NA TURE 



[January 9, 1902 



It is gratifying to find a writer on sociology actjuainted 

 with modern inatheniatical methods of statistics, and one 

 who clearly recognises the value of such methods, but the 

 definitions given in Chapter iii. of the introduction rec|uire 

 some rewording. The word " number " on p. 2 1 is appar- 

 ently used in the sense of "magnitude of the variable" 

 instead of in the more natural sense of " frequency," but 

 even in this sense it would not be correct to define the 

 median as "the number midway between the lowest and 

 highest"; it is correctly defined by the statement that 

 magnitudes greater and less than the median occur with 

 equal frequency, so that the median will not in general 

 coincide with the middle of the observed range. Again, 

 it is hardly correct to speak of a measure of variation as 

 the " mode of the deviation " ; mode is used in the 

 sense of " most frequent value," and the most frequent 

 deviations in the case of symmetrical distributions will be 

 those approximating to zero. The term " standard 

 deviation " was defined by Prof Pearson, its introducer, 

 in the sense of root-mean-square deviation, and it is apt 

 to lead to misunderstanding if used in a vague sense, 

 as in the text. The section on the " law of sympathy," 

 pp. 108-110, would also be the better for, at least, some 

 additional e.xplanation ; it is from its curtness almost 

 incomprehensible as it stands, and some of the symbols 

 used appear to be only defined in the appendix. 



The book is suggestive of many possible lines of 

 research by means of indirect statistical index-numbers, 

 but we cannot help feeling that the author has tried to 

 cover ground too wide for a single \olume. The work 

 as it stands is so abstract that it is almost impossible to 

 estimate the practical value of the author's ideas, and 

 such abstractness alienates the sympathy of the statis- 

 tician. A much more liberal discussion of examples in 

 the text would be both valuable and refreshing. 



C. U. V. 



Optical Lanterns and Accessories. Edited by Paul N. 

 Hasluck. Pp. 160. (London : Cassell and Co., Ltd., 

 1901.) 



This handbook forms one of a series of practical 

 manuals, and it brings together the more important and 

 useful information in relation to the construction and 

 management of optical lanterns. For the main part the 

 editor has utilised material which has been published 

 from time to time in the weekly journal Work, and has 

 coordinated it in such a form that it will be found very 

 serviceable to those who have much to do with lanterns. 

 There are also chapters on the making of ordinary 

 photographic, coloured and mechanical lantern slides, 

 and some useful hints regarding the management of 

 klnematographs. The book is well illustrated and should 

 be found very handy. 



Plane Geometrical Drawini^, including numerous Exer- 

 cises and Army Examination Papers, 7iiit/t Solutions. 

 By R. C. Fawdry, M.A. Pp. xi+185. (London ; E. 

 and F. N. Spon, Ltd., 1901.) Price 6.?. net. 

 This is a work of quite an elementary character, and 

 very well suited to candidates for admission to Woolwich 

 and Sandhurst. A good feature of the book is that it 

 either gives a proof for each construction or refers to 

 the particular proposition of Euclid on which the con- 

 struction is founded. In addition to constructions re- 

 lating to right lines, triangles, polygons and circles, there 

 is a short chapter on the ellipse, which, in a second 

 edition, might very well include a treatment of the 

 parabola, inasmuch as the parabola is at once one of the 

 simplest and the most useful of curves in the applications 

 of mathematics. There are two good chapters, on the 

 use and construction of scales, and the book concludes 

 with several specimens of papers set in the subject at the 

 Woolwich and Sandhurst examinations, together with 

 the solutions of the questions. 



NO. 1680, VOL. 65] 



LETTERS TO THE EDITOR. 



[ The Editor does not hold himself rcsponsilile for opinions ex- 

 pressed by his correspondents. Neither can he underlake. 

 to return, or to cot respond with the writers of, reiecie I 

 manuscripts intended for this or any other part of NatUKE, 

 No notice is taken of anonymous communicalions.'\ 



The "Chestnuts" of the Horse. 



These structures are well known and have been variously- 

 interpreted. But I believe that a suggestion as to their nature 

 which I shall now put forward has not yet been made. Some 

 months since I called attention in this Journal (vol. Ixii. p. S-i) 

 to the general prevalence among mammals that use their fore 

 limbs as grasping or climbing organs — in fact, in all other ways 

 excepting as mere organs of progression — of a tuft of long hairs 

 upon the wrist. I have since th.it time examined a large 

 number of mammals, and find these vibrissic in a considerable 

 number of genera belonging to the orders Marsupialia, 

 Kodentia, Carnivora, Lemuroidea (in which latter group the 

 vibri.ssa; in question were first noted by Mr. Bland Sutton). 

 They are absent from the Ungulata with the exception of 

 hyrax, an admittedly ancient type of ungulate. L'sually, but 

 not always, a stout branch of the radial nerve of short extent 

 ends in this patch of integument which bears the vibrissa;. 

 The vibrissa are quite similar to those found upon the head of 

 the same mammals, for example the " whiskers ' of the cat. 

 The general occurrence of this carpal tactile (?) organ makes it, 

 at least on a priori grounds, reasonable to suppose that traces 

 might be met with in the ungulates, other than hyrax, where 

 it unquestionably exists. There might not at first sight appear 

 to be much in common between the callous pad, such as is the 

 "chestnut" of the horses and a.sses, and this tuft of vibrissa; ; 

 but the conditions which I found to obtain in an armadillo 

 {/)as}pus iiillosus) suggested the comparison. In that animal 

 the carpal tuft of vibrissa; is present ; but insteiid of being a 

 closely compacted tuft of about six hairs, as is usually the case, 

 the hairs in the armadillo are not much larger than those of the 

 skin generally, and are spread over a patch of integument of 

 about half an inch in length and are more numerous. The 

 patch of skin which bears them is thickened. If this were to 

 proceed further the more strongly cornified epidermis would 

 cease to bear vibrissa;, which would be, so to speak, driven into 

 a corner beyond the specially thickened tract of skin. This 

 stage, moreover, is not hypothetical ; for in Leiiiiir catta pre- 

 cisely this state of affairs exists, i.e., a callous tract of skin close 

 lo which is a tuft of vibrissa;. If the latter were lost we should 

 have the "chestnut" of the horse. The chestnuts on the fore 

 feet, be it observed, occupy the right position, a little above the 

 wrist. Fkank E. Beddard. 



Frost Patterns. 

 As I was responsible for opening the discussion in these 

 columns in 1892 and as I am able to confirm Dr. Catherine 

 Raisin's observation as to the recent recurrence of the 

 phenomenon on December 15, I am glad of the present op- 

 portunity of .sending a few lines on the same subject in order to 

 rectify an omission. In 1873 Prof. Joseph Henry, of the 

 Smithsonian Institution, Washington, forwarded to Prof. 

 Tyndall on behalf of Prof Lockett, of the Louisiana State 

 University, a beautiful photograph of "plumes produced by 

 the crystaUisation of water," the said pattern having been 

 formed in the coloured sediment in the bottom of a basin in 

 which the water had frozen during the night. This photograph 

 is reproduced as a plate in Tyndall's "Lectures on Light" 

 (I have only the second edition, 1875). It escaped my notice 

 during the correspondence in 1892 or I should certainly have 

 called attention to it. R. Meldola. 



Roads and National Welfare. 



In Nature of December 19, 1901 (p. 149) is given a 

 criticism of a work, in which some essential points in the 

 making and maintenance of roads are strongly insisted on. 

 At p. 156 of the same number there appears an excellent 

 commentary on Mr. Balfour's speech to the students of the 

 Goldsmiths' Institute at New Cross on December 12. With 

 your comments I am in thorough sympathy, and would beg 

 leave to point out that the two subjects are far more closely 

 connected than might at first appear. lOxcellence and superiority 



