September 30, 1897] 



NATURE 



515 



representations, and is an interesting example of the 

 manner in which the theory of electricity and magnetism 

 is treated on the continent. 



It is assumed that electric phenomena are due to 

 motion of some sort going on in every volume element 

 of the ether, and the displacement produced by this 

 motion is represented by a vector called the " tonic 

 i vector." Quadratic functions of the time differentials 

 r of the components of this vector are then assumed for 

 the kinetic energy and the rate of conversion of electrical 

 energy into heat, while the potential of the forces which 

 resist the tonic motion is assumed to be a quadratic 

 function of the curls of the same vector. The applica- 

 ■ tion of Hamilton's principle at once gives the equations 

 j of motion of the ether, and these, by a slight modifi- 

 cation, become identical with Maxwell's equations. This 

 modification is described by the author as a change in 

 the system of units, but it is really a change in the 

 system of quantities discussed. 



In nearly all works on electricity this subject of units 

 is treated in such a way that it presents a serious 

 stumbling-block to the student. He is, for instance, 

 almost led by the phraseology to suppose that quantities 

 of electricity in the electrostatic and electromagnetic 

 systems are quantities of precisely the same nature, just 

 as are a pound and a gramme of water, for example ; but 

 that, being regarded from different points of view, they 

 have somehow different dimensions in terms of the funda- 

 mental units ; and not infrequently, by an exercise of 

 faith rather than of reason, he believes this. A quantity 

 of water may be measured either by its mass or by its 

 volume, and, loosely speaking, either result is the measure 

 of the quantity of water. But, speaking accurately, we 

 cannot measure the quantity of water ; we can measure 

 certain properties of that quantity, of which one is the 

 mass and another and different property is the volume. 

 In a precisely similar manner electricity measured by the 

 electrostatic system is one property of the electricity, 

 and electricity measured by the electromagnetic system 

 is another property ; either may be arbitrarily defined as 

 the quantity of the electricity, but it is inconsistent and 

 misleading to describe both properties by the same 

 name. 



The concrete representation suggested as an inter- 

 pretation of the Maxwellian equations is modelled on 

 the theory of von Helmholtz, and is characterised by 

 three main features. The first of these is the familiar 

 t conception of two incompressible fluids, the positive and 

 negative real electricities ; in a dielectric the real elec- 

 tricity is supposed to be bound, so that it cannot move 

 out of the volume element in which it exists ; but in a 

 conducting medium it is capable of moving, and does so 

 with a velocity proportional to the force acting on it. It 

 is then found that, in the electrostatic state, the force 

 acting on the real electricity is such as would be due to 

 a certain distribution throughout space of a substance 

 which repels the real electricity according to the law 

 of the inverse square. An arbitrary multiple of the 

 density of this supposed substance is defined as the 

 density of the free electricity, and this constitutes the 

 second main feature of the concrete representation. 

 To bring about some simple relation between these 

 two sorts of electricity the third main feature is 

 NO. 1457. VOL. 56] 



introduced, namely the conception of electric polar- 

 isation ; it is supposed that the real electricity within 

 any volume element is capable of moving in such 

 a way under the influence of electromotive force that 

 positive electricity appears at one end of the element 

 and negative at the other ; thus there arises a density 

 of electricity due to electric polarisation, and the defini- 

 tions are such that at any point the density of the free 

 I electricity proves to be equal to the sum of the densities 

 i of the real electricity and of that due to polarisation. 

 j Round these three conceptions are gathered several 

 I subsidiary definitions and suppositions, the mathematical 

 I reasoning being intricate and detailed ; the whole con- 

 ] stitutes a scheme of considerable complexity, of which 

 indeed it is difficult to form a clear conception ; as a 

 physical theory, it would of course be extremely un- 

 natural, but as a mere illustrative analogy it is instructive. 

 After considering Maxwell's equations of action at a 

 distance. Dr. Curry shows by what assumptions and 

 what modifications of the concrete representation we 

 may pass from them to von Helmholtz's scheme ; and 

 i he then considers the independent derivation of the 

 i latter from empirical laws. 



j There is an interesting chapter on the theory of the 

 Hertzian oscillations, founded on Hertz's own memoir, 

 but with the analysis given in greater detail. Other 

 chapters deal with cyclic motions and illustrative 

 mechanisms, with longitudinal ether oscillations, and 

 with the theory of electric and magnetic striction. 



The work is, on the whole, characterised by a clear 

 style, though several serious difficulties are ignored, and 

 some of the main features in the reasoning are not 

 emphasised as their importance deserves. Thus in the 

 transition from Maxwell's to von Helmholtz's equations 

 the reader is left in considerable doubt as to whether 

 certain of the suggested modifications are purely arbitrary 

 assumptions corresponding to radical changes in the 

 i concrete representation, or merely a presenting of the 

 old differential equations in a slightly altered form. 

 There are also some serious errors which greatly dis- 

 figure the book, though fortunately they do not invalidate 

 the leading argument. Thus on page 33 we are offered 

 two different schemes of the dimensions of the quantities 

 of the electrostatic system in terms of the fundamental 

 units, a result due to a confusion of angular momentum 

 with density of angular momentum. The kinematics on 

 page 10 are faulty ; and on page 23 we find the dissi- 

 pation function spoken of as an energy function, and 

 actually treated as such in the application of Hamilton's 

 principle. J. G. L. 



OUR BOOK SHELF. 



Reform of Chemical and Physical Calculations. By C. 



J. T. Hanssen, C.E. Pp. xvi -H 72. (London : E. and 



F. N. Spon, Ltd., 1897.) 



The book deals specially with calculations of specific 



and latent heat, and heat of combustion of various 



substances. In the preface the author states that all his 



deductions are based upon the natural laws of atomic 



combination, heating, expansion and compression of 



aeriform substances, upon a few of the best substantiated 



experiments, and upon the fact, discovered by the author, 



j that, near the 41' of latitude, the specific gravity of 



