Notices respecting New Books. 323 



" pilot " balloons, i. e. carried no instruments, and served solely 

 to give information as to the direction and velocity of the wind 

 at different levels. The balloons were observed sometimes with 

 two theodolites, at the ends of a measured base, sometimes 

 with one theodolite only. In the latter event the rate of rise of 

 the balloon must be supposed known. Usually it seems to have 

 been assumed to be uniform. The balloon was recovered in some 

 30 per cent, of the cases, after travelling in several instances over 

 150 kilometres. Pp. 109-141 consist entirely of diagrams, showing 

 the results obtained for the direction and velocity of the wind in 

 selected cases, with the corresponding distribution of wind and 

 barometric pressure at ground level over Western Europe. In 

 addition there are 47 illustrations in the text. Theoretical 

 questions are somewhat lightly dealt with, but there is a good deal 

 in the book likely to interest meteorologists and aeronauts. 



Monographs on Topics of Modern Mathematics, relevant to the 

 Elementary Field. Edited by J. W. A. Young. Longmans, 

 Green & Co. : New York & London, 1911. 



Professor Young's aim in the preparation of this series of mono- 

 graphs is to bring within reach of secondary teachers and college 

 students " a scientific treatment of some of the regions of advanced 

 mathematics which have points of contact with the elementary 

 field." There are nine monographs in all, each contributed by a 

 different writer. Oswald Yeblin writes on the foundations of 

 Geometry, Holgate on Modern Pure Geometry, and F. S. Woods 

 on non-Euclidian Geometry. Then we have the fundamental 

 propositions of Algebra treated by Huntington, and the algebraic 

 equation by G. A. Miller. G. A. Bliss follows with a discussion 

 of the Function Concept and the fundamental notions of the 

 Calculus ; and Young himself contributes a memoir on the Theory 

 of Numbers. L. E. Dickson discusses Constructions with Ruler 

 and Compasses ; Eegular Polygons ; and the book closes with the 

 History and Transcendence of x by Davad Eugene Smith. The 

 authors are all men of repute in the mathematical world ; and 

 their conjoint work has undoubtedly fulfilled the object aimed at. 

 It does not require a large acquirement of mathematical knowledge 

 for an intelligent reader to benefit by the perusal of its pages. 

 Yet he will not find it altogether easy reading. Many of the 

 processes and proofs have not yet found their way into the 

 recognized textbooks the aims of which are practical rather than 

 logical. It is important, however, that teachers of mathematics 

 should have some knowledge of the logical foundations of the 

 science they teach ; and a better introduction could not be put 

 into their hands than this series of tracts, which, though written 

 by different authors, form a remarkably united sequence. 



