November 26, 1908] 



NATURE 



97 



conciseness it assumes a mathematical training which 

 many of them have never had, and which is much 

 more difficult to acquire even than a knowledge of 

 continued fractions. In some measure, no doubt, it is 

 they who are at fault, and certainly they are the 

 losers. 



Such criticism is, obviously, to some extent beside 

 the mark. But it recurs inevitably with the appear- 

 ance of each fresh Cambridge text-book on geometrical 

 optics. \n excellent book; but if only the author 

 had written something which would more obviously 

 advance the practice of optics and the manufacture 

 of optical instruments ! 



To our mind, the most interesting part of this ad- 

 mirable little tract is contained in sections ix. and x. 

 Section ix. gives a simple and concise explanation of 

 the occurrence and physical importance of von Seidel's 

 five third-order aberrations, very palatable and nutri- 

 tious for the mathematician ! .And in section x. is 

 to be found an up-to-date abstract of the elementary 

 theorv of the characteristic function, which will be 

 helpful to manv. The contents of the tract will have 

 been sufficiently indicated if we add that the titles 

 of sections vii. and viii. are respectively " Entrance 

 and Exit Pupils " and " Chromatic Defects of the 

 Image." 



In conclusion, we venture to assert that Mr. 

 Leathern 's exposition of the Gauss theory will be 

 adopted as the most serviceable by every optician who 

 takes the trouble to become familiar with this book, 

 and we would add that he will find his trouble well 

 repaid. 



Hints for Crystal Drau'i)ig. Bv Margaret Reeks. 

 With a preface by Dr. John W. Evans. Pp. xx-l- 

 148; with 5 figures and 44 plates. (London : Long- 

 mans, Green and Co., 1908.) Price 3.S. 6d. net. 

 The importance of accurate drawings of crystals in 

 any crystallographical discussion was recognised by 

 Hauy, the father of crystallography, but the prin- 

 ciples upon which such drawings should be made 

 were not clearly explained until the publication by 

 Haidinger of his well-known paper among the 

 memoirs of the \\"ernerian Societv many years later. 

 It is essential that edges which are parallel on the 

 crystal should be represented by parallel lines on the 

 drawing, a condition which entails the supposition 

 that the eye views the crystal from an infinite distance. 

 Consequently, in such a special case as a skeletal 

 cube in which the edges are drawn of equal thick- 

 ness, the eye would be puzzled as to which is the 

 front, and the cube would appear constantly to be 

 turning inside out; but, as a rule, no such ambiguity 

 would arise. It is also important that the directions 

 of the edges in the drawing should be determined 

 with mathematical precision, even when the crystal 

 is shown in perspective. 



In this book Miss Reeks presents Naumann's modi- 

 fication of Haidinger's method. She explains how 

 the projection of the fundamental axial svstem may 

 be found graphically in the six different systems, and 

 discusses many examples, all of which are illustrated 

 bv full working details. It might have been made 

 clearer on p. 7 that the particular rotations employed 

 to give the customarv perspective were adopted, not 

 haphazardly, but because the tangents of the angles 

 have the simple ratios given. The student who care- 

 fully reads this book cannot fail to master the prin- 

 ciples of the method with which it deals ; the author's 

 exposition is lucid, and the illustrations, which have 

 been reproduced from her own drawings, are admir- 

 able. It may, however, be questioned whether in 

 most cases it be not quicker and easier to draw a 



XO. 2039, VOL. 79] 



crystal from a stereographic or a gnomon ic projec- 

 tion by the method devised by Goldschmidt, which 

 was fully explained to English readers by Penfield 

 in one of his illuminating papers. 



House-painting, Glazing, Paper-hanging, and \Vliite~ 

 washing. A Book for the Householder. By A. H. 

 Sabin. Pp. v-l-121. (New York: John \\'iley 

 and Sons; London : Chapman and Hall, Ltd., 1908.) 

 Price 4^. 6d. net. 

 Mr. Sabin may be known to some readers of Nature 

 as the author of a pleasantly discursive volume on 

 the technology of paint and varnish. In the present 

 little work he expounds one branch of that tech- 

 nology for the benefit of householders. He describes 

 simply and plainly how to use various preservative 

 coatings in the protection and embellishment of 

 ordinary dwelling-houses. 



There is no chemistry in the book, but a chemist 

 tells of the materials to use — of the white lead, tur- 

 pentine, oil, driers, putty, varnish, and whitewash — as 

 also of the points to note and the pitfalls to avoid in 

 applying the preparations. \\"hether many house- 

 holders will benefit is perhaps doubtful. Possibly, in 

 .'\merica, where isolated homesteads are more frequent, 

 the householder may be more often than in this 

 country tempted to do his own painting and paper- 

 ing. Here it would rarely seem worth while. There 

 is a proverb about spoiling a horn and not making 

 a spoon, and probably the unskilled user of paint, 

 paper, and varnish would generally do well to get his 

 work done better by a trained craftsman. Even so. 

 however, there is no harm in knowing what are the 

 best materials, how to get the most durable results, 

 and the general why and wherefore of the matter. 

 For anyone who contemplates either trying his own 

 skill or overlooking the proceedings of a workman, 

 Mr. Sabin 's book appears, as he claims in the pre- 

 face, to " set forth fairlv safe and sound practice." 



C. S. 



Mountain Panoramas from the Pamirs and Kucn 

 Lun. Photographed and annotated by Dr. M. 

 Aurel Stein. Pp. 36. (London : Royal Geo- 

 graphical Society, 1908.) 

 When Dr. Stein visited Central Asia in 1900-1, to 

 explore the ruined cities of Chinese Turkestan, he 

 included in his equipment a phototheodolite, with 

 which a number of panoramas were taken. These 

 not only served as a basis for the production of a map, 

 but gave an excellent idea of the character of the 

 country passed through. The Royal Geographical 

 Society has now published a selection from them 

 which will prove of interest to both geographers and 

 geologists. A feature common to a large number of 

 the photographs is the manner in which they illus- 

 trate the progressive desiccation of the region lying 

 north of the Himalayas; the sharp crested ridges, 

 separating deeply-cut valleys, produced by the action 

 of rain and rivers, are seen to be gradually merging 

 into rounded contours under a growing mantle of 

 wind-borne loess. We may also direct attention to 

 the remarkably perfect specimens of embankment 

 moraines in the Ab-i-Panja valley, where glaciers, 

 now vanished, have advanced into the main valley 

 over embankments of the debris which they have car- 

 ried along with them. 



Thomas Linacre. Bv Dr. William Osier. F.R.S. 

 Pp. vi-l-64. (Cambridge : The L'niversity Press, 

 1908.) Price 2S. 6d. net. 

 This little volume is the text of the Linacre lecture 

 for 1908, the first under tlie nev.- regulations. Prof. 

 Osier begins by recapitulating the few facts 



