls 

 to remembrance is the marvellous " Madagascar " of 

 the late M. Grandidier. The debt due by naturalists 

 ol all branches and of all countries to the enterprise, 

 the zeal, and the perseverance of both Messrs. Salvin 

 and Godman, and to the munificence of the latter, for 

 without that all the rest would have availed little or 

 nothing, is one that can never be repaid. A. N. 



VECTOR MECHAMCS. 

 Die Griindlagen der Bewegitiigslehre von eiiiem 

 tnodernen Standpunkte aus. By Dr. G. Jaumann. 

 Pp. vi-l-422. (Leipzig: J. A. Barth, 1905.) 



T'HIS work is intended as a systematic general in- 

 troduction to mechanics ; as in the recent 

 English exposition of Webster, the whole field of 

 solid and deformable bodies is considered, so that the 

 book has a wide range — a feature which must neces- 

 sarily be purchased to some extent at the expense 

 of depth. 



Dr. Jaumann, following a method which now 

 enjo3's some popularity on the Continent, treats 

 the subject by vectorial methods throughout. The 

 first chapter introduces the ideas of velocitv and 

 acceleration, and with them the ideas of the vector 

 and the scalar and vector products of two vectors. 

 This is very natural and well written ; it is, however, 

 followed by the introduction of dyads, which was 

 scarcely to be expected at this early stage of the work ; 

 and when the author, as is the habit of those writers 

 who apply vectors, takes the libertv of making some 

 additions to the vector calculus itself, and plunges 

 us forthwith into an able but somewhat difficult dis- 

 cussion of " rotary " dyads, we are thrown into doubt 

 as to the class of readers for whom the book is 

 designed. 



-After this we come back to the ideas of partial and 

 absolute acceleration, illustrated bv astronomical con- 

 siderations, and to the conception of gravitation, with 

 an account of Kepler's laws. This closes the first 

 section of the book, which, though interesting, leaves 

 an unsatisfied and helpless feeling behind it, for the 

 student (if the book is written for students) has not 

 learnt how to find for himself the path of a point in a 

 given field of acceleration, which is surelv the main 

 problem of this part of the subject. Thus, although 

 Foucault's pendulum is described, the theory of it — 

 which would make no greater demand on the mathe- 

 matical capacity of the reader than the rotary dvads 

 require — is not worked out. 



The author now introduces the idea of mass, which 

 is defined (as in most good modern works) by means 

 of what used to be called the principle of action and 

 NO. 1855, VOL. 72] 



reaction; in other words, the ratio of the masses of 

 two particles is defined as the ratio of the accelerations 

 which they induce in each other when moving under 

 each other's influence, and the idea of " force " is 

 altogether abandoned. These ideas are again supple- 

 mented by astronomical illustrations, even the tides 

 being worked into the scheme ; and after this we have 

 more vector calculus, with Stokes's theorem in the 

 vector notation. 



Dr. Jaumann next discusses rigid bodies, rigidity 

 itself being defined by a vector equation ! He discusses 

 the constants of inertia, and solves some very 

 elementary problems, and then passes on to a sketch 

 of acoustics. 



The last principal division of the book deals with 

 deformable media — elastic solids, liquids, and gases. 

 The treatment here is good so far as it goes, but too- 

 slight to be very satisfying. 



Considering the work as a text-book, it must be 

 said that the difficulty of the vectorial methods sO' 

 freely used is hopelessly out of proportion to the 

 results achieved. The student who has mastered the 

 whole machinery of the treatise will still be unable to 

 solve for himself any but the most rudimentary of the 

 actual problems of dynamics. The author seems to 

 overlook the cardinal fact that the solution of every 

 moving material system depends ultimately on the 

 integration of the associated differential equation, or 

 some equivalent process, and that this is the really 

 difficult part of the subject, the rest being child's play 

 in comparison. A book which devotes scores of pages 

 to symbols and formulae, and yet never brings the 

 reader into close grip with this essential kernel of the 

 subject, is open to the charge of beating about the 

 bush. 



GREATER AUSTRIA. 

 Geologic der Umgebung von Sarajevo. By Ernst 

 Kittl. Part iv. of the Jahrhiich der k.k. geolo- 

 gischen Reichsniistalt for 1903. (Vienna : R. 

 Lechner, 1904.) 



nPHIS general essay, with its plates of fossils and 

 -I- numerous geological sections in the text, corre- 

 sponds to one of the memoirs on special districts issued 

 by our own Geological Survey. It includes, moreover, 

 a folded geological map on the scale of i : 75,000, 

 and is thus a complete guide for future scientific 

 visitors. The map itself reminds us of the charm of 

 the Bosnian capital, set in its semicircle of craggy 

 hills, where the gorge of the Miljacka broadens out 

 towards the alluvial basin of Ilidze. We trace the 

 mountain-road from the Ivan Pass coming out 

 suddenly on this cultivated plain, and see again the 

 minarets of Sarajevo shining like white masts under 

 the background of Triassic precipices. 



The author's introduction shows how the geo- 

 logical survey by .■\ustrian observers followed hard' 

 upon the capture of the city, which had risen fanatic- 

 ally to arms. The famous ammonite-locality of Han 

 Bulog, on the way to Mokro, was thus discovered 

 as early as 1880; and the important part played by 

 Triassic rocks east of Sarajevo was made known by^ 



