May 17, 1900] 



NATURE 



51 



•completely satisfied, the work may fairly be regarded as 

 the mature expression of his deliberate thought on the 

 subject. 



The book opens with a preface by Helmholtz, followed 

 by the author's preface ; then there is an introduction, 

 and the author's theory is formulated in two books : — 

 Book i. : Geometry and kinematics of material systems ; 

 Book ii. : Mechanics of material systems. Helmholtz's 

 preface contains an account, which might be called an 

 appreciation, of the scientific work of Hertz, and is further 

 remarkable for the statement that, while Kelvin, Maxwell 

 and Hertz appear to have derived fuller satisfaction from 

 €xplanations of physical facts founded on some simple 

 }»eneral conception, such as Hertz's " straightest path," 

 he, for his part, had felt safer in adhering to the repre- 

 sentation of physical facts and laws by systems of 

 differential equations. In his own preface the author 

 tells us that his object was " to fill up the existing gaps, 

 and to give a complete and definite presentation of the 

 laws of mechanics which shall be consistent with the 

 state of our present knowledge, being neither too re- 

 stricted nor too extensive in relation to the scope of this 

 knowledge " ; and that what he hoped was new in his 

 work was " the arrangement and collocation of the whole 

 —the logical or philosophical aspect of the matter." 



In the introduction the author criticises the received 

 theory of dynamics and the more modern doctrine of 

 energetics, and proceeds to explain the character of the 

 new theory which he proposes. The novelty consists in 

 this : whereas the other two theories started from four 

 fundamental concepts— space, time, mass and force, or 

 energy — he requires only three — space, time and mass — 

 and the hypothesis of concealed masses. In Book i. 

 relations concerning spaces and times are considered, and 

 we have a generalisation of ordinary kinematics, including 

 definitions of the path and velocity of a material system, 

 and its shortest and straightest paths. By a material 

 system is meant what in the ordinary presentation of 

 dynamics would be called a system of particles with in- 

 variable connections. Some of the definitions referred 

 to contain arbitrary elements, but they are, at any rate, 

 simple. The definition of mass might have been omitted 

 with advantage. In Book ii. the author enunciates his 

 "fundamental law"— that every free system moves in a 

 straightest path. This law may be looked upon as an 

 interpretation of the principle of least action for systems 

 of which all the energy is kinetic, or as an extension of 

 Gauss's principle of least constraint. He proceeds to 

 show how the motions of systems which are not free can 

 be brought under the fundamental law by means of the 

 hypothesis of concealed masses — the visible system is 

 regarded as linked on to another system by invariable 

 connections — and it is proved that the equations of 

 motion of the system contain terms which correspond to 

 the " forces " of ordinary dynamics. It is, perhaps, not 

 remarkable that the dynamics of distant gravitating 

 bodies, which was the immediate object of the received 

 theory, should offer special difficulties from the present 

 point of view (§ 469) ; on the other hand, it is claimed 

 that the new minimum principle is applicable to invariable 

 connections of the type of pure rolling, in which the 

 velocities are connected by non-integrable equations, and 

 that it thus includes more phenomena than the principle 

 NO. 1594, VOL, 62] 



of least action. A considerable portion of Book u. is 

 taken up with the consideration of cyclical systems. 

 Hertz has here developed important conceptions due to 

 Helmholtz. Throughout both books the " older synthetic 

 method," that of a chain of propositions, has been adopted 

 in order that the logical purity of the theory might be 

 beyond dispute. 



Whatever may be the influence exerted on the progress 

 of mechanics by Hertz's kinematical generalisations and 

 fundamental law, there cannot be any doubt of the value 

 of his criticisms of existing dynamical theories. He has 

 explained, in the clearest manner, the object of physical 

 theories, and stated the conditions which such theories 

 must satisfy. He has tested the received theory of 

 dynamics — that which is associated with the names of 

 Galilei, Newton, d'Alembert and Lagrange — in respect of 

 logical permissibility, and in respect of appropriateness 

 as an expression of facts. Concerning this representation 

 of physical experience, he asks : " Is it perfectly distinct ? 

 Does it contain all the characteristics which our present 

 knowledge enables us to distinguish in natural motions ?" 

 And his answer is "a decided — No." He has put his 

 finger on the weakest part of the theory — the relation of 

 the notion of internal stress to that of equal and opposite 

 distance-actions. He makes the supposition that the 

 theory can, even here, be rendered rigorous, and prefers 

 to base his attack on the complexity of the various actions 

 which the theory needs to assume. In a somewhat 

 similar spirit he discusses the representation of physical 

 facts by means of the theory of energy, although it is 

 rather the logical permissibility than the appropriateness 

 of this representation that is called in question. 



The translators have done their work well on the 

 whole. Here and there they have been too literal, or not 

 literal enough ; they have left some obvious misprints in 

 the German text, and some in the translation, un- 

 corrected ; but these are slight blemishes, and we must 

 be grateful to them for a rendering which admirably 

 conveys the spirit of the original. Their translation 

 should serve to make more widely known a book which 

 certainly ought to be read by all who wish to have clear 

 ideas concerning the most fundamental of the physical 

 subjects. A. E. H. L. 



ASSYRIAN AND BABYLONIAN ASTROLOGY, 

 The Reports of the Magicians and Astrologers of 



Nineveh and Babylon. By R. C. Thompson. Vol. i. 



Pp. xviii -I- 85 plates of cuneiform text. Vol. ii. 



Pp. xci -H 148. (London : Luzac and Co., 1900.) 



IT is now about thirty-five years ago since the late 

 Edward Hincks, whose name will be honourably 

 coupled with the history of cuneiform decipherment, 

 astonished many folk by declaring that he had discovered 

 in the British Museum tablets which related to the 

 pseudo science of astrological astronomy. And it is not 

 surprising that such a declaration evoked general interest, 

 because reasonable grounds existed for hoping that when 

 the texts on the tablets had been deciphered, some trust- 

 worthy information about Chaldean astronomy might be 

 forthcoming. The labours of Hincks were followed by 

 those of Lenormant and Oppert, but they had little 



