464 



NATURE 



[April 13, 1876 



We have said enough to indicate the richness of the 

 ground which Dr. Ball has broken, and we would com- 

 mend his treatise to the careful attention of mathema- 

 ticians. 



We could wish that a sharper line had been drawn 

 between real and imaginary solutions, and also between 

 results that are only true for screws of finite pitch and 

 those that are true without this restriction. We also 

 think that the convention which Dr. Ball proposes (foot- 

 note, p. 11) for removing ambiguity from the expression 

 for the virtual coefficient, is defective, partly because he 

 has overlooked the fact that the virtual coefficient of two 

 screws is essentially signless until positive as distin- 

 guished from negative directions have been arbitrarily 

 selected along them. When this selection has been 

 made, the virtual coefficient is the value of the quater- 

 nion expression - pS afi -\- S a^y, where p denotes the 

 algebraical sum of the pitches, a and /3 unit- vectors 

 parallel to the two selected positive directions, and y 

 the vector perpendicular from the screw a to the screw /3. 

 To express the same thing unambiguously without qua- 

 ternions would require such a long specification as would 

 weary the patience of our readers. 



The value of Dr. Ball's book is enhanced by an appen- 

 dix containing a very clear and interesting resume of the 

 literature of the subject, from Poinsot downwards. We 

 may supplement this list by a reference to §§ 200, 201 of 

 Thomson and Tail's " Treatise on Natural Philosophy," 

 where one degree of constraint is shown to be reducible 

 to the condition that " every longitudinal motion of a 

 certain axis must be accompanied by a definite propor- 

 tion of rotation about it." This comes very near to the 

 indication of the one reciprocal screw by which such 

 constraint may be defined. J. D. E. 



OUR BOOK SHELF 



Mittheilun^en mis dem k. Zoologischen Museum zu 

 Dresden. Herausgegeben mit Unterstiitzung der Gene- 

 raldirection der k. Sammlungen fiir Kunst und Wissen- 

 schaft. Von Dr. A. B. Meyer, Director des konigl. 

 zoologischen Museums, i Heft mit Tafel i.-iv. (Dres- 

 den : Verlag von R. v. Zahn, 1875.) 



There can be no question that the establishment of 

 a journal in connection with a scientific institution is 

 one of the very best methods of promoting the interests 

 of the latter and obtaining for it more extended support. 

 While the institution remains in one place, its journal 

 travels about the world, makes its most recent acquisi- 

 tions known to its supporters and correspondents, and 

 encourages them to promote its welfare by further dona- 

 tions. Such being the case, Dr. Meyer has acted most 

 wisely in endeavouring to resuscitate the somewhat de- 

 cayed zoological branch of the Royal Museum of Dresden, 

 by starting the present periodical. Dr. Meyer's recent 

 travels and discoveries in the Eastern Archipelago have 

 brought him much and deserved credit, to which, no 

 doubt, he partly owes his present appointment. They 

 have likewise supplied him with abundant materials for 

 contributing valuable memoirs to his journal. Not un- 

 naturally, therefore, the first number of the new periodical 

 commences with papers containing the results of some of 

 his own researches in the Eastern Islands. The first of 

 them contains an account of a new Bird of Paradise, not 

 actually discovered by Dr. Meyer himself, but by one of 

 his correspondents since his return to Europe. Diphyl- 

 lodes Gulielmi III., as this splendid bird is named, in 



honour of the King of Holland, is said to be from the little 

 known Papuan island of Waygiou, and vies in brilliancy 

 of plumage and elaborate excess of feathered ornaments 

 with the finest species of this gorgeous family. Descrip- 

 tions of other novelties in the class of birds discovered 

 by Dr. Meyer himself, together with additional notes on 

 little known species, complete this interesting memoir. 

 Another paper by Herr Kirsch contains descriptions of 

 new beetles from Malacca, from a large collection sent by 

 Herr Eichhorn to the Royal Museum, and a third, which 

 will be of special interest to our anthropological friends, is 

 devoted to an account of 135 Papuan skulls obtained in 

 New Guinea and Mysore by Dr. Meyer himself. We 

 observe that a second part of the Mittheilungen is an- 

 nounced for publication early in the present year, so that 

 we may expect shortly to have an opportunity of bringing 

 further labours of Dr. Meyer and his assistants to the 

 knowledge of our readers. 



Table of British Sedimentary and Fossiliferous Strata. 

 By Henry William Bristow, F.R.S., F.G.S., Director of 

 the Geological Survey of England and Wales . The 

 Description of Life Groups and Distribution by R. 

 Etheridge, F.R.S. Second Edition, revised. (Lon- 

 don : Edward Stanford.) 



This is an admirable and evidently very carefully prepared 

 table, which is well suited for the use of students, science 

 classes, and schools. In it Mr. Bristow has managed to 

 embody a vast amount of information, which could only 

 be obtained and verified by the consultation and com- 

 parison of a great number of maps and documents ; and 

 for this service all engaged in teaching the science of 

 geology are greatly indebted to him. The foreign equi- 

 valents of the British rocks are only given in such cases as 

 that of the Trias, in which our own series is incomplete. 

 Mr. Etheridge's contribution to the work consists in a 

 very valuable palgeontological digest, in which the order 

 of succession of the different forms of plants and animals 

 is clearly described. The only points which seem to 

 call for critical remark in this excellent work is the use of 

 the term Laurentian for the so-called " Fundamental 

 Gneiss " of Scotland, and the manner in which the name 

 of Cambrian is employed. There is absolutely no 

 evidence whatever whereby the geologist is able to 

 correlate the azoic rocks on the opposite sides of the 

 Atlantic, and therefore the application of the term 

 Laurentian to any British formation would scarcely ap- 

 pear to be justifiable. In the long-vexed question as to 

 the boundary between the Silurian and Cambrian systems, 

 we regret to find Mr. Bristow adopting the extreme views 

 of the late Sir Roderick Murchison, and confining the 

 name of Cambrian to a few almost unfossiliferous rocks 

 quite at the base of the series. The line of division at the 

 top of the Tremadoc slates, which was adopted both by 

 Lyell and Phillips, has the advantage of making the British 

 Cambrian system, as now defined by Hicks, very closely 

 agree with the " Primordial " of Barrande ; and we hope 

 that in a future edition of this table, which we doubt not 

 will soon be called for, the author may see his way to the 

 adoption of it. 



Catechism of Chemistry. New edition by Robert James 

 Mann, M.D., &c. (London : Edward Stanford, 1876.) 



Perhaps no better illustration of the truth of Pope's 

 line — 



" For fools rush in where angels fear to tread " — 



can be cited than the method employed in the manufac- 

 ture of many of the so-called scientific elementary text- 

 books, a series of which jnust be put forth by every 

 publisher. The " Catechism " before us is a typical 

 example of a book constructed on this most pernicious 

 method. The author appears to have learned a little 

 chemistry frorn works which were in vogue a quarter of a 

 century ago, and to have tacked on to this knowledge a 



