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NATURE 



217 



THURSDAY, JANUARY 5, 1905. 



MODERN OPTICAL METHODS. 



Die Bildcrzeugung in optischen Instrumenten, vom 

 Slandpunkte dcr geometrischen Optik. By the 

 Scientific Staff of Carl Zeiss's \Vorks. Edited by 

 M. von Rohr. Pp. 58S; with 133 woodcuts. (Berlin: 

 Julius Springer, 1904.) 



Grundziige der Tlicorie der optisclien Iiistnimcnte 

 nach Abbe. By Dr. Siegfried Czapski. Second 

 edition. Edited by Dr. O. Eppenstein, with the 

 assistance of M. von Rohr. Pp. 490; with 176 

 woodcuts. (Leipzig : Joliann Ambrosias Barth, 

 1904-) 



THE old geometrical optics which we used to read 

 at Cambridge was a delightful subject. It 

 would have been a still more delightful subject had 

 examiners set better questions on it. Probably no 

 other branch of mathematics would lend itself so well 

 to the kind of treatment which is now fortunately 

 coming into fashion, viz. the use of graphical and ex- 

 perimental methods. If the German system of Lehr- 

 freiheit prevailed in this country I would rather teach 

 geometrical optics to an elementary class than 

 geometry adapted to modern requirements. 



This elementary optics, however, bears about the 

 same relation to the optics treated in the first of these 

 books that Newton's deductions from Kepler's laws 

 bear to the planetary theory. The analogy is the more 

 complete in that both the optician and the astronomer 

 have found it impossible to obtain an exact solution by 

 direct methods, and they have therefore been led to em- 

 ploy the method of trial and error in order to obtain 

 successive approximations giving the desired results 

 to closer and closer degrees of accuracy. As Messrs. 

 Czapsky and Siedentopf point out (p. 25), the exact 

 determination of the forms of the refracting surfaces 

 required to produce exact images subject to given 

 conditions has never been effected, except in a few 

 cases, such as the Cartesian oval, in which rays from 

 one focus converge to a point in the other. We 

 therefore take spherical surfaces, and by calculating 

 the various kinds of aberration, show how they may 

 be corrected. It is, however, interesting to learn that 

 the theory of non-spherical surfaces has quite r&cently 

 been put into practice in the Zeiss works for the first 

 time in the construction of lenses other than large 

 reflectors and refractors for telescopes. It has, in fact, 

 been found possible to correct certain residual 

 aberratipns by applying finishing touches to the lenses 

 giving them a slight deviation from sphericity. 



The analogy between the problems of the optician 

 and the astronomer is made still closer by observing 

 how different specialists have confined their attention 

 to particular kinds of aberration in the one case and 

 of perturbation in the other, and have devised special 

 methods for simplifying the calculation of the corre- 

 sponding terms. 



In his preface Dr. Czapski tells us that the present 

 work owed its origin to the demand for a revised 

 edition of his " Theorie der optischen Instrumente 

 NO. 1836, VOL. 71] 



nach Abbe," published in 1S93. Being unable to 

 undertake the work himself, the idea suggested itself 

 that a better purpose would be served by obtaining 

 the collaboration of a number of joint authors, and 

 that no better body of men could bc> found for the 

 purpose than the scientific staff of the Zeiss firm. 



The work has been divided among the seven joint 

 authors as follows :— The first chapter, dealing with 

 the fundamental principles of optics, including the laws 

 of relraction, the principle of minimum path, and the 

 characteristic function, is contributed by Drs, Czapski 

 and Siedentopf; Drs. Konig and von Rohr contribute 

 the second chapter, on formulae of calculation, and the 

 fifth, on spherical aberration, in which latter is con- 

 tained a complete exposition of Abbe's method of in- 

 variants and its application to the determination of the 

 ten corrections determined by the problem of Seidel. ' 

 The chapters on chromatic aberration and on deter- 

 mination of optic systems according to the theory of 

 aberrations (chapters vi., vii.) are contributed by Dr. 

 Konig alone. " The Geometrical Theory of Images 

 after E. Abbe " is the title of the third chapter, by Dr. 

 Mandersleb. In the fourth chapter, by Dr. P. Cul- 

 mann, on the realisation of optical images, we actually 

 do find our old friend the formula 



V II r ' 



in a position, however, of subsidiary importance. Dr. 

 Lowe contributes a chapter on prisms, while Dr. von 

 Rohr is responsible for the last two chapters, dealing 

 with the breadths of pencils, penetration, brightness 

 of images, and similar matters. 



The second of these books is of a more elementary 

 and practical character. It contains a general dis- 

 cussion of images formed by small pencils, and illus- 

 trated descriptions of the principal optical instruments. 

 The corrections are discussed, but the discussions are 

 less mathematical. The theory of conjugate foci re- 

 ceives fairly full treatment, and among the interesting 

 features which we notice at a first glance, attention 

 may be directed to the series of sections of a pencil of 

 light on p. 24, and the figures of an object and its 

 image on p. 40, where the object is an arrow in a 

 plane through the axis of a lens, and is bisected by 

 the focal plane of the lens. 



This is the second edition of a book of which the 

 first edition was written for Winkelmann's " Hand- 

 buch der Physik. " Of matter new in this edition. Dr. 

 Eppenstein contributes chapters on screens, on pro- 

 jection apparatus, and on the illumination of objects; 

 chapters on vision, on photographic objectives, and on 

 spectacles are contributed by Dr. M. von Rohr. 



The perfection to which the manufacture of optical 

 instruments has been brought by the Zeiss firm is well 

 known, and it is also pretty generally realised that 

 the results attained could not have been accomplished 

 by an establishment run on purely business lines by 

 " practical men '" falsely so-called. The usual stock 

 form in which the last named class of individual re- 

 commends his wares to the public is the stereotyped 

 statement that " The materials used in the preparation 

 of these goods are of the best quality obtainable." 



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