402 



NATURE 



[November 25, 1920 



observed that Archimedes does not give a so- 

 called "statical proof" of any purely geometrical 

 theorem ; this would be contrary to Greek ideas 

 of mathematical propriety. But the theorem 

 having suggested Itself as probable from me- 

 chanical (or other) considerations, strict methods 

 were applied to test it — such, for instance, as the 

 process of "exhaustion." In connection with this 

 exhaustion method it is properly pointed out that 

 the Greeks virtually laid the foundations of the 

 integral calculus, much in the same way as Apol- 

 lonius, in his "Conies," virtually anticipates the 

 results of modern analytical geometry. 



Scattered about the book there are numerous 

 references to Greek discoveries and speculations 

 which are not so well known as they ought to be. 

 Thus Archimedes determined the angular diameter 

 of the sun to a comparatively close degree of 

 accuracy (p. 47) ; Aristarchus of Samos enunciated 

 the Copernican hypothesis (p. 46) ; and, of course, 

 all mathematicians of the time assumed the earth 

 to be a sphere, and had a very fair idea of its 

 dimensions. 



The book is well printed and attractive in ap- 

 pearance ; it is adorned by a frontispiece which 

 is a reduced facsimile of that in Torelli's edition 

 of Archimedes' works. The original is a good 

 example of eighteenth-century copper-plate — 

 amusing in one respect, because, although the 

 landscape is put into proper perspective, two 

 mathematical diagrams supposed to be drawn on 

 the sand are drawn in their proper shape in the 

 plane of the paper. The process reproduction 

 appears to be very satisfactory, considering the 

 amount of reduction involved. G. B. M. 



Australian Meteorology. 



Australian Meteorology : A Text-hook, includitig 

 Sections on Aviation and Climatology. By Dr. 

 Griffith Taylor. Pp. xi-f3i2. (Oxford : At the 

 Clarendon Press, 1920.) Price 125. 6d. net. 



THIS text-book of meteorology is written for 

 readers in the southern hemisphere, where, 

 as the author truly points out, European and 

 American text-books are to some extent inap- 

 plicable by reason of the' fundamental difference 

 in the wind circulation around centres of high 

 and low pressure in the two hemispheres. The 

 examples introduced for purposes of illustration 

 in the present work are mainly drawn from Aus- 

 tralian conditions, though the author's wide know- 

 ledge of world climatology is also freely used. 

 The 300 or so pages of the book are divided into 

 twenty-six chapters, which cover the practical 

 NO. 2665, VOL. 106] 



work at observing stations, as well as the more 

 theoretical aspects of dynamical meteorology and 

 climatology. The author has achieved his object 

 in producing a work which will give the reader 

 of fair intelligence, but without advanced know- 

 ledge of mathematics or physics, a good general 

 grounding in the subject. In this connection the 

 pages devoted to pressure gradient and Ferrel's 

 law may be particularly commended. One or two 

 parts are less satisfactory, and in particular the 

 reviewer suggests that in a future edition the 

 chapter devoted to upper-air research might be re- 

 cast, giving less space to the methods employed, 

 and more to the very important results which 

 have been obtained during the past few years in 

 this field. At the same time, a little more atten- 

 tion might be devoted throughout the book to 

 defining the technical terms used, and to explain- 

 ing in more detail a few of the less obvious types 

 of diagram, which do not at first glance convey 

 much meaning to the unaccustomed reader. 



In chap, xviii. a novel theory is put forward 

 to account for the origin of the tropical lows 

 which form over Australia and drift away to the 

 south-eastward. The theory postulates that domes 

 of warm ascending air are formed over the hottest 

 inland regions in summer, and that the upper 

 north-westerly current, striking these fixed domes, 

 forms gigantic eddies which pass away to the 

 south-eastward, being marked at the surface by a 

 low-pressure centre and often by falls of rain. Any 

 theory of the formation of depressions will be re- 

 ceived with interest. The one here put forward 

 is certainly not lacking in originality. It is sur- 

 prising to learn that the words "backing" and t 

 "veering" are used in Australia in the sense of 

 turning against and with the sun respectively in- 

 stead of with the meanings counter-clockwise and 

 clockwise as recommended by the International 

 Meteorological Committee in 1905. In a modern 

 text-book of meteorology one misses any refer- 

 ence to G. I. Taylor's eddy conductivity. In deal- 

 ing with the diurnal change of wind at the surface 

 and in the lower layers the simple convection 

 theory of Espy is referred to, but no reference is 

 made to the more complete explanation put for- 

 ward by G. I. Taylor, in which the observed facts 

 are well accounted for on the reasonable assump- 

 tion of a diurnal variation of "K." 



In his preface the author offers a half apology 

 for the roughness of the diagrams with which the 

 book is illustrated, but this seems scarcely neces- 

 sary, as the numerous figures form one of its most 

 valuable features, being mainly of small size, and 

 yet showing just the details required to illustrate 

 the point under discussion. J. S. D. 



