August 3, 1905] 



NA TURE 



329 



reptiles. Dr. Dickson, Dr. Mill and others are studying the 

 effects of changes of climate on sea organisms generally. 

 Agriculturists are more dependent on the weather than 

 any other class of persons. Were it possible to issue fore- 

 casts for a longer period in advance, farmers would be 

 much benefited. Captain Barker considers that the effect 

 of weather upon health has not received a fair amount of 

 scientific notice. While medical officers write voluminous 

 reports on the public health, many of them ignore the 

 meteorological conditions of the districts under review. 

 We think we are justified in claiming exception for the 

 reports of the various registrars-general, which contain 

 carefully prepared meteorological statistics. 



In the Rcndicoiiii of the Lombardy Academy, xx.Kviii., 

 2, Prof. Ernesto Pascal gives a classification of the 

 various forms of twisted sextic formed by the intersection 

 of a quadric and a cubic, with special reference to the 

 number of their real tritangent planes. 



We have received the third edition of Dr. Richard 

 Dedekind's pamphlet on " Stetigkeit und irrationale 

 Zahlen," which may now fairly claim a place among the 

 mathematical classics. It originated about the year 1858, 

 whe.n the author was charged with a course of lectures 

 on the calculus, and found no satisfactory treatment of 

 the continuity hypothesis in existence. On November 24, 

 1858, Dedekind discovered a definition of continuity which 

 he imparted to Dur^ge a few days later, and the present 

 pamphlet was written in 1S72 in commemoration of his 

 father's jubilee. 



In the Bulletin of the American Mathematical Society 

 for June, Dr. Edward Kasner directs attenlion to a 

 significant dialogue in Galileo's " Discorsi e dimostrazioni 

 mathemetiche " of 1638, in which modern concepts of 

 infinity as laid down by Bolzano, Cantor, and Dedekind 

 appear to have been foreseen by that philosopher. In 

 this dialogue Salviati points out to Simplicio that since 

 every number has a square there must be as many squares 

 as there are numbers, but, on the other hand, since there 

 are many numbers which are not squares there must be 

 more numbers than squares. In answer to Simplicio 's 

 question " What is to be our conclusion? " .Salviati gives 

 the following remarkable reply : — " I see no escape except 

 to say : the totality of numbers is infinite, the totality of 

 squares is infinite, the totality of roots is infinite ; the 

 multitude of squares is not less than the multitude of 

 numbers, neither is the one greater than the other ; and, 

 finally, the attributes of equal, greater and less are not 

 applicable to infinite but solely to finite quantities." 



Mr. J. J. Hicks, of Hatton Garden, has submitted a 

 two-toot rule designed by Mr. Scott which is worthy of 

 notice. When opened out like an ordinary carpenter's 

 rule one face shows inches and sixteenths along one edge 

 and millimetres along the other, while between them the 

 divisions are repeated in juxtaposition for the purpose of 

 more accurate comparison. It is the other face of the 

 rule, however, where the greater novelty is 'to be found. 

 Here there are four double comparison scales of English 

 and French measures of length, weight, capacity, and fluid 

 measure. Taking the first as an example of the system, 

 a length of about 10 inches shows comparison quantities 

 from I inch to 60 miles juxtaposed, but the divisions are 

 not equispaced, as in that case nothing much less than a 

 mile would be visible. They are therefore spaced 

 logarithmically, so that the first inch covers a space of 

 nearh' half an inch. This is divided into eighths, and each 

 NO. 1866, VOL. 72] 



of these by estimation could be read to tenths. The next 

 two inches occupy the same space, and so, of course, do 

 the next four, and so on. In a distance of ij inch or 

 38 millimetres, a reading is increased ten-fold. Of course 

 such comparison scales have the advantage of the ordinary 

 slide rule that at all parts of the scale readings are made 

 with the same proportional accuracy. For instance, on 

 the scale now referred to i inch is opposite 25 and a small 

 half-millimetre, 11^ yards is opposite loj metVes, 5 miles 

 is half the thickness of the. line beyond 8 kilometres, and 

 similarly 50 beyond 80. In short, the accuracy with which 

 any of these comparison scales may be read is the same 

 as that which would apply to a slide rule in which the 

 .\ line from i ... 100 was 3 inches long. For quick 

 and fairly accurate comparison of lengths, weights, cubic 

 and fluid measures, this face of the rule is most convenient. 



W'e have received several papers dealing with projects 

 (not performances) of artificial flight the general character 

 of which is sufficiently shown by the following brief 

 summaries : — .-Arnold Samuelson, in a lecture published at 

 Hamburg (London : E. and F. N. Spon), asserts that all 

 flying animals (insects and birds) have flat, not curved, 

 wing surfaces, that the normal air-pressure on a thin 

 supporting plane is independent of the angle of incidence 

 at which the plane moves forward, that the pressure on a 

 rectangular plane decreases uniformly from front to back, 

 giving a centre of pressure at one-third the distance from 

 the front to the back surface, and other conclusions equally 

 at variance with many generally accepted theories. Dr. 

 Federico Sacco, in a paper entitled " L'Aerovoie " (Turin: 

 P. Gerboni), proposes a captive balloon attached to a 

 small trolley running along a kind of elevated cable rail- 

 way as a cheap and rapid means of locomotion which 

 would be unaffected by such trifling terrestrial obstacles 

 as rivers, mountains and lakes ; in windy weather a 

 voyage on such an apparatus would doubtless be highly 

 thrilling. For the argument of cheapness Dr. Sacco is 

 responsible. M. Ren6 de Saussure, writing in the Revue 

 scientifique for May 27, describes the " h^licoptire 

 aeroplane" of MM. H. and A. Dufaux, which, roughly 

 speaking, consists of a pair of double-surface gliders placed 

 fore and aft, with two screw propellers arranged side by 

 side between them rather nearer to the front than to the 

 back gliders. Of this apparatus only small models have 

 been tried, and a large sized machine 8 metres long and 

 3 metres broad which has been constructed has not yet 

 been experimented on ; the authors, however, give full 

 details as to how to start the machine and to land safely. 

 The latter operation, as shown in the diagram accompany- 

 ing the article, bears a rather ominous resemblance to the 

 motion of a dynamically unstable glider previous to cap- 

 sising. We cannot close the list without referring to a 

 paper bv Mr. F. W. H. Hutchin;^on, read at Cambridge 

 and published in Knowledge and Scientific News for June, 

 describing experiments on models with bird-like wings, 

 which have already yielded some interesting results in the 

 study of natural flight. The wings in this case were not 

 assumed to be flat, but of the curved form, which the 

 author describes as the '" Hargreave curve." 



Messrs. Witherbv and Co. have issued the prospectus 

 of a book on " The Birds of Hampshire and the Isle of 

 Wight " which they have in preparation. The work is by 

 the Rev. J. E. Kelsall and P. W. Munn, and is claimed to 

 be the first complete history of the birds of Hampshire and 

 the Isle of Wight published. The work will contain a 

 large-scale coloured map, and be illustrated by reproduc- 

 tions of drawings and photographs. 



