310 Notices respecting New Boohs. 



Period to the present time there have elapsed 414 x 10 8 years, while 

 the theologians, we believe, allow us some 6 x 10 3 years from the 

 very beginning of the Earth's existence. 



The next two chapters constitute nearly the whole of the 

 volume. The first of them deals with the diffusion of electric 

 displacement, and is largely occupied with the electrodynamics of 

 cables. The reader is struck with the power and succinctness of 

 the operational method of integrating the various differential 

 equations and Mr. Heaviside's complete mastery over the process. 

 It will, however, take the ordinary student of Physics a very 

 considerable time to grasp the logic of this method and to satisiy 

 himself of its validity. Such operations, for example, as 



,tf\* t£\~*, &c.,are treated with as much freedom and as little 



courtesy as if they were mere arithmetical magnitudes ; but the 

 key to a large portion of the subject consists in the understanding 

 of the equation 



ph = {nt)~i, 



which is deduced by a kind of empirical method at the beginning 

 of the volume, and runs throughout almost the whole of the sub- 

 sequent work, a further help towards the understanding of it 

 being given in p. 288, when the author begins his treatment of 

 Electromagnetic Waves. Here, again, we are introduced to a 

 novel kind of generalised differentiation — in such an expression, 



for example, as ( — I — and this requires some conventionalities 



as regards factorials. Thus, we have to understand | — \ as 

 meaning v$r. 



A great merit of the operational method consists in the concise 

 form in which it presents the solutions of differential equations. 

 As a comparatively simple example may be cited the problem of 

 determining the potential and the current strength at any point 

 of a cable, at any time, when the origin of the cable is subject to 

 an alternating voltage of the form e sin r nt, and the four constants, 

 K, S, R, L, of leakage, permittance, resistance, and inductance 

 are all concerned. The equation to be solved for V, the potential 

 at any point of the cable, is 



dx~ 



where ^^(Rr+Lp^K-l-Sp)*, p being, as usual, -r. The 

 solution is simply 



V=e-?*V , (/3) 



V being e sin nt. To make this solution readily comprehen- 

 sible — i.e., to " algebrise"' it, as Mr. Heaviside says — we observe that 



