Notices respecting Nexo Books. 381 



tuning-fork curves ; taking equal angular steps, and then dropping 

 perpendiculars on the initial line to set off: the radii of the con- 

 centric circles. 



In a G-reekless age the Greek alphabet must not be left 

 undefined. And we lind no description of the Vernier or Nonius. 



The whole book is very elegant and stimulating, and carries 

 Perry's pioneering ideas to a high stage of development and pitch 

 of perfection. 



An Elementary Coarse of Infinitesimal Calculus. (Revised Edition.) 

 By Horace Lamb, Professor of Mathematics in the Victoria 

 University of Manchester. 

 Cambridge : at the University Press, 1919. 530 pp. 



The large page and clear spaced print will be much appreciated 

 by the reader, and the diagrams are frequent enough to give 

 reality to the argument. The author is happily not of the school 

 of Lagrange, in banishing appeal to the eye in a geometrical 

 figure. 



He does not get to work in the Differential Calculus, as under- 

 stood formerly, till Chapter II. A preliminary Chapter I seems 

 written in fear of the school of Rigour, and explains at length the 

 modern abstractions of continuity, sequence, convergency, dis- 

 continuity, and the limit, before the beginner has had occasion to 

 form any concept of their meaning. " Man must act first, before 

 proceeding to discuss the rationale of his activities." 



An experienced old-fashioned instructor is likely to recommend 

 a skip of this chapter on to Chapter II, reserving the consi- 

 deration of the abstruse ideas of Chapter I till the need has 

 arisen in the mind of the learner. It is well not to raise a 

 difficulty in the mind of the beginner, until it has found a place 

 in his own thought. 



The differential coefficient defined in Chapter II is given a 

 geometrical interpretation ; but the author does well to introduce 

 immediately another illustration, as the expression of a velocity ; 

 this will appeal to most minds more powerfully as a physical 

 realization. 



The author takes a very cautious, but useful, line of treatment 

 in Chapter III of the Exponential Theorem and Function, and 

 its inverse, the logarithm : and here again he goes in fear of 

 attack from young Rigour, but entrenches himself very skilfully ; 

 making a start from the Differential Equation which defines the 

 function. 



Applications follow in Chapter IV of the functions employed 

 in the course of the treatise, algebraical, circular, exponential, 

 logarithmic, hyperholic, direct and inverse. 



Successive differentiation is treated in Chapter V, with its 

 geometrical application to curvature, so that Integration is not 

 reached till Chapter Vf. 



