12 SCIENCE PROGRESS 



the maximum distance between parallel tangent planes, and the 

 radius R of the smallest sphere which contains the body, viz*. : 



i 



d 



<R<\/ "^ d 



2{n + i) 



were given by Jung in 1901 ; H. Lebesgue {Liouville, 4, 

 1 92 1, 67-96) gives new proofs and also discusses " courbes orbi- 

 formes," or " curves of constant breadth." The existence of 

 such curves, other than the circle, was first noticed by Euler in 

 1778 in a memoir " de curvis triangularibus." They also arise 

 in connection with Buff on 's needle problem in the theory of 

 probability. An important result, of which Lebesgue gives a 

 proof, is that the curve of given constant breadth which has 

 the least area is that formed by three equal circular arcs de- 

 scribed with their centres at the vertices of an equilateral 

 triangle and with radius equal to a side of the triangle. (The 

 curve with maximum area is, of course, a circle.) 



G. Tiercy {Tohoku Math. Journal, 18, 1920, 90-115; 19, 

 192 1, 149-63) also deals with these curves and with the 

 corresponding " surfaces of constant breadth." The latter 

 are usually defined as convex surfaces for which every two 

 parallel tangent planes are at the same distance apart. K. 

 Reidemeister {Math. Z5.,10, 1921, 2 14- 16) shows that they may 

 equally be defined as surfaces of constant diameter, viz. such 

 that for each point Py of the surface there is at least one point P„ 

 of the body bounded by the surface, such that PP' ^ PPm =• d, 



where P' is any point of the body and a? is a constant. 



The same author also {Math. Ann., 83, 1921, 1 16-18) gives 

 a more elementary proof than that of Blaschke of a theorem 

 concerning the existence of double integral connected with 

 the area of a convex surface. 



J. Y^3\{Math. Ann., 83, 1921, 311-19) investigates the closed 

 convex curves which can be described by the ends of a straight 

 line of unit length moving in a plane, showing that the oval of 

 smallest area so obtainable is an equilateral triangle of unit 

 height. 



METEOROLOGY. By E. V. Newnham, B.Sc, Meteorological Office, 

 London. 



On the Dynamics of Wind {Q.J. Met. Soc, vol. xlviii. No. 201, 

 January 1922). In this valuable paper Dr. Jeffreys attempts 

 a classification of winds from purely dynamical considerations. 

 The practice as regards classification has usually been to select 

 those more obvious characteristics of a wind which strike a 

 casual observer. Thus, winds blowing from the sea to the land 

 during the hottest part of the day are " sea-breezes " ; " mon- 

 soon " winds, on the other hand, being seasonal phenomena, are 



