NATURE 



409 



rHURSDAV. ALCLST 22 



APPLIED OPTICS. 



A System of Applied Optics, being a Complete System 

 of Vormitlae of the Sennid Order, and the Found- 

 ation (if a Complete System of the Third Order, with 

 examples of their Application. By H. Dennis Taylor. 

 Pp. xvi+334, with 24 plates. (London: Macmillan 

 and ("(.., Ltd., 1906.) Price t,os. net. 



TH.\T branch of geometrical optics which deals with 

 the properties of lenses and lens systems has 

 unfortunately been shamefully neglected in England 

 during recent years. This neglect has extended from 

 the theory to its practical applications, and the design 

 and construction of lenses has, to a great extent, been 

 relegated to other countries, notably Germany; 

 although in the time of Dollond, M. .Anth^aume was 

 obliged to send to England in order to obtain lenses 

 to c.'irry into practice llw. theory of achromatism 

 devised by M. Clairaut. Before the publication of the 

 book which forms the subject of this review, there was 

 no work, in English, by the guidance of which an 

 ordinary photographic Iins could be worked out in all 

 particulars; and the fart that there h.is been practi- 

 cally no demand for translations of the numerous 

 books on applied optics which have been published in 

 Germany, shows how completely the subject has been 

 neglected. If we seek for a reason to explain this 

 state of affairs, it is not far to seek. The books on 

 geometrical optics which have appeared in England 

 during recent years have, for the most part, been 

 written by mathematicians who could boast little or 

 no acquaintance with the practical design of lenses; 

 and as the formulae which can be obtained for the cor- 

 rection and elimination of errors in lenses do not 

 possess that " eleganci' " which is dear to the heart of 

 the pure mathematician, practically no progress has 

 been made since the time of Airy and Coddington : 

 almost the only modern work which exhibits origin- 

 ality of treatment is a small volume ' by Mr. Blakesley, 

 publi>.hid in 1903. 



In these circumstances we cannot feel too grateful 

 to Mr. Dennis Taylor for the volume before us. In 

 this, everything which could aid the student in master- 

 ing the subject in the easiest and most pleasant way 

 has bfin done, and done well. The numerous dia- 

 grams (drawn to scale, or as nearly to scale as is 

 practicable), which are included in the twenty-four 

 plates, must alone have entailed many hours of 

 tedious labour. The principles underlying each pro- 

 blem that is attacked and solved are clearly and fully 

 explained, while the steps in the analysis which have 

 been omitted can easily bi- supplied bv a reader with 

 very moderate mathematical acquirements. But the 

 chief interest of the book lies in the fact that it is the 

 outcome of a successful attempt to design lenses for 

 practical purposes. Finding that the formulae arrived 

 at by Coddington, for the curvature of the image 

 formed by a lens, were not quite satisfactory, an 



* "Geometrical Optics 

 a/id Co., 1903.) 



By T. H. Blakesley. (London: Whittoker 

 NO. 1973, VOL. 76] 



attempt was made to solve the problem by some method 

 not dependent on the calculus; .-ind after several dis- 

 appointments, Mr. Taylor was successful. 



In this investigation the formula; relating lo 

 " coma " or " side flare " were arrived at ; it is signi- 

 ficant that there is scarcely a book in English which 

 even mentions this defect of lenses — a defect which is 

 often of greater importance than those due to spheri- 

 cal aberration or astigmatism. As a practical outcome 

 of the investigation, the Cooke lens was designed ; and, 

 finally, Mr. Taylor has embodied his investigations in 

 the book before us. 



It is, perhaps, a pity that Mr. Taylor has not adopted 

 the usual convention as regards the signs of the quan 

 titles II, V, and r. In the end, one convention (when 

 mastered) is as good as another; therefore, it would 

 appear that the most suitable one is that which is 

 most generally adopted. The convention adopted by 

 Mr. Taylor makes u positive or negative (for a parti- 

 cular position of the object), according as the lens is 

 collective or dispersive, while the signs of v, and the 

 radii of curvature are determined in a similar manner. 

 There appears to be no advantage in this procedure 

 that is not shared equally with the one generally in 

 use; and the reader accustomed to the latter is likely 

 to experience some unnecessary difficulty in following 

 Mr. Taylor's reasoning. This is, however, a detail of 

 no vital importance. 



The first chapter of Mr. Taylor's book is devoted 

 10 a brief recapitulation of the ordinary formulae, of the 

 first order of approximation, applied lo mirrors and 

 lenses. In the second chapter the " theorem of ele- 

 ments " is explained : a thick lens is shown to be 

 equivalent to two thin lenses (called " elements "), and 

 a plane parallel sheet of glass. The 'heory of thick 

 lenses, and lens combinations, is discussed in chapter 

 iii. ; this theory, as explained by .Mr. Taylor, is inuch 

 simpler than that usually given in books on geometri- 

 cal optics, although a- further simplification is possible 

 and desirable. .\t this early stage the reader is brought 

 into touch with practice by using the formulae that 

 have been evolved, to calculate the focal lengths of 

 some well-known lens combinations, including the 

 Cooke process lens. .Such calculations occur at short 

 intervals throughout the book, and add much to its 

 value. 



Spherical aberration is discussed in chapter iv. The 

 ordinary formula to the second degree of approxi- 

 mation is obtained, and is simplified by the aid of a 

 device due to Coddington ; a formula to the third 

 degree of appro.ximation is also worked out, but the 

 reader may omit the investigation leading lo this on 

 a first reading, as it is somewhat complicated, though 

 presenting no difficulty other than those generally 

 met with in dealing with unwieldy formulae. A geo- 

 metrical device ' due to Mr. Blakesley, might have 

 been mentioned here with advantage. It can be easily 

 proved that if all rays proceeding from a point on the 

 axis of a lens pass through the lens in such a manner 

 that the deviation of each is a minimum, then the 

 spherical aberration is a minimum also; and Mr. 



^ "Geometrical Optics." By T. H. Blakesley, pp. 94-1 tr. 



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