September 23, 1915J 



NATURE 



85 



let " without the title-r61e. Considering^ the excel- 

 lent photomicrographical apparatus now available 

 such an omission is not easy to understand. 

 More than twenty years ago the reviewer prepared 

 and showed to his students in the form of lantern 

 slides numerous photomicrographs of the crystal- 

 line products of chemical reactions. The book of 

 Haushofer (which does not appear to be men- 

 tioned at all by Prof. Chamot), published so long 

 ago as 1885, although- faulty in many respects, 

 contained a large number of reproductions of 

 careful drawings of the appearances on the micro- 

 slip, and the later work of Behrens was also well 

 illustrated in a similar manner. 



Another defect obvious to British readers is the 

 very slight mention of, or even complete omission 

 of any reference to, much of the important work 

 achieved by British workers in this domain, 

 especially as regards instruments. For instance, 

 the splendid crystallographic microscopes con- 

 structed in London by Swift are ignored, 

 although, after using almost all the Continental 

 microscopes, the reviewer considers no instrument 

 can compare for efficiency or elegance with the 

 later forms of the Dick microscope as made by 

 Swift. Such omissions, however, are not at all 

 uncommon in the recent books and memoirs of 

 United States authors. For example. Prof. F. E. 

 Wright, in a recent memoir on "A New Crystal- 

 grinding Goniometer," an instrument for prepar- 

 ing accurately orientated surfaces on crystals, 

 while making considerable reference to very 

 inferior German apparatus, merely makes a foot- 

 note reference to the refined, rigidly stable, very 

 efficient, and much more complete instrument 

 for this purpose constructed long ago by Messrs. 

 Troughton and Simms for the reviewer, and 

 with which the thousands of section-plates 

 and prisms have been prepared for his pro- 

 longed work on the sulphates and selenates and 

 numerous double salts. Perhaps the lessons of 

 the war will enable our cousins in the United 

 vStates to appreciate more fully the important 

 pioneer work in science done in this country, and 

 to be less ready to accept the much more widely 

 advertised German work as being alone worthy 

 of consideration. 



When such defects as have been referred to 

 are discounted, a very valuable aid to chemical 

 microscopy will be afforded by Prof. Chamot 's 

 bcx)k. One of the most interesting chapters is 

 one on ultra-microscopes. It is shown that the 

 ultra-microscope renders visible particles so 

 niinute that their diameters may be only slightly 

 s^reater than the half-wave-length of the light 

 employed, on the principle of the "Tyndall effect," 

 that which is evident in the dust scintillations 

 NO. 2395, VOL. 96] 



(diffractions) of a beam of light passing through 

 an orifice into a darkened room. Good illustra- 

 tions and explanations are given of the Cotton and 

 Mouton, Cardioid, and Zsigmondy ultra-micro- 

 scopes, the Jentsch ultra-condenser, and the slit 

 ultra-microscope. There is, moreover, a good 

 chapter on the determination of index of refrac- 

 tion by means of the microscope, and also one on 

 attempts at quantitative analysis by the same 

 instrument, including an account of the Barger 

 method of determining molecular weights by 

 micrometric measurement. 



The small amount of crystallography, about a 

 dozen pages, is both antiquated and not always 

 accurate; no student could possibly obtain a true 

 idea of the subject without previous or further 

 study. In the preface Prof. Chamot states that 

 his book is intended for students who have passed 

 through a course in crystallography. If there 

 should be many such happy students in the United 

 States they are much more fortunate than their 

 British cousins. Indeed this book only adds one 

 more to the many examples for the very urgent 

 need, both in America and in this country, for the 

 provision of efficient instruction in a subject which 

 is now an essential one to the correct understand- 

 ing of either chemistry, physics, metallurgy, or 

 any of their many specialised ramifications. 



A. E. H. TuTTON. 



MATHEMATICAL THEORY AND PHYSICS. 



(i) The Mathematical Analysis of Electrical and 

 Optical Wave-Motion on the Basis of Maxwell's 

 Equations. By Dr. H. Bateman. Pp. vi+159. 

 (Cambridge : At the University Press, 1915.) 

 Price 75. 6d. net. 



(2) Homogeneous Linear Substitutions. By Prof. 

 H. Hilton. Pp. 184. (Oxford : At the 

 Clarendon Press, 1914.) Price 125. 6d. net. 



ORIGINAL, and in fact fundamental, work in 

 mathematics proceeds very rapidly in these 

 days, and in so many departments, that even the 

 expert mathematician frequently complains that it 

 is impossible to keep pace with any but a restricted 

 field. In these circumstances, we can well imagine 

 the position of the unfortunate student who wishes 

 to do mathematical work of a post-graduate 

 nature, and even knows where his inclinations lie, 

 but is appalled by the difficulty of discovering the 

 present condition of any branch of the subject. 

 There is room at present for many volumes which 

 shall fulfil one or more of three main functions — 

 collect together the fragments of a fundamentally 

 important body of theory from their hiding-places 

 in periodicals and text-books on other subjects, 

 give the student exhaustive references to and criti- 



