﻿156 Notices respecting New Books. 



book : the sum total of the mathematics employed is contained in 

 the text of the two propositions of the third book of Euclid which 

 assert that if any line drawn through a point O meet a circle in P 

 and Q, the rectangle OP . OQ is constant, and that the sum of a 

 pair of opposite angles in a quadrilateral inscribable in a circle is 

 two right angles. 



Mr. Heaviside concludes his third chapter with a discussion of 

 a linear operator in general (p. 283), and the means of inverting 

 it, together with a deduction of Hamilton's cubic. The linear 

 operator is treated all through by Mr. Heaviside exactly as it 

 appears in the general theory of strain and stress — namely, as 

 consisting of coefficients expressing the relations between the three 

 components of one vector and those of another, these coefficients 

 being, in general, nine, as when the components of strain in a 

 solid are expressed in terms of direction ; but sometimes reducing 

 to six, as when components of stress are expressed in terms of 

 direction. 



Mr. Heaviside's mode of treatment will be found to be a valuable 

 side-light to the discussion of the linear vector function in Tait's 

 treatise. Of course, the rather high-sounding phrase " inversion of 

 a linear operator 5 ' denotes nothing more than the solution of 

 three homely simple equations ; nevertheless, there are some neat 

 relations involved. 



This review has already gone much beyond the usual limits, and, 

 in confining itself chiefly to controversial matters, has omitted to 

 notice the most valuable portion of Mr. Heaviside's work, the 

 greater part of which appears in the last chapter. This part of 

 the work has recently been treated, with great commendation, by 

 Professor Fitzgerald in * The Electrician.' All readers of this 

 volume will agree in regarding it as an able work, and, indeed, 

 one which is of immense assistance to advanced students in 

 Physics. 



One final instance of Mr. Heaviside's regard for accuracy and 

 desire for scientific completeness must be mentioned. It is found 

 in Art. 192, in which he justly objects to the equation by which 

 Maxwell expresses the relation between magnetic induction, 

 magnetic force, and magnetization at any point of a medium, viz., 

 B=H+ 47rl. To this Mr. Heaviside objects that it makes induc- 

 tion and magnetization identical in kind with magnetic force, which, 

 as he says, " is more than mischievous in theory." His own form 

 of the equation, B=/* (1 + &)F, where F is the magnetic force, is 

 in all respects much better. 



G. M. Mlnchin. 



