September 6, 1900] 



NATURE 



453 



alions relating to more or less isolated groups. The list of great 

 names, including Kelvin, Maxwell, Helmholtz, that have been 

 Associated with the employment of the principle for the elucida- 

 tion of the relations of deep-seate 1 dynamical phenomena 

 is a strong guarantee that we shall do well by making the most 

 of this clue. 



Are we then justified in treating the material molecule, so far 

 as revealed by the spectroscope, as a dynamical system coming 

 under this specification ? Its intrinsic energy is certainly per- 

 manent and not subject to dissipation ; otherwise the molecule 

 would gradually fade out of existence. The extreme precision 

 and regularity of detail in the spectrum shows that the vibrations 

 which produce it are exactly synchronous, whatever be their 

 amplitude, ami in so far resemble the vibrations of small 

 amplitude in material systems. As all indications point to the 

 molecule being a system in a state of intrinsic motion, like a 

 vortex ring, or a stellar system in astronomy, we must consider 

 these radiating vibrations to take place around a steady state of 

 motion which does not itself radiate, not around a state of rest. 

 Now not the least of the advantages possessed by the Action 

 principle, as a foundation for theoretical physics, is the fact that 

 its statement cm be adapted to systems involving in their con- 

 stitution permanent steady motions of this kind, in such a way 

 that only the variable motions superposed on them come into 

 consideration. The possibilities as regards physical correlation 

 of thus introducing permanent motional states as well as per- 

 manent structure into the constitution of our dynamical systems 

 have long been emphasised by Lord Kelvin ; ^ the effective 

 adaptation of abstract dynamics to such systems was made 

 independently by Kelvin and Routh about 1877 ; the more 

 recent exposition of the theory by Helmholtz has directed general 

 attention to what is undoubtedly the most significant extension 

 of dynamical analysis which has taken place since the time of 

 Lagrange. 



Returning to the molecules, it is now verified that the Action 

 principle forms a valid foundation throughout electrodynamics 

 and optics ; the introduction of the Kther into the system has 

 not affected its application. It is therefore a reasonable hypo- 

 thesis that the principle forms an allowable foundation for the 

 dynamical analysis of the radiant vibrations in the system 

 formed by a single molecule and surrounding tether ; and the 

 knowledge which is now accumulating, both of the orderly 

 grouping of the lines of the spectrum and of the modifications 

 impressed on these lines by a magnetic field or by the density 

 of the matter immediately surrounding the vibrating molecule, 

 can hardly fail to be fruitful for the dynamical analysis of its 

 constitution. But let it be repeated that this analysis would be 

 complete when a formula for the dynamical energy of the mole- 

 cule is obtained, and would go no deeper. Starting from our 

 definitely limited definition of the nature of a dynamical system, 

 the problem is merely to correlate the observed relations of 

 the periods of vibration in a molecule, when it has come 

 into a steady state as regards constitution and is not under 

 the influence of intimate encounter with other molecules. 



It may be recalled incidentally that the generalised Maxwell- 

 Boltzmann principle of the equable distribution of the acquired 

 store of kinetic energy of the molecule, among its various possible 

 independent types of motion, is based directly on the validity of 

 the Action principle for its dynamics. In the demonstrations 

 usually offered the molecule is considered to have no permanent 

 or constitutive energy of internal motion. It can, however, be 

 shown, by use of the generalisation aforesaid of the Action 

 principle, that no discrepancy will arise on that account. Such 

 intrinsic kinetic energy virtually adds on to the potential energy of 

 the system ; and the remaining or acquired part of the kinetic 

 energy of the molecule may be made the subject of the same 

 train of reasoning as before. 



Let us now return to the general question whether our 

 definition of a dynamical system may not be too wide. As 

 a case in point, the single principle of Action has been shown 

 to provide a definite and sufficient basis for electrodynamics ; yet 

 when, for e.xample, one armature of an electric motor pulls the 

 other after it without material contact, and so transmits mechani- 

 cal power, no connection between them is indicated by the 

 principle such as could by virtue of internal stress transmit the 

 pulL The essential feature of the transmission of a pull by stress 

 across a medium is that each element of volume of the medium 



1 For .-i classical exposition see his Brit. Assoc. Address of 18S4 on " Steps 

 towards a Kinetic Theory of Matter," reprinted in " Popular Lectures and 

 Addresses," vol. i. 



NO. 16 10, VOL. 62] 



acts by itself, independently of the other elements. The stress 

 excited in any element depends on the strain or other displace- 

 ment occurring in that element alone ; and the mechanical effect 

 that is transmitted is considered as an extraneous force applied 

 at one place in the medium, and passed on from element to 

 element through these internal pressures and tractions until it 

 reaches another place. We have, however, to consider two 

 atomic electric charges as being themselves some kind of strain 

 configurations in the tether ; each of them already involves an 

 atmosphere of strain in the surrounding Kther which is part of 

 its essence, and cannot be considered apart from it ; each of 

 them essentially pervades the "entire space, though on account 

 of its invariable character we consider it as a unit. Thus we 

 appear to be debarred from imagining the aether to act as an 

 elastic connection which is merely the agent of transmission of 

 a pull from the one nucleus to the other, because there are already 

 stresses belonging to and constituting an intrinsic part of the 

 terminal electrons, which are distributed all along the medium. 

 Our Action criterion of a dynamical system, in fact, allows us to 

 reason about an electron as a single thing, nothwithstanding 

 that its field of energy is spread over the whole medium ; it is 

 only in material solid bodies, and in problems in which the 

 actual sphere of physical action of t he molecule is small compared 

 with the smallest element of volume that our analysis considers, 

 that the familiar idea of transmission of force by simple stress 

 can apply. Whatever view may ultimately commend itself, 

 this question is one that urgently demands decision. A very 

 large amount of effort has been expended by Maxwell, 

 Helmholtz, Heaviside, Hertz,, and other authorities in the 

 attempt to expre.ss the mechanical phenomena of electrical action 

 in terms of a transmitting stress. The analytical results up to a 

 certain point have been promising, most strikingly so at the 

 beginning, when Maxwell established the mathematical validity 

 of the way in which Faraday was accustomed to represent to 

 himself the mechanical interactions across space, in terms of a 

 tension along the lines of force equilibrated by an equal pressure 

 preventing their expansion sideways. According to the views 

 here developed, that ideal is an impossible one ; if this could 

 be established to general satisfaction the field of theoretical 

 discussion would be much simplified. 



This view that the atom of matter is, so far as regards 

 physical action.=, of the nature of a structure in the tether in- 

 volving an atmosphere of tethereal strain all around it, not a 

 small body which exerts direct actions at a distance on other 

 atoms according to extraneous laws of force, was practically 

 foreign to the eighteenth century, when mathematical physics 

 was modelled on the Newtonian astronomy and dominated by its 

 splendid success. The scheme of material dynamics, as finally 

 compactly systematised by Lagrange, had therefore no direct 

 relation to such a view, although it has proved wide enough to 

 include it. The remark has often been made that it is probably 

 owing to Faraday's mathematical instinct, combined with his 

 want of acquaintance with the existing analysis, that the modern 

 theory of the tether obtained a start from the electric side. 

 Through his teaching and the weight of his authority, the notion 

 of two electric currents exerting their mutual forces by means 

 of an intervening medium, instead of by direct attraction across 

 space, was at an early period firmly grasped in this country. In 

 1845 Lord Kelvin was already mathematically formulating, with 

 most suggestive success, continuous elastic connections, by whose 

 strain the fields of activity of electric currents or of electric dis- 

 tributions could be illustrated; while the exposition of .Maxwell's 

 interconnected scheme, in the earlier form in which it relied on 

 concrete models of the electric action, goes back almost to i860. 

 Corresponding to the two physical ideals of isolated atoms exert- 

 ing attraction at a distance, and atoms operating by atmospheres 

 of tiethereal strain, there are, as already indicated, two different 

 developments of dynamical theory. The original Newtonian 

 equations of motion determined the course of a system by ex- 

 pressing the rates at which the velocity of each of its small parts 

 or elements is changing. This method is still fully applicable to 

 those problems of gravitational astronomy in which dynamical 

 explanation was first successful on a grand scale, the planets 

 being treated as point-masses, ea:h subject to the gravitational 

 attraction of the other bodies. But the more recent development 

 of the dynamics of complex systems depends on the fact that 

 analysis has been able to reduce within manageable limits the 

 number of varying quantities whose course is to be explicitly 

 traced, through taking advantage of those internal relations of 

 the parts of the system that are invariable, either geometrically 



