Notices respecting New Books, 391 



count of the chief properties of the Parabola, Ellipse, and Hyperbola 

 considered as distinct curves. Under the head of the Ellipse, how- 

 ever, the author has distinguished those properties vi^hich belong to 

 the Conies in common. He states that the work is the " result of 

 an attempt to reduce the chaos of Geometrical Conies to order," 

 and that he has " endeavoured to reconstruct it on a uniform plan, 

 taking as a standard, whereby to regulate the sequence of the proofs, 

 the principle that Chord properties should take precedence of Ta?i- 

 gent properties.''^ Accordingly each curve is discussed in two chap- 

 ters, the former treating of its chord properties, the latter of its tan- 

 gent properties. E. g. in the case of the parabola two simple proofs 

 are given of the proposition that the locus of the middle points of any 

 system of parallel chords is a straight line parallel to the axis ; and 

 that the bisecting line meets the directrix on the straight line through 

 the focus perpendicular to the chords. From this the relation QV^ 

 =4SP . PV is easily proved. Before passing to the tangent proper- 

 ties the author mentions, with brevity and clearness, several ways in 

 which a chord may be made to assume a position of taugency. One 

 marked peculiarity of the book is the detailed treatment of the rect- 

 angular hyperbola — a curve vi^hich stands to the hyperbola in the 

 same relation as the circle stands to the ellipse ; its numerous pro- 

 perties are deduced with great simplicity. The book, as a whole, is 

 not easy to describe : it consists, as all such books must consist, of 

 proofs of a number of well-known properties of the Conic Sections; 

 its merit lies in the arrangement of the propositions and the way in 

 which they are proved ; but this merit can hardly be duly appreciated 

 unless the book be compared page by page with one of the older 

 treatises on the same subject. It is designed for the use of rather a 

 high class of students, and will meet their wants admirably, both in 

 regard to the text and the numerous examples and exercises with 

 which it is furnished. 



The Laws of the Winds prevailing in Western Europe. — Part I. By 

 W. Clement Ley. London: E.Stanford. 1872. 

 In this work, which is an admirable companion to the Weather 

 Maps of the Meteorological Office, Mr. Ley has treated a subject of 

 no little difficulty and complexity with great clearness and perspicuity. 

 Those of our readers who daily consult the Weather Maps are doubt- 

 less familiar with the " baric depressions " which are every now and 

 then specified as travelling eastward. These meteorological pheno- 

 mena the author has specially examined, the data being the "daily 

 weather reports " from numerous stations in Western Europe, and 

 finds that they are associated invariably with extensive areas of pre- 

 cipitation of aqueous vapour, in the central portions of which ascend- 

 ing columns of air are induced, and to which an indraught is esta- 

 blished. This indraught by the rotation of the earth is so modified as 

 to produce circulatory currents or winds of a cyclonic character, 

 moving in a direction contrary to that of the hands of a watch. This 

 circulatory movement brings successively over a tract of country two 

 oppositely conditioned winds, the south-westerly in advance of the 

 baric minimum, or lowest barometer, laden with aqueous vapour from 



