NA TURE 



[Ju/y 3 i, 1884 



study of natural history, and of mountains in the field ; 

 (5) by excursions to the plantations and mountains." 



With regard to the status of forest officers in different 

 parts of Europe they are described as taking rank with 

 military men and other Government officers of recognised 

 social position, and having in many instances an official 

 uniform and a higher salary than is accorded to military 

 officers, by way of compensation for the monotonous life 

 they are called upon to lead in the forests, which often 

 has a depressing influence — " day after day, month after 

 month — trees, trees, trees everywhere, trees and shade, 

 trees and shade — shade that reminds one of the expression 

 ' the valley of the shadow of death! " 



" Forestry in Norway " is a book of a different character 

 from the preceding. It treats of the general features of 

 the country in its various aspects, with especial regard of 

 course to its arboreal vegetation, and the effects of tem- 

 perature, rainfall, rivers, lakes, mountains, valleys, &c. 

 The book is for the most part very pleasant reading. 



In Chapter IV., under the head of Geographical Dis- 

 tribution of Trees in Norway, Dr. Brown shows that he 

 has made himself acquainted with the modern literature 

 of the subject, especially with the well-known report and 

 maps prepared by Dr. F. C. Schubeler, Professor of 

 Botany in the University of Christiania. From this and 

 from the numerous other works cited the conclusion is 

 drawn that the true forests of Norway are composed 

 almost entirely of the Norway spruce fir {Picea excelsa, 

 Link.) and the Scotch fir (Pinus sylvestris, L.), though 

 some other trees, as the elder, beech, and oak, are found 

 forming little woods. We must here point out that nearly 

 the whole of this chapter requires careful editing. There 

 is no excuse for the retention of old and exploded names, 

 still less perhaps for absolute mistakes. On p. 39, for 

 instance, it is stated that the Norway spruce is generally 

 known as Abies communis, a name under which very few 

 indeed would know it except those well versed in the 

 synonymy of the plant. On the same page Millaw is 

 printed for Miller, Lank for Link ; and a page or two 

 further on, the Norwegian birch is referred to Betula 

 odorata, Bechet, when it should be B. alba, L. Again 

 on p. 45 we are told that two species of oak "are found 

 growing wild in Norway, the sessile-fruited oak, Quercus 

 robur. W., and the common oak, Q. pedunculata, \Y." 

 The fact is that the sessile-fruited oak is Q. scssiliftora, 

 Sm., and the pedunculated oak, Q. pedunculata, Ehr. 

 both of which are now placed by most modem authorities 

 under the one name of Quercus robur, L. Similar instances 

 occur further on, as well as misspellings, all of which could 

 be easily rectified, and the book made more trustworthy. 



The general readable nature of the bulk of the book 

 will no doubt cause it to be read by those into whose 

 hands it may fall, whether they are specially interested in 

 forestry or not, and will thus form one means of pro- 

 moting the extended use of the volume. 



LENSES 

 Lenses and Systems of Lenses. By Chas. Pendlebury> 

 M.A., F.R.A.S., Senior Mathematical Master of St. 

 Paul's. (Cambridge: Deighton, Bell, and Co., 1884.) 



WE are glad to welcome at last an English book 

 on this subject, on which up to the present but 

 little has been written in our language. An abstract of 



Gauss's paper in Taylor's Scientific Memoirs, and a paper 

 by Maxwell in the second volume of the Quarterly Jour- 

 nal of Mathematics form, so far as we are aware, the 

 main English literature of the subject. Of course since 

 the time of Gauss foreign writers have used it freely : 

 Listing, Helmholtz, and Carl Neumann in Germany, 

 Verdet and others in France, have introduced it with 

 more or less modification into their works. We would 

 suggest that a list of books and memoirs on the subject 

 would forma valuable addition to Mr. Pendlebury's book. 

 The author gives frequent references in footnotes to books 

 or papers from which he has drawn information, but a 

 complete list would be a great help to others studying the 

 subject. The method itself is very elegant and attractive, 

 though somewhat barren of results ; perhaps this is the 

 reason why it has been neglected in England. It enables 

 us to obtain a beautiful solution of the problem to a first 

 approximation when all the rays make but small angles 

 with the axis, but refuses to help us further. 



The book before us is clear and well written, though 

 perhaps unnecessarily long. Mr. Pendlebury has three 

 chapters successively on refraction at a single surface, at 

 two surfaces, and at any number of surfaces. This would 

 be very well for a student who was supposed to begin 

 the study of optics with this book, but such a student is 

 hardly likely to exist ; and one who has read the ordinary 

 text-books on the subject could easily follow at once the 

 reasoning of the most complicated case, and might be 

 left to deduce the others so far as they differ from it as 

 corollaries. 



Referring, however, to some points in the book, we 

 think that in Fig. 4 it would have been better to take as 

 the standard case one in which the points x and x' both 

 lie to the same side of a, the case usually considered in 

 text-books on optics. This would have obviated the 

 necessity of having to put a negative sign to the symbol u 

 in the algebraical work. Attention also might with 

 advantage be called to the point that one of the two focal 

 distances is negative. 



Again, a difficulty occurs when we compare the results 

 of Sections 67 and 74 ; in the one we have 



1 _ 1 _ 1 



v u ~y 



while, using the same notation, the results of the other 

 may be written 



V u J 



The explanation, of course, is that Fig. iS, from which 

 the last result is deduced, is not drawn for the standard 

 case of a lens forming a virtual image of an object. 

 There is another small point of arrangement which it 

 seems to us might be slightly modified with advantage ; 

 we would draw a rather more definite line between the 

 analytical and geometrical methods of treating the subject. 



If we assume that a pencil of rays diverging from a point 

 will, after refraction, pass through a point, we can prove 

 geometrically the existence of the principal points, the 

 focal points, and the nodal points. We cannot, however, 

 without analysis, find the position of these points in terms 

 of the curvatures and distances between the various re- 

 fracting surfaces. 



Again, if we assume the position of the focal and. 



