NA TURE 



405 



THURSDAY, AUGUST 28, 1884 



THE "ENCYCLOPEDIA BR1TANNICA" 



The Encyclopedia Britannica. Ninth Edition. Vol. 



XVII. Mot-Orm. (Edinburgh : A. and C. Black, 



'THE present volume of the "Britannica" contains 

 an unusual number of articles of moderate length 

 but of great importance. Among them are numerous 

 articles of scientific interest, and of these we note especially 

 the following : — 



The article Optics, by Lord Rayleigh, is so good that 

 it is to be regretted that considerations of space had 

 to be attended to. The subject is one which has hitherto 

 been presented in a form somewhat repulsive to the 

 student ; and the writer, who has contrived to make even 

 Primary and Secondary Focal Lines attractive as well as 

 interesting, deserves high credit. The general subject of 

 Geometrical Optics had already been sketched in the 

 article Light, so that the present article deals, almost ex- 

 clusively, with the second (and sometimes higher) approxi- 

 mations. But Lord Rayleigh has not confined himself to 

 the postulates of that science ; he has freely availed 

 himself of the principles of the wave-theory, whenever 

 they were required to simplify a demonstration or to 

 explain a result. And he intersperses, here and there, 

 hints as to the easier methods of exhibiting and testing 

 the results of theory, hints which will be of great advan- 

 tage to the student. 



Commencing with the theorem that a set of rays, 

 originally perpendicular to a surface, can, after any 

 number of reflections and ordinary refractions, be cut 

 orthogonally by another surface, the author develops 

 generally the properties of Caustics and Focal Lines. 

 He then proceeds to apply these properties to prisms, 

 mirrors, and lenses. The practical adjustment of the 

 collimating and observing telescopes for spectroscopic 

 work, and the accurate measurement of refractive indices 

 are described. Here we have some interesting remarks on 

 the reasons for employing the position of minimum devia- 

 tion in the observation of spectral lines. Next we have 

 the formation of a pure spectrum, specially for the purpose 

 of securing a visual field uniformly illuminated with 

 homogeneous light. This leads to a general sketch of the 

 methods and results of von Helmholtz and Clerk-Maxwell 

 with regard to compound colours. Then we have a dis- 

 cussion of Spherical and Chromatic Aberration, with 

 some brief but highly practical remarks on the construc- 

 tion of achromatic and aplanatic lenses for different pur- 

 poses. Stokes' important results as to the secondary 

 spectrum are here given with some detail ; and the 

 methods of Foucault and Toppler for detecting slight 

 defects of figure, or slight irregularities of refractive index, 

 are explained. Next come the important questions of the 

 brightness of an image, and the resolving power of an 

 optical instrument. The limits to resolving power, with 

 the important difference, in this respect, between the 

 telescope and the microscope, are well, but only too 

 briefly, given : — and we have also a short re'sume' of the 

 author's own important discussion of the same question 

 Vol. xxx. — No. 774 



for spectroscopes and gratings. We conclude with the 

 remark, which has been forced on us at almost every 

 paragraph, that while brevity is often a most desirable 

 virtue, it is one whose exercise should be permitted only 

 to those (no doubt the majority) who have nothing to say. 

 Lord Rayleigh would do a great service to science if, 

 taking the present essay as a skeleton, he would develop 

 it into a handy volume. 



Prof. Cayley handles the subject of Numbers, from the 

 mathematician's point of view, in two compact articles. 

 That on the Partition of Numbers, which is little more 

 than explanatory of the term, we pass over. That 

 on the Theory of Numbers is a very carefully written 

 account of the past condition and present position 

 of a subject, " which, originating with Euclid, has in 

 modern times, in the hands of Legendre, Gauss, Lejeune- 

 Dirichlet, Kummer, Kronecker, and others [we may inter- 

 polate the names of Cayley, Sylvester, and Henry Smith], 

 been developed into a most extensive and interesting 

 branch of mathematics." The branch is well known to 

 be one of limited interest, for does not De Morgan write 

 that the subject is an isolated part of mathematics, which 

 may be taken up or not at the choice of the student ? 

 "It may possibly at some future time be connected with 

 ordinary analysis ; that is to say, the determination of the 

 integer solutions of a set of equations may not be so dis- 

 tinct a thing from that of a mere solution, integer or not, 

 as it is at present." The author distinguishes between 

 the ordinary (or simplex) theory and the various complex 

 theories. " In any theory, ordinary or complex, we have a 

 first part, which has been termed the theory of congruences ; 

 a second part, the theory of homogeneous forms ; and a 

 third part, comprising those miscellaneous investigations 

 which do not come properly under either of the foregoing 

 heads." The details are too technical for these columns, 

 but the resume" of results is drawn up in a manner likely 

 to be most useful to a student, as it clearly indicates the 

 present condition of matters, being brought down to the 

 very latest date by a master who has done good work in 

 this very direction. There are a few typographical inac- 

 curacies ; besides we note the following trifling (we think) 

 oversights : — In Article 15 it is said : " If p is not a prime 

 number, then 1, 2, 3 . . . (p - 1) = o (mod./)," — surely 

 it should be added, "except when p = 4"; in Art. 16, 

 line 13, last bracket, for x - 3 read x - 4 ; in Art. 19, 

 lines 9, 10, interchange 11 and 17; in Art. 20, line 15, 

 should not 13 and 35 be relegated to the next line ? The 

 whole article is so carefully printed that we have thought 

 it not out of place to point out these oversights. 



Capt. Moriarty's reputation as a practical navigator has 

 given an unusual interest to the article on Navigation, in 

 which he may have been expected to impart to others the 

 trick of his own skill. We must confess to a certain 

 amount of disappointment. The essay is well enough, 

 but it is not what we expected ; not what, we still think, 

 we had a right to expect. It is in fact little more than a 

 short elementary treatise on the subject, comprising some 

 of the simpler and more familiar problems, but taking 

 little note of the more exact or more convenient methods 

 which are often required, not perhaps for the daily deter- 

 mination of a ship's position at sea, but for the checking 



