May 13, 1920] 



NATURE 



321 



however, by the heavy crops in India and Argen- 

 tina. Australia considerably increased her wheat 

 area, as did also the United States and Canada ; 

 indeed, during the first year of the war the wheat 

 area of the world was extended by more than 

 18,000,000 acres. In the later years of the war the 

 difficulty was one of transport rather than of total 

 supply ; a great effort was therefore made after the 

 close of 1916 to increase food production in the 

 United Kingdom. The methods and results have 

 been discussed from time to time in these columns : 

 the general result was a steady increase in pro- 

 duction right up to 1918, the figures for the 

 United Kingdom being in thousands : — 



This high production was obtained at a time 

 when manures were scarce and implements difficult 

 to repair, and when most of the skilled men were 

 gone, their places being taken by old people, 

 women, and children. But these substitutes 

 worked with a will, and amply made up in en- 

 thusiasm what they lacked in skill. Even the 

 high production of 1918 was not the maximum 

 possible, and had the conditions persisted, even 

 higher results could have been obtained. 



The last section of the book deals with post- 

 war conditions. Serious fears had been enter- 

 tained as to the food supplies of the world ; 

 fortunately, these have not been realised, and 

 although food is undoubtedly scarce and will re- 

 main so there is no reason to fear famine, and 

 in the main the people of Europe, though still 

 suffering privation, are better fed than they were 

 in 1918. It is difficult to say what the position 

 is likely to be in the near future, but the redeem- 

 ing feature is the rapidity with which agriculture 

 has been restarted in the devastated areas of France 

 and Belgium, Of the 4,000,000 acres damaged 

 l)y the war, nearly a quarter were handed back 

 to the cultivators before a year had elapsed. 

 On the other hand, agriculturists in our own coun- 

 try are not producing so much as they did. The 

 withdrawal of the women from the land and their 

 replacement by men coincided with a considerable 

 fall in production, which is distinctly unfortunate. 

 A further fall is anticipated as a result of the 

 shortened hours of labour. 



Other countries, however, are in a worse pre- 

 NO. 2637, VOL. 105] 



dicament. Russia, formerly one of the chief 

 wheat-producing countries of the world, is unlikely 

 to have any exportable surplus, and the position 

 in Central Europe is still very obscure. Sir 

 Henry Rew is not greatly perturbed, but thinks 

 that if the social and political conditions of Europe 

 became settled, its food production would rise to 

 pre-war level in the course of two or three years. 

 He is also quite hopeful about the position in this 

 country. No student of British agriculture can 

 ever give up hope of the future, and Sir Henry 

 Rew is one of the leaders of the helpful band of 

 optimists. E. J. Russell. 



Differential Geometry. 



The Elementary Differential Geometry of Plane 

 Curves. By R. H. Fowler. (Cambridge Tracts 

 in Mathematics and Mathematical Physics. 

 No. 20.) Pp. vii-l-105. (Cambridge: At the 

 University Press, 1920.) Price 65. net. 



DIFFERENTIAL geometry is a fascinating 

 subject, because it gives us vivid and pic- 

 turesque embodiments of theorems obtained by 

 the combination of several branches of pure 

 analysis, such as algebra, function-theory, and the 

 infinitesimal calculus. It presents us with prob- 

 lems of all degrees of difficulty, from the compara- 

 tively simple theory of curvature and torsion to 

 the provokingly difficult question of geodesies. 



The present tract is just what its title indicates, 

 except that there are a few digressions on twisted 

 curves and on surfaces. The work has two con- 

 spicuous merits ; in applying the differential cal- 

 culus, the assumptions made are explicitly pointed 

 out, and proper attention is paid to the deter- 

 mination of sign. The latter point is particularly 

 important, not only because an error in sign is 

 the one most frequently committed in computation, 

 but also because, if a consistent determination of 

 sign is not strictly adhered to, the formulae of 

 analytical and even of pure geometry cease to 

 have general validity. Even now our text-books, 

 especially in analytical geometry, pay so little 

 attention to this matter that a university teacher 

 has to spend much valuable time on this topic with 

 intermediate students, and too frequently finds, to 

 his disgust, that even an honours student is not so 

 careful as he should be in the matter of sign. 



Mr. Fowler's chapters on tangents and normals, 

 curvature, contact and envelopes, leave little, if 

 anything, to be desired. The chapter on envelopes 

 is the most thorough-going, and suggests a couple 

 of remarks. The elimination of o from the equa- 

 tions f{x,y,a)z:^o,d/jda = o leads to a definite locus 



