312 Notices respecting New Books. 



and this, with the distortionless relation, gives C=[t^ IV, or 



= J_ ; so that C is everywhere proportional to V, and has its value 

 ~Lv 



at once from (y). 



No more simple or beautiful treatment of such a problem is 

 possible, and many such will be found in this extremely valuable 

 volume of Mr. Heaviside's. (It may be noted that in line 6, 

 p. 299, "turning p to p + p" should be changed to " turning 

 p to j?— p.") The general case of a wave — i.e., the case in which 

 distortion exists as well as attenuation— is attacked in p. 316 ; aud, 

 by a simple and ingenious manipulation of the operator q in its 

 general form, the problem is deprived of almost all its difficulty. 

 This part of the subject is terminated with a full discussion of the 

 reflexion of waves at the ends of wires aud their absorption by 

 bridges, the experiments of Barton and Bryan being specially 

 noticed inasmuch as they did not succeed in completely verifying 

 the results which they expected from Heaviside's theory. 

 The author shows that, under the circumstances, complete extinc- 

 tion was not to be expected ; but he gives (p. 371) the value of 

 the resistance per unit area of a plane resisting sheet terminating 

 a circuit, for which complete absorption may be expected. Theu 

 follows the discussion of the reflexion of long waves by various 

 reflectors — condensers, inductance-coils, &c. 



The last chapter of the book is devoted to Generalised Differ- 

 entiation and Divergent Series, in which is expounded the general 

 theory of the operational work employed in the preceding part of 

 the volume, and a great deal more. The student who is interested 

 mainly in the physical questions treated by Mr. Heaviside need 

 not be frightened by this chapter, which covers much more than 

 is required for the physics of Electromagnetic Theory. 



Mr. Heaviside's work is, as has been already stated, of enormous 

 importance in the domain of Electricity and Magnetism. 

 He has to a great extent, in this volume and in its predecessors, 

 revolutionized the treatment of the subject and founded a special 

 school. This is a great achievement. But this acknowledgment 

 does not exhaust his public character. His writings are almost 

 as entertaining as those of Gulliver; while for rapidity in the 

 production of knowledge his Operational Method will compare 

 favourably with the wonderful machine in the Academy of Lagado. 

 We never know the moment when we may find ourselves im- 

 pulsively compelled to a burst of laughter by some remark which 

 turns up in the course of what is (to judge from a look at the page) 

 a mass of the driest, or the most sedate, mathematical investigation. 

 Of course this is all very improper and terribly unorthodox ; but, 

 nevertheless, it greatly facilitates perception ; and we suspect that 

 even the most dignified of us enjoy these bold departures from 

 propriety — unless we are wholly devoid of the sense of humour. 



G. M. M. 



