February 15, 1900] 



NATURE 



;65 



which have been suggested, and which are here quoted, 

 for determining the radius of the star image, or deriving 

 the photographic magnitude, were admittedly only con- 

 venient methods of interpolation, and any attempt to 

 show that such formuUc possess a physical basis is of 

 doubtful policy, and will hardly be everywhere accepted ; 

 but the practical value of the chapter is high, and gains 

 immensely from the fact that the author incorporates 

 much of the results of his own original investigations. 



In the history of photography we come naturally upon 

 more popular ground. We have an instructive, and on 

 the whole complete, picture of the achievements of photo- 

 graphy applied to the heavens. The section treats each 

 object, such as the moon, the sun, &c., separately, the 

 history of each being treated independently of the others. 

 The later results obtained from recent eclipse expeditions 

 are of course wanting, and possibly a little too much 

 space is given to the Transit of Venus. The photo- 

 graphic reproductions that illustrate this section are 

 excellent, and make a handsome addition to a very 

 valuable treatise. A bibliography accompanies the work, 

 which already needs extension, so frequent are the con- 

 tributions to this attractive development of astronomy. 



OUR BOOK SHELF. 



Euclid's Elements of Geometry. By Charles Smith and 

 Sophie Bryant. Pp. vi + 127. (London: Macmillan 

 and Co., Ltd., 1899.) 

 This book deals only with Euclid's Books IIL and IV. 

 Although the original order of the propositions has been 

 maintained, there are many divergences as regards the 

 treatment of his methods. In the modern teaching of 

 Euclid's propositions the student is not so restricted as 

 to particular methods of solution as long as the method 

 he employs is accurate. The learning of propositions 

 by heart is, we hope, a relic of the past, and the com- 

 pilers of this work encourage the ingenuity of the student. 

 In Book III. the method of superposition is used with 

 advantage. In addition to numerous exercises, the 

 appendix contains many interesting and important 

 theorems and problems. As a school course this edition 

 should be found useful. 



A First Book in Statics and Dynamics. By Rev. J. R. 



Robinson. Pp. viii + 98. (Longmans, Green and Co., 



1899.) 

 This book is intended only for beginners, and specially 

 for those who are preparing for the matriculation in the 

 University of London and for the elementary stage of 

 South Kensington examination. For this reason only 

 a limited knowledge of Euclid, algebra and trigonometry 

 is assumed in the treatment of the subject, and the text 

 is accompanied by numerous representative examples. 

 The author's large experience in teaching the subject has 

 enabled him to place clearly before his readers portions 

 which are usually stumbling-blocks for the beginner, and 

 the numerous clearly-printed diagrams add greatly to 

 the explanations in the text. 

 Life and Happiness. By Auguste Marrot. Pp. 90. 



(London : Kegan Paul, Trench, Triibner and Co., 



Ltd. Paris : Libraire Fischbacher.) 

 Happiness is too much a matter of temperament for the 

 perusal of these chatty little essays on the laws of health, 

 the development of the mind, and similar subjects, to 

 very much affect the reader's share of this desirable 

 possession. But there can be very little doubt that the 

 observance of some of the rules for the preservation of 

 health here laid down will do a great deal in removing 

 definite causes of physical discomfort— and in this way 

 unhappiness may, at least, be diminished. 



NO. 1581, VOL. 61] 



LETTERS TO THE EDITOR. 



{The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of, rejected 

 manuscripts intended for this or any other part of Naturh. 

 No notice is taken of anonymous communications.] 



On the Carriers in the Kathode Rays. 



In a former communication to these columns of Nature 

 (January 19, 1899), I showed that an upper limit for the density 

 of the matter composing the kathode rays can be deduced 

 from the fact that a shaft of rays emitted from a plane kathode 

 retains its cylindrical form. The result arrived at was that the 

 density must be small compared with lo^*' grams per cubic 

 centimetre. In a subsequent note (P^ebruary 16), I called atten- 

 tion to some results of E. Riecke, which seemed to indicate a 

 value as low as io~-'" grams per cubic centimetre. 



The researches of Prof. J. J. Thomson have now put us in 

 possession of information as to the mass of the individual carriers. 

 Using the value which he has given (Phit. Mag. December 1809) 

 for the mass of a " corpuscle " in connection with the above 

 estimate of the density of the stream, we can obtain a limiting 

 value for the number of corpuscles per cubic centimetre. I find 

 that this leads to a number very much smaller than that indi- 

 cated by the kinetic theory for the average number of molecules 

 per cubic centimetre in the vacuum tube. 



We have, in round numbers, 2 x io~^ for the charge on a 

 corpuscle in electromagnetic units, and 6 x lo" for the ratio of 

 charge to mass, giving ^ x lo"'"'^*' grams for the mass. If then, 

 the density is small compared with io~>-^ grams per cubic centi- 

 metre, the number per cubic centimetre must be small compared 

 with 3 X 10". In Meyer's " Kinetic Theory of Gases " (English 

 translation, p. 333) the number of molecules present in a cubic 

 centimetre of gas at atmospheric pressure is given as 60 x 10^^, so 

 that in the vacuum tube the number would be of the order of lo^*. 

 Thus the carriers in the kathode stream are very sparsely 

 scattered as compared with this average. 



Another point which may be worth mentioning arises in con- 

 nection with Prof. Thomson's suggestion, that the mass of the 

 corpuscle may be of electrical origin. He shows {loc. cit., 

 p. 563) that, in order to account for the effective mass in this 

 way, the radius of the corpuscle, supposed spherical, would 

 require to be of order 10 '•' centimetre. The various lines of 

 argument employed to arrive at an estimate of the size of a 

 molecule, or of the "molecular sphere," agree in making its 

 dimensions comparable with 10 " centimetre. In order that a 

 molecule of this size should be built up of, say, two atoms, each 

 consisting of a complex of even a thousand corpuscles of radius 

 io~*-^ centimetre, these ultimate elements of a molecular struc- 

 ture would require to be very widely spaced in proportion to 

 their dimensions. W. B. Morton. 



(,)ueen's College, Belfast, February 6. 



Drunkenness and the Weather. 



Nature, in its issue for November 16 (1899), did me the 

 honour of devoting considerable space to a modest publication 

 of mine, "Conduct and the Weather," a fact to which I feel 

 free to allude, since the reviewer found so little to praise. One 

 remark of his, however, was suggestive to one " bound hand and 

 foot by the demon of statistics." In commenting upon the 

 indicated excesses of arrests for assault and battery during the 

 hot summer months he says, " In our own ignorance we were 

 rather tempted to attribute these lapses of good conduct to too 

 free indulgence in alcoholic beverages in the hot weather."' 

 Here was a cue worth following out. The data were available, 

 why not use them ? 



'i'he plan followed was the same that found so little merit in 

 the eyes of the jocular reviewer, hut even at the risk of tempting 

 him to again couch his lance, I shall outline it somewhat in 

 detail. The general plan is that of comparing the normal 

 daily prevalence of any abnormality of conduct with its preva- 

 lence under definite weather conditions. It necessitates a daily 

 record of the crime to be studied, and some daily record of the 

 weather conditions. 



In the study of drunkenness, the data were taken from the 

 records of the New York City Police Force. From them were 

 copied the exact number of arrests for that crime for each one 

 of the 1095 days of the three years 1893-94-95 ; 44,495 in all 

 (males). The necessary meteorological data were obtained at 



