1 lO 



NATURE 



[September 22, 192 1 



systems in accordance with the theory of aberra- 

 tions), the latter probably the most important of 

 the whole book, from the point of view of the 

 designer; von Rohr himself, although responsible 

 for the editing of the entire collection, has actually 

 written only chaps. 9 (on the theory of stops) and 

 10 (on the photometry of optical instruments) ; 

 while he and Koenig are jointly responsible for 

 chaps. 2 (on the computation of rays through an 

 optical system) and 5 (on the theory of spherical 

 aberration). 



In the circumstances it is inevitable that there 

 should be a certain lack of cohesion, which gives 

 one the impression of a number of separate treat- 

 ises bound together rather than of an ordered and 

 progressive exposition. 



To rernedy this an attempt has been made to 

 set up a rigorously uniform nomenclature through- 

 out. A list of symbols is given at the end, but 

 this list occupies six large pages of print, and the 

 very sight of it seems likely to paralyse the reader. 

 If symbols are to be standardised, then they 

 should be as few and as fundamental as possible, 

 so that they can be readily learnt and retained in 

 the memory. This has the additional advantage 

 of releasing a mass of symbols for use in special 

 problems, where they may be usefully employed in 

 simplifying the algebra. 



Even with all these precautions the notation is 

 not always clear; thus in formula (7), at the foot 

 of p. 350, x' apparently refers (although this is 

 not stated) to the intercept on the axis made by 

 a principal image ray of a particular colour ; but 

 on the very next page .\-' is used to denote the 

 intercept on the axis made by the image plane, 

 and these two are not the same. 



The suffix notation is based on refracting sur- 

 faces, quantities after refraction being accented. 

 In many respects a notation which assigns odd 

 suffixes to refracting surfaces (or to given com- 

 binations of them) and even suffixes to media is 

 more convenient ; it saves the use of accents, 

 which are always confusing, making them avail- 

 able for other uses. 



The main trouble, however, is that throughout 

 the book the learner is not led up progressively 

 from the easy to the difficult. Fundamental prin- 

 ciples and results which must be grasped and re- 

 membered are not sufficiently extricated from a 

 mass of detail which is best put on one side for 

 reference if and when it is needed. Each chapter 

 takes the reader to the limits of its particular 

 domain, and leaves him there, somewhat bewil- 

 dered at the multiplicity of results. What is 

 really required in a mathematical subject of con- 

 siderable algebraic complexity such as geometrical 

 NO. 2708, VOL. 108] 



optics (or, say, theory of elasticity, or lunar 

 theory) is a guiding thread, knotted at intervals 

 into fundamental theorems. For such a guiding 

 thread one looks in vain in von Rohr's treatise. 



One notices, too, that characteristic tendency 

 of most German works towards needless elabora- 

 tion. Thus Fig. 15 and almost the whole of 

 pp. 45 and 46 could be dispensed with by 

 simply applying to the triangles BB„0„ and 

 BBuO,j' in Fig. 14 the rule that the sides of a 

 triangle are proportional to the sines of the oppo- 

 site angles, which leads immediately to formula (6) 

 of p. 46. Instead, we are given two pages of 

 algebra, with several new symbols, including an 

 auxiliary angle. This is only one of many 

 examples. 



On the other hand, the work is not free from 

 the converse defect of introducing statements 

 made on unconvincing grounds. Thus on p. 351 

 we are told that V^=o when Sjk'=oo , because 



Sk-Xk ^' 



But in this case we have usually ^ = 00 and 

 \'i'j.'=oo, so a proof that V)8 = o would involve 

 a discussion of awkward indeterminate forms, of 

 which nothing is said. 



Such failures, however, are few. On the whole, 

 the subject is treated with complete thoroughness, 

 and the discussion is exhaustive, if laborious, 

 von Rohr's theory of optical instruments is, and 

 must remain, a classic and an admirable book of 

 reference. But one must regretfully admit that 

 the ideal book which is to fire the enthusiasm of 

 the young British optical designer has still to be 

 found. 



(2) Far more attractive to the reader, and con- 

 ceived in quite a different spirit, is another book 

 by von Rohr, which appeared last year in Berlin, 

 to wit, the second edition of his "Binocular In- 

 struments." This is an eminently readable and 

 interesting monograph dealing with the develop- 

 ment of stereoscopic instruments, a branch of 

 optical design in which German manufacturers had 

 made very great progress before the war. The 

 chapter dealing with the early investigations 

 before the time of Wheatstone has been enlarged 

 and rewritten. 



The book opens with a chapter on the theory 

 of stereoscopic vision, but the bulk of it is his- 

 torical and descriptive, and the reader gradually 

 builds up his knowledge of the subject by follow- 

 ing the evolution of successive Instruments. We 

 would strongly recommend the study of this work 

 to the British optical manufacturer. Its language 

 is non-mathematical, and the geometrical argu- 

 ments are easy to follow. The diagrams are not 



