REVIEWS 153 



This is the latest volume in " Bell's Mathematical Series for Schools and Colleges," 

 and in it " no attempt whatever has been made to base the subject on the modern 

 concept of Number and the Continuum " (p. v) Surely nobody would doubt the 

 wisdom of the authors on this point. Again : " It is assumed that the student has 

 drawn a considerable number of graphs dealing with statistical data, physical 

 phenomena, etc., and that he has a clear-cut notion of what these curves are like 

 as they present themselves in practical work" (p. v). First comes an historical 

 introduction in which the most novel part is the abundant credit given to Isaac 

 Barrow in the history of the development of the infinitesimal calculus : of course 

 this innovation is based on the striking results of the research of Mr. J. M. Child. 

 The whole book is extremely simply written and forms a very easily grasped 

 introduction to the calculus— though one might wish that the authors had not let 

 the task of history cease with the provision of a few pages of biography. The 

 principal features are the extensive use made of graphs on squared paper and the 

 treatment of differential coefficients as rates of gradients (pp. I, 10, 17). It is 

 to be noted that " differential equations " are spoken of (p. 78) even when they are 

 of the form that leads only to the problems of the ordinary " integral calculus.'' It 

 would, perhaps, have been advantageous from a student's point of view if the 

 character of the book were even more geometrical than it is : the example of 

 Barrow's work must have shown the authors how a systematic calculus might be 

 written starting from the treatment of the problems of tangents and areas and then 

 unfolding the discovery — which is the real gist of the whole matter — that these 

 are inverse problems. On pp. 55-6 there is a rather unsatisfactory treatment of 

 curvature: the formula is given, but it is remarked that its deduction " requires too 

 hard mathematics for the present stage of the student." The book concludes with 

 useful applications of the calculus to centres of gravity, moments of inertia, and 

 centres of pressures ; miscellaneous examples ; and an index. 



Philip E. B. Jourdain. 



ASTRONOMY 



The Binary Stars, By Robert Grant Aitken, Astronomer in the Lick 

 Observatory. [Pp. xii + 316, with 5 plates and 12 figures]. (New York : 

 Douglas C. McMurtrie, 1918. Price $3.15 net.) 



This volume forms one of a series of Semi-centennial Publications issued by 

 the University of California. The fact that it is written by one of the foremost of 

 living double-star observers is a guarantee that the practical point of view has 

 been kept throughout in the forefront and the volume will therefore be of special 

 use to the practical double-star observer. It should also prove of great value in 

 the astronomical library as a reference volume on questions connected with 

 double stars. For this purpose the volume has not been spoilt, as so frequently 

 happens, by insufficient indexing. The indexes are very thorough, and give 

 references not only to names and subjects, but also to the star systems to which 

 reference is made in the text. 



In the first two chapters the author gives an historical sketch of double-star 

 observation, in which reference is made to all the important early literature. 

 Chapter III deals with methods of observation, and includes a description of the 

 double-star micrometer. Sections on the resolving power of a telescope, eye- 

 pieces, diaphragms, etc. are included. The whole of this chapter should be care- 

 fully studied by the embryo observer, as it is full of practical hints. Even the 

 veteran may pick up some useful hints. Chapter IV deals with methods of 



