2l8 



NATURE 



[July 9, 1903 



optics. There are few points in this book calling 

 for remark, except, perhaps, the very arbitrary limit- 

 ations of the subject-matter. Thus, chromatic aberra- 

 tion and dispersion, the "power" of a lens and its 

 measurement in dioptres, the use of lenses as spec- 

 tacles or magnifying glasses, and the optical system 

 of the eye itself, alike remain unmentioned. The 

 mathematical theory of thick lenses is discussed, 

 although the subject of lens combinations is neglected. 

 No experimental methods with regard to lenses are 

 described, and no problems tor solution by the student 

 are appended. 



In taking- up the study of light, students generally 

 commence with the laws of geometrical optics. 

 Further on in their studies they find that the instru- 

 ments used for even the simplest investigations com- 

 prise various combinations of lenses and mirrors, 

 which can be understood and appreciated only when 

 a competent knowledge of geometrical optics has been 

 acquired. In spite, however, of the manifest import- 

 ance of this branch of knowledge, it has in recent 

 years received scant attention from investigators, and 

 has shown few marks of progress. This is un- 

 doubtedly due in part to the fact that the subject of 

 geometrical optics affords a happy hunting-ground for 

 the mathematician, who may, or may not, have any- 

 thing more than a passing acquaintance with the prac- 

 tical side of the subject; while the attention of experi- 

 mental investigators has mostly been absorbed in 

 other directions. Let us consider, for instance, the 

 subject of lens combinations. Gauss showed that a 

 thick lens, or combination of lenses, possesses four 

 important points on the axis — the two principal points 

 and the two principal foci. If the distances of the 

 object and image are respectively measured from the 

 first and second principal points, then the formula for 

 the combination takes a form similar to that applic- 

 able to a single thin lens. In a sense, then, the work 

 of Gauss affords a complete method of solving any 

 problem connected with lenses ; it labours under the 

 disadvantage, however, that in most problems the 

 necessary analysis is of a somewhat clumsy character. 

 It has thus been left for Mr. Blakesley to introduce a 

 remarkable simplification, by measuring the distances 

 of the object and image, not from the first and second 

 principal points, but from the first and second principal 

 foci. The resulting equations in u and v, as well as 

 those relating to the magnification, now take forms 

 amenable to simple analytical treatment. The focal 

 length of a lens, or lens combination, is taken as a con- 

 stant of one dimension in space, not necessarily 

 measured from any particular point ; in this respect it 

 resembles the coefficient of self-induction of a coil. 



The advantage of this method is well illustrated by 

 the investigation on the combination of a lens and a 

 mirror, on pp. 67-71. It also readily adapts itself to 

 the needs of experimental investigations. A dis- 

 tinguishing feature of the book is the attention de- 

 voted to practical determinations of the constants of 

 lens systems ; those involving the use of a microscope 

 are particularly worthy of remark, though all are in- 

 teresting. It is to be regretted, however, that Mr. 

 Blakesley has preferred to speak of Gauss's principal 

 NO. 1758, VOL. 68] 



points as "the points i of the diagram "; a section 

 on the graphical construction of images, using Gauss's 

 principal planes, would also make many problems 

 clearer. In view of their practical importance, with 

 respect to the optical system of the eye. Listing's 

 nodal points also claim some mention. Chapter xi., 

 on forms of lenses for minimum deviation of rays, is 

 of great interest and practical importance. It is to 

 be feared, however, that the geometrical relations ot 

 circles, which are cursorily alluded to in the text as 

 " quite clear," may greatly puzzle many students whose 

 leaning is toward practical physics rather than toward 

 pure mathematics. Further, the theory of the achro- 

 matisation of an eye-piece (p. 1 10) could bear amplifica- 

 tion. Many students arrive at the conclusion that 

 Huyghens's eye-piece has advantages, with respect to 

 ordinary chromatic aberration, over a single thin lens 

 used as a magnifying glass — a conclusion which is 

 demonstrably erroneous. Mr. Blakesley gives data 

 from which a student, if sufficiently enthusiastic and 

 persevering, might arrive at the truth of this 

 matter; but a page or so devoteu to the question 

 would have enhanced the value of the book. It is 

 further to be regretted that a series of problems, to be 

 solved by the student, has not been appended; a loose 

 leaflet containing five such problems, issued as adver- 

 tising the scope of Mr. Blakesley's book, shows how 

 attractive work of this kind may be made. Finally, 

 however, it must be said that a more interesting and 

 stimulating book than that under consideration is 

 seldom likely to come in the way of the student. Mr. 

 Blakesley has, moreover, effected a notable advance in 

 geometrical optical theory. 



The stereoscope is probably mentioned, more or less 

 briefly, in most lecture courses on optics ; but it is 

 seldom realised that this instrument is something more 

 than a plaything or a scientific curiosity. Yet it is 

 undeniable that, in many branches of science, the 

 stereoscope could be used as a most valuable aid to 

 instruction. In commencing the study of analytical 

 geometry of three dimensions, for example, the chief 

 difficulty of a student is to realise the actual signi- 

 ficance of the more or less conventional diagrams 

 which he must use; there can be little doubt that, if 

 provided with proper diagrams to be viewed stereo- 

 scopically, he would avoid much profitless labour, and 

 gain, in the end, much clearer notions of the signi- 

 ficance of the processes employed. In practical solid 

 geometry, architecture, crystallography, &c., there are 

 other wide fields for the use of the stereoscope. Prof. 

 Manchot mentions a further novel use to which the 

 stereoscope can be put. If two bank notes are viewed 

 stereoscopically, slight differences, which could scarcely 

 be detected by the eye, will give the printing an 

 appearance of relief or depression, so that a false note 

 can easily be detected. 



That the stereoscope is not more largely used is 

 doubtless due to the fact that, in the forms ordinarily 

 met with, the pictures or diagrams are limited to too 

 small a size for the full benefit of the instrument to 

 be felt. Prof. Manchot has invented a stereoscope 

 which can be adapted to viewing diagrams of any 

 size whatever, and this instrument is fully described. 



