December 27, 1900] 



NATURE 



203 



OPTICAL SCIENCE. 

 A Treatise on Geometrical Optics. By R. A. 

 Herman, M.A., Fellow of Trinity College, Cam- 

 bridge. Pp. X + 344. (Cambridge : University Press, 

 1900.) 

 TN the preface to a recent book dealing with photo- 

 graphic optics. Prof. S. P. Thompson expressed the 

 view that Sir John Herschel's article, "On Light," in 

 the "Encyclopaedia Metropolitana " of 1840 marks the 

 culminating point of English writers on optics. Whether 

 this is still the case or not perhaps need hardly be 

 discussed ; it may safely be said that Mr. Herman's 

 book, which contains many novel points, constitutes a 

 marked advance, and brings before English students a 

 quantity of information which was not easily accessible 

 to them before. 



At the same time, the book undoubtedly suffers as a 

 treatise on the subject from being a text-book for 

 mathematical students at Cambridge. Mr. Herman has 

 aimed at attracting a wide circle of students. The most 

 elementary proofs of the simplest theorems are given 

 alongside of mathematics which require a considerable 

 training to follow easily. The book would have gained 

 as a treatise if the author had assumed his readers to 

 possess some elementary knowledge of the subject and 

 its simplest formulae. A Cambridge coach might put 

 it in the hands of a beginner, marking, say, two-thirds 

 as to be omitted at first reading ; that two-thirds, with 

 some slight re-arrangement and addition, would make 

 a more interesting book for the more advanced student 

 than the actual volume now under review. Thus the 

 theory of geometrical foci, the methods of constructing 

 a figure to find the image of a small object placed per- 

 pendicularly to the axis, of a system of spherical reflecting 

 or refracting surfaces and similar problems could all be 

 put more briefly. 



In Chapter ix. (General Theorems) we come to 

 Fermal's theorem ; the general theory of geometrical 

 foci is here given, based on this theorem. The author 

 remarks that all the theorems hitherto obtained for 

 small pencils passing directly through a coaxial refracting 

 system might be obtained from the formulas arrived at ; 

 the advanced student would have gained a closer grip of 

 the subject as a whole had this course been taken. The 

 formulae can be extended to establish the collinear 

 relation between the object space and the image space, 

 and, when once this is done, the existence of the principal 

 and nodal points follows, and the geometrical construc- 

 tions based on a knowledge of their position are easily 

 generalised. The introductory methods of Drude's 

 recent " Lehrbuch der Optik " seems, in this respect, 

 more suited to a treatise on the subject than those 

 chosen by Mr. Herman, who appears to have been 

 deterred from using them by his wish to make it clear 

 throughout that the method of geometrical foci is only 

 an approximation. But in spite of this the merits of the 

 book are very great. The author, in his introduction, 

 states that it has been one of his aims 



" to introduce a new method of determining the proper- 

 ties of a symmetrical optical instrument in which the 

 angle of divergence of a small pencil, rather than any 

 coordinate of its origin, has been adopted as a leading 

 feature." 



NO. 1626, VOL. 6^'] 



The method rests on a combination of Cotes' theorem 

 of the apparent distance, and Helmholtz's expression for 

 the linear magnification. 



The simplification that results from its use in the case 

 of a symmetrical pencil traversing a coaxial system of 

 lenses is most marked ; the lengthy calculation of the 

 continued fraction by means of which the results are 

 arrived at in Gauss's treatment of the subject is entirely 

 avoided. The application of the method to the deter- 

 mination of the axial aberration of such a system is a 

 striking example of its power ; this is easily seen by 

 comparing Chapter viii. (Aberration) with the corre- 

 sponding portion of some earlier text-book. 



In the chapter on instruments the discussion of tele- 

 scopes is very satisfactory. The same can hardly be 

 said for that on microscopes ; probably it would be too 

 much to expect an explanation of the complete theory 

 within the limits of space which could be assigned to the 

 subject, but the discussion should have come after the 

 chapters on aberration and achromatism ; it would then 

 have been possible to refer to the problem of the manu- 

 facture of suitable glasses which Abbe set himself to 

 solve in 1881 — this is alluded to in a perfunctory manner 

 in § 123 — and to indicate in a general way the outlines of 

 the theory and the methods in which the defects of one 

 lens are corrected by the next. 



The problems to be solved in the construction of 

 photographic lenses can, perhaps, hardly be discussed 

 fully without more complete calculations of the aberra- 

 tions of oblique pencils than is possible in a general 

 treatise ; still, space might have been found for a refer- 

 ence to von Seidel's work, and some discussion of the 

 physical meaning of his five equations of condition 

 would have been interesting and valuable even if the 

 reader had been referred to the original papers for a 

 proof of the conditions. In fact, the book would 

 be improved in many places if the account given of 

 modern German work were more complete ; in the 

 chapter on achromatism, for example, full details are sup- 

 plied of the refractive indices and dispersive powers of 

 several specimens of crown and flint glass ; details as to 

 Abba's glasses, which contain salts of boron, phosphorus 

 and barium, together with some note as to the effects 

 produced on the optical properties of the glasses by these 

 salts, might well have been added. The book is so 

 notable and valuable an addition to the literature of a 

 rather neglected subject, that it is a pity it is not more 

 complete in these respects. It is printed by the Pitt 

 Press in its usual admirable style ; the collection of 

 examples, both worked and unworked, is specially full, 

 and will be found very useful to the student. As a 

 text-book it is a marked advance on anything yet pub- 

 lished in England. 



OUR BOOK SHELF. 



By Land and Sky. By the Rev. John M. Bacon, M.A., 

 F.R.A.S. Pp. viii-l-275. (London: Isbister and 

 Co , Ltd., 1900.) 



Members of the British Association who were at the 

 Dover meeting may find in this book, among other 

 things, some account of the intentions and the perform- 

 ance of the balloon that occupied for so long a time the 

 grounds of Dover College. 



