W SCIENCE PROGRESS 



" The Arabic original could not have been a direct translation from Euclid, and 

 probably was not even a direct adaptation of it ; it contains mistakes and un- 

 mathematical expressions, and, moreover, does not contain the propositions about 

 the division of a circle alluded to by Proclus. Hence it can hardly have contained 

 more than a fragment of Euclid's work" (p. 9). But in an Arabian manuscript 

 found by Woepcke at Paris, and translated by him into French and published in 

 1 85 1, we have apparently a translation of much of Euclid's work. " It is expressly 

 attributed to Euclid in the manuscript and corresponds to the description of it by 

 Proclus. Generally speaking, the divisions are divisions into figures of the same 

 kind as the original figures — e.g., of triangles into triangles ; but there are also 

 divisions into ' unlike ' figures — e.g., that of a triangle by a straight line parallel to 

 the base. The missing propositions about the division of a circle are also here : 

 ' to divide into two equal parts a given figure bounded by an arc of a circle and 

 two straight lines including a given angle,' and 'to draw in a given circle two 

 parallel straight lines cutting off a certain part of a circle.' Unfortunately the 

 proofs are given of only four propositions (including the two last mentioned) out of 

 thirty-six, because the Arabian translator found them too easy and omitted them " 

 (quotation from Woepcke on p. 9). It is on Woepcke's text and on a manuscript 

 in the Vatican Library, written by Leonardo Pisano in 1220 and named Practica 

 Geometric?, that Prof. Archibald's restoration of Euclid's work (pp. 30-77) is based. 

 As Prof. Archibald says (p. vii) : " A score of the propositions are more or less 

 familiar as isolated problems of modern English texts, and are also to be found in 

 many recent English, German, and French books and periodicals. But any 

 approximately accurate restoration of the work as a whole, in Euclidean manner, 

 can hardly fail to appeal to any one interested in elementary geometry or in Greek 

 mathematics of twenty-two centuries ago." Thus it is easy to see that this 

 restoration is of great value as a source of elementary geometrical problems. But 

 Prof. Archibald's work has a value far beyond this : in the introduction on the 

 various manuscripts which come into consideration (pp. 1-18), in the account of 

 writers prior to 1500 who have dealt with propositions of Euclid's work (pp. 19-28), 

 and in the selection from the very extensive bibliography of the subject since 1500 

 (pp. 78-85), Prof. Archibald has shown so much research, critical power, and 

 profound learning that his little book will take a permanent place in the literature 

 of the history of mathematics. 



Philip E. B. Jourdain. 



METEOROLOGY 



Atmospheric Circulation and .Radiation. A Meteorological Treatise on the 

 Circulation and Radiation in the Atmospheres of the Earth and of the Sun. 

 By Frank H. Bigelow, M.A., L.H.D. [Pp. xii + 432, with 78 figures.] 

 (New York : John Wiley & Sons, Inc. London : Chapman & Hall, Ltd., 

 1915. Price i\s. net.) 



Meteorology is a science in which an enormous mass of observations have 

 been collected, but in which little has been done in the direction of theoretical 

 discussion of the observations leading to definite results which could be of use in 

 what is essentially the final aim of meteorology— to understand the causes which 

 are operative in producing the circulation in the atmosphere and to apply the 

 information so gained to foretell the probable weather. So much is this the case 

 that a correspondent in Nature could comparatively recently assert, not without 

 some justification, that a mere rule-of-thumb mechanical " prediction " would be 

 at least as often correct as the official predictions. Prof. Bigelow, who from 



