NA TURE 



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THURSDAY, FEBRUARY i6, 191 1. 



A PRACTICAL MODERN TREATISE ON 

 GEOMETRICAL OPTICS. 



The Principles and Methods of Geometrical Optics, 

 especially as Applied to the Theory of Optical In- 

 struments. By Prof. J. P. C. Southall. Pp. xxiii + 

 626. (New York : The Macmillan Company ; Lon- 

 don : Macmillan and Co., Ltd., 1910.) Price 255. 

 net. 

 T T is safe to assert that this volume will at no very 

 -»- distant date be in the hands of every serious 

 English-speaking student of geometrical optics. We 

 know of no other work in the Eng^lish language in 

 which the attempt has been made to give a thorough 

 anu systematic account of the fundamental principles 

 and methods of geometrical optics, so far as these are 

 necessary for dealing with the problems of the optical 

 workshop. There are in existence several conscien- 

 tious text-books of deservedly good repute, which, as 

 Silvanus Thompson has said, serve — rather, perhaps, 

 served — admirably to get up the subject for the tripos, 

 and are dotted with ingenious and fascinating 

 problems, e.g. to find the equation of the bright curve 

 seen on the spokes of a bicycle wheel rotated rapidly 

 in the sun ; but these leave untouched a vast number 

 of questions of fundamental importance to the prac- 

 tical optician. More recently Dennis Taylor, whose 

 practical knowledge and e.xperience are unquestion- 

 ably of the highest order, has attempted to provide a 

 handbook which would assist in practical lens calcu- 

 lations ; unfortunately the methods employed are un- 

 necessarily cumbrous, while, as originally published, 

 the book was marred by accidental, but serious, errors. 

 The need of such a work in English as the present 

 has been often stated, and with sufficient emphasis; 

 an Englishman may be pardoned for regretting that 

 it now only reaches him from the other side of the 

 Atlantic. 



To the reader who is familiar with Czapski's 

 "Grundzuge der Theorie der optischen Instrumente 

 nach Abbe " and with " Die Theorie der optischen 

 Instrumente " (vol. i.), published by the members of 

 the Zeiss firm, a glance through the pages of Prof. 

 Southall's volume will be sufficient to show how 

 largely he is indebted to these works, both as regards 

 method of treatment and detail ; a debt, indeed, which 

 he warmly acknowledges. The author exhibits, fur- 

 ther, a wide acquaintance with recent French and 

 German optical literature, to which most useful refer- 

 ences are given throughout the work. But the book 

 is no mere translation or compilation. It is a 

 thorough, logical, comprehensive account of the funda- 

 mental principles of geometrical optics and of the 

 theory of optical instruments, written bv one who 

 not only has an exceptionally extensive knowledge of 

 the work done by others, but has also an unusually 

 complete grasp of his subject and of the essentials 

 necessary to its clear presentment. 



In a work on geometrical optics nomenclature and 



notation are both of the greatest importance, and to 



these special attention has been given. The results 



are, we venture to think, on the whole conspicuously 



NO. 2155, VOL. 85] 



successful. The notation adopted is suggestive, clearly 

 stated, agrees in most important respects with estab- 

 lished usage, and is carefully held to throughout the 

 work. Great assistance is given by an index and 

 e.xplanation at the end of the book of the symbols 

 used. The use of thick face type to indicate points 

 on the chief ray of a bundle is especially convenient. 

 As regards nomenclature, it may be noted that the 

 term pencil of rays is confined to rays in one plane, 

 the word bundle being employed for a systerri of con- 

 current rays in space; the term "chief ray," Sylvanus 

 Thompson's translation of " Hauptstrahl," has been 

 adopted as denoting especially the ray which passes 

 through the centre of the aperture-stop in an optical 

 instrument, or, in the object space, through the centre 

 of the entrance pupil; and the words " Eintrittsluke," 

 " Austrittsluke," are well rendered by the terms 

 "entrance-port," "exit-port," denoting the virtual 

 apertures or windows which bound the field of view 

 in the object space and image space respectively. 



The general discussion of refraction through a prism 

 or prism system is given early in the book. In the 

 treatment much use is made of the work of Burmester. 

 This is followed by chapters on the reflexion and 

 refraction of paraxial rays at spherical surfaces and 

 their refraction through thin lenses. The discussion 

 of the relations between object and image in these 

 simple cases leads up to the important chapter on 

 Abbe's theory of optical imagery, of which a full 

 account is given in Czapski's volume above referred 

 to. In Abbe's theory the assumption is made of a 

 point-to-point correspondence, by means of rectilinear 

 rays, between object and image, and from this, with- 

 out any hypothesis as to the image-forming optical 

 instrument, the fundamental laws expressing the rela- 

 tionship between object and image are deduced, 

 whether for a simple or a compound optical system. 

 In his clear and full treatment of this part of his 

 subject Prof. Southall makes great use of geometrical 

 methods, which are, of course, specially appropriate. 

 It is possible that some practical opticians who are 

 unacquainted with the elements of modern geometry 

 may find this a deterrent, but the amount of know- 

 ledge necessary is so slight and so easily acquired 

 that it would be unreasonable to give such an objec- 

 ti.on serious consideration. The results are applied in 

 the succeeding chapter to the Gauss system of centred 

 surfaces. 



The general discussion follows of the exact methods 

 of tracing the path of a ray through a system of 

 centred surfaces when the angles of incidence are not 

 necessarily small. The computation formulae given 

 are those of Kerber and von Seidel, and some illus- 

 trations of their use are afforded. In the subsequent 

 account of the approximate theory of the spherical 

 aberrations the author has followed somewhat closely 

 the plan adopted by Konig and von Rohr in the 

 chapter devoted to this subject in " Die Theorie der 

 optischen Instrumente." Thus the spherical aberra- 

 tion on the axis, distortion, astigmatism, curva- 

 ture of field, and coma, are separately considered, 

 while in conclusion a somewhat modified presentation 

 is given of von Seidel's theory, of which an excellent 

 account is provided in Silvanus Thompson's transla- 



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