74 



NATURE 



[May 26, 1892 



edition dated 1891 might have included some of the 

 mathematics of hysteresis. 



Electrostatics is treated as fully as it should be, though 

 perhaps a single chapter on the law of the inverse square, 

 containing most of the theorems required in magnetism 

 and electricity, would have given a sounder view of the 

 mathematics involved. It was hardly to be expected 

 that a mathematician should avoid the temptation of de- 

 scribing Mossotti's theory of dielectrics-without a warning 

 that it can hardly be complete, and in consequence gives 

 the electrical displacement as 

 K-i 



instead of -^ times the electrical force, thus making 



the displacement zero in a vacuum, and justifying this by 

 saying that the results differ very little, while it would 

 really overturn the whole electro-magnetic theory of light. 

 This same overturning is calmly got over when the electro- 

 magnetic theory of light is considered further on by a 

 reference to this place, and this very remarkable state- 

 ment that K - I differs but little from K. There seems 

 to be some confusion, arising from the fact that in electro- 

 magnetic measure K is nearly lo^S but such a muddle is 

 inexcusable. He further on gives the theory of pene- 

 tration of electric force into conductors, without referring 

 back to an investigation he has previously given of the 

 concentration of alternating currents on the surface of a 

 wire, not appearing to appreciate that they are the same. 

 He also actually explains wave propagation in dielectrics 

 by induction from layer to layer because the inducing 

 force is very small initially at a distance. He has not 

 learnt the A B C of action by means of a medium, but 

 is still hampered by the dry bones of theories o f action at a 

 distance. In consequence of this, his investigation of the 

 magnetic action of electric currents is all bristling with 

 the action of elements upon one another, and little or 

 no attention given to the energy stored in the medium, or 

 how it goes from place to place. 



The chapter on solids begins with some rather doubtful 

 physical paragraphs that are out of place in a mathematical 

 work. Is it sound to call heat a force {Kraft) that holds 

 the particles of bodies asunder ? Is it sound to say that the 

 difference between solids and liquids is the difficulty of 

 separating the parts of the former, when it is known that 

 it often takes hundreds of pounds per square inch to 

 separate the parts of a liquid from one another, and when 

 it is the resistance of the material to shear that he really 

 uses as the characteristic of solids ? That mistake of 

 making the difficulty of separation and not the difficulty 

 of shearing the characteristic of solids seems quite 

 common : it occurs in many books. The mathematical 

 theory of elasticity is given in the usual analytical way^ 

 and applied to some of the simpler cases of bending, &c. 

 Periodic motion is then introduced, and the more im- 

 portant cases of wave motion and vibrations of solids con- 

 sidered. In the consideration of torsion he omits to give 

 any warning as to difficulties arising in the case of non- 

 cylindrical prisms. The chapter concludes with an 

 investigation of the impacts of solid spheres in a manner 

 that brings it into connection with the kinetic theory of 

 gases. 



The chapters on liquids and gases are fairly complete. 



NO. 1 1 78, VOL. 46] 



There is an interesting numerical calculation of the 

 height of a statical tide : this is an example of how com- 

 plete and varied are the physical questions of which the 

 mathematics is given by Herr von Lange. The ele- 

 mentary kinetic theory of gases is given, but without any 

 discussion of the distribution of velocities amongst the 

 molecules. Van der Waals's modification of the simple 

 gaseous laws is discussed, and along with it the theory of ^1 

 cubic equations is given in a rather skimpy form — an j 

 example of how difficult it is to teach the higher physical , . 

 mathematics in a way that applies to the particular case 

 in hand, except by teaching the part of the higher 

 mathematics involved from a wider point of view than the 

 particular solution requires. 



The chapter on light is hardly so full as such an im- 

 portant subject demands. Diffraction is run through, but 

 the absence of bands inside a shadow is not discussed, 

 and the theory of definition in telescopes is separated from 

 the same question in microscopes in a very unscientific 

 way. There is a lot of reflection theory, and a paragraph 

 on the direction of the vibration relative to the plane of 

 polarization ; but no notice is taken of the theory of the 

 blue sky, nor of the electro-magnetic method of determina- 

 tion, nor of Wiener's proof that it is the electric force 

 which acts on silver salts, and is consequently the one 

 probably effective in most chemical actions, and there- 

 fore in irritating the retina. It is possible, however 

 that iron salts may be acted on by the magnetic force. 



The last chapter is on conduction of heat and on the 

 mechanical theory of heat. The first part is an account 

 of the simpler parts of Fourier, as any book on conduction 

 of heat must be, and the latter is a good account of 

 thermodynamics. , It is to be regretted that he does not 

 give some mechanical illustrations of temperature, though 

 a discussion, of the nature of temperature would have 

 been out of place. The chapter concludes with a variety 

 of applications of thermodynamics to such questions as 

 the relations of electromotive force, compressibility, and 

 surface tension, to temperature, as well as the usual one, 

 vapour pressure. It is much easier to point out defects 

 than adequately to describe excellences. It must not 

 therefore be concluded from the fact that much of this 

 review is concerned with the former that the defects pre- 

 ponderate over the excellences of Herr von Lange's 

 work. On the contrary, the work is full of excellences. 

 The way in which physics and mathematics are tending 

 to grow each purer — one in the direction of mathe- 

 matical abstractions, complexes, matrices, and such like ; 

 the other in the direction of experimental methods, 

 accuracy, phenomena, and such like — makes it daily more 

 important for physical investigators especially to have by 

 them a convenient resume of those parts of mathematics 

 that are most often useful to them in their investigations,. 

 and this has been ably supplied by Herr von Lange. 



PHASES OF ANIMAL LIFE. 

 Phases of Animal Life, Past and Present. By R. 

 Lydekker, B.A. (Cantab.). (London : Longmans and 

 Co., 1892.) 



THE sixteen essays which make up the volume are 

 reprints, with a few alterations, of articles origin- 

 ally published in Knowledge. " They are intended," the 



