220 



NA TURE 



[July 7, 1887 



one of the most difficult parts of the subject to present in 

 an elegant manner, on account of the non-symmetrical 

 character of the necessary approximations. The treat- 

 ment here given seems to leave nothing to be desired. 



Chapter VIII. begins with an exposition of the proper- 

 ties of a general system of rays : this with the cardinal 

 result that the rays are all bi-tangents to a focal surface is 

 ascribed to Kummer. They had, however, been pre- 

 viously given by Hamilton in his memoir on " Systems of 

 Rays," in the discussion of ray- systems in a crystaUine 

 medium where the wave-surface no longer cuts the rays 

 at right angles ; and he in turn refers back to the same 

 papers of Malus which contain the theorem of orthogon- 

 ality in isotropic media. 



The theory of the characteristic function is next applied 

 to the solution of the general problem of the refraction of 

 a narrow beam at a surface of double curvature ; and to 

 the analytical determination of the relation between the 

 forms of such beams before and after passing through a 

 general optical instrument whose internal structure is not 

 specified. In these discussions the author has closely 

 followed a series of papers by Clerk Maxwell which ap- 

 peared about fifteen years ago in the Proceedings of the 

 London Mathematical Society, and which presumably 

 were to find a place in a book on optics then contem- 

 plated by their lamented author. It does not seem to have 

 been much noticed in this country that the same formulae 

 for oblique refraction were developed a long time ago by 

 Sturm and others, in a direct geometrical manner, from 

 Malus's theorem ; but the conciseness and precision 

 which arise from defining a beam by means of its charac- 

 teristic function give them an enhanced importance in 

 optical theory. Their application is here given to some 

 cases which we do not remember having seen published 

 before : thus the modification impressed on a beam by 

 refraction centrically through a single thin lens is ex- 

 pressed by means of very simple formulse, from which 

 several properties of considerable elegance and some 

 practical value might be directly drawn. 



The theory of dispersion and achromatism is treated 

 in the ordinary way. In the chapter on vision are intro- 

 duced discussions, chiefly from Helmholtz, of the mechan- 

 ism of accommodation and the principles of binocular 

 vision. Then follows a clear and valuable chapter on 

 telescopes and microscopes, a chapter on miscellaneous 

 optical instruments, and a brief account of atmospheric 

 refraction, mirage, rainbows, and halos. 



It may seem ungracious to expect more where so much 

 is given, but we could have wished that the theory of 

 refraction through general systems had been treated more 

 from an historical standpoint. A difficulty often felt in 

 this part of the subject arises from the way in which the 

 geometrical and analytical methods of different writers 

 are liable to be intermixed. The book was probably in 

 the press before a recent note by Lord Rayleigh had 

 brought again into prominence the large share taken by the 

 English opticions of last century, notably Cotes and 

 Smith, in the development of the general theory of this 

 branch of the subject. 



The list of treatises and memoirs might be improved 

 by consulting the bibliographies given by Helmholtz and 

 Verdet. 



It is a misfortune incident on the scheme of the book 



that it is seldom able to say the last word in relation to 

 the more delicate arrangements of telescopes and micro- 

 scopes, where diffraction plays an important part. This 

 becomes very patent, for example, in the account of im- 

 mersion objectives. The theory of diffraction as applied 

 to optical construction is for the most part purely geome- 

 trical, and it would much increase the value and interest 

 of books on geometrical optics if that theory were 

 explicitly included, and the subject introduced by the 

 consideration of light as wave-motion, instead of the 

 artificial conception of the reflexion and refraction of 

 rays. 



As is usual in English text-books, selections of problems 

 have been added at the ends of the chapters. In this 

 case, Cambridge examination-papers of recent years have 

 been largely drawn upon for questions, with the result 

 that some are included which are not of much value as 

 illustrations of the subject, though they may be very use- 

 ful as tests of mathematical power. Indeed it seems open 

 to question whether the practice of adding large collec- 

 tions of examples is not now overdone in this country ; 

 it certainly in some cases tends to unfit the books which 

 contain them for the use of students who do not possess 

 the advantage of tuition, or some guidance in selecting 

 the few that will be of value for them. 



The treatise is, on the whole, a most welcome addition 

 to our optical text-books. Much of its contents, though 

 fundamental and elementary, has only hitherto been 

 accessible in English through Mr. Pendlebury's treatise 

 on "Systems of Lenses"; and there is more that now 

 appears in a text-book for the first time. The printing 

 and general appearance of the book reflect great credit 

 on all concerned with it. J. Larmor. 



OUR BOOK SHELF. 



Shores and Alps of Alaska. By H. W. Seton Karr, 



F.R.G.S. (London: Sampson Low, 1887). 

 This is a very interesting account of a journey of explora- 

 tion in a country which, as the author says, is probably 

 destined soon to become better known. The most import- 

 ant part of the book is that which relates to the attempt 

 made by Mr. Seton Karr and his companions upon 

 Mount St. Elias. When this attempt was made, the com- 

 bined " alpinism " of the climbers was " insignificant." 

 Nevertheless, they achieved considerable success, and 

 the writer has been able to present a vivid and striking 

 record of their observations. The height of Mount St. 

 Elias was differently estimated by the old navigators, and 

 Mr. Seton Karr points out that it is the only mountain 

 the real height of which has exceeded the first estimates 

 made of it. The latest determination taken from Yakatat 

 and from the United States Coast Survey schooner 

 Yukon ^ gives 19,500 and possibly 20,000 feet. From its 

 massive shape the mountain does not convey the impres- 

 sion of being quite so high as this, although " its whole 

 altitude is presented to the eye, from its sharp summit 

 down to the ocean at its foot." Of the scenery of which 

 Mount St. EHas is the most prominent feature, Mr. 

 Seton Karr writes most enthusiastically. He even goes 

 so far as to say that " without a doubt the scenery at 

 Yakatat is the most wonderful of its kind in the \yhole 

 world." Seen early in the morning, when the air is re- 

 markably transparent, the mountains seem " too ethereal 

 to have any actual existence." The observer feels that 

 " they cannot be anything except some unholy illusic 

 that must dissolve and disperse when the sun rises." 



