Notices respecting New Boohs. 613 



rotational strain. Then a charged surface, or the surface of 

 an electron, might be considered as a surface at which there 

 is given normal discontinuity in (X, Y, Z) ; such a surface 

 in motion is also the seat of a first order discontinuity in 

 (?? *7> ?)? the tangential discontinuities in the electric and 

 magnetic forces being given by equations (22) in the case of 

 compatibility in the first order. Thus if a charged surface 

 S' be suddenly given a velocity v, sl first-order discontinuity 

 will arise at S' and will be propagated outwards as a wave- 

 front S moving with normal velocity c and leaving behind it 

 the steady state corresponding to S' moving with uniform 

 velocity v. 



LXVIIL Notices respecting New Books. 



Mathematische Einfulirung in die Elelctroneniheorie. Von Dr. A. H. 

 BtCHEEEE. Teubner : Leipzig, 1904. 



fTTtllS is an able presentation of the modern electron doctrine as 

 -*- developed by Lorentz, J. J. Thomson, Heaviside, and others. 

 The modifications which the assumption of tbis theory make on 

 Maxwell's equations are clearly stated ; and the various interesting 

 problems associated with the motion of charged particles, spheres, 

 and ellipsoids are discussed in considerable detail. The Zeeman 

 effect, the aberration of light, and the electromagnetic theory of 

 dispersion form the concluding sections. The general mathe- 

 matical theorems are given in the particular modification of the 

 Quaternion vector analysis which is familiar to readers of 

 Heaviside's important papers ; and an appendix summarizes the 

 meanings of the formulae and symbols used. Any one familiar 

 with quaternions will have no difficulty in understanding the 

 notation, although he will never cease from wondering why vector 

 analysts like Dr. Biicherer should be content with such a 

 comparatively weak imitation of Hamilton's powerful calculus. 

 The author gives five theorems connecting volume, surface, and 

 line integrals, and connects each with the name (presumably) of 

 its discoverer. Gauss and Stokes very properly get their due ; 

 but if other theorems of fundamentally the same character as 

 these are to be named after later investigators, it is simple justice 

 to give the name of him who first published them. Theorems (25) 

 and (26) ascribed to Foppl and B (Biicherer ?) were given long 

 ago by Tait ; and all the five are special cases of a fundamental 

 theorem first given in its most complete form by McAulay. 

 This historic inaccuracy springs of course from the culpable 

 neglect of quaternions at the hands of certain modern vector 

 analysts, who have wasted time and energy in rediscovering truths 

 thirty, forty, and even fifty years old. 



