Transactions of section a. G23 



ultimately commend itself, this question is one that urgently (lem<ands decision. 

 A very large amount of effort baa been expended by Maxwell, Ilelmholtz, 

 Heaviside, Hertz, and other authorities in the attempt to express 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 hues of force equilibrated by an equal 

 pressure preventing their expansion sideways. According to the views here deve- 

 loped, 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 actions, of 

 the nature of a structure in the tether involving an atmosphere of sethereal 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 waut of acquaintance with the existing analysis, that the 

 modern theory of the a3ther obtained a start from the electric side. Through his 

 teaching and the weight of his authority, the notion of two electric currents 

 e.xerting 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 distributions 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 1860. 

 Corresponding to the two physical ideals of isolated atoms exerting attraction at 

 a distance, and atoms operating by atmospheres of sethereal strain, there are, as 

 already indicated, two ditt'erent developments of dynamical theory. The original 

 Newtonian equations of motion determined the course of a system by expressing 

 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, each 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 or dynamically. Thus, to take the simplest 

 case, the dynamics of a solid body can be confined to a discussion of its three com- 

 ponents of translation and its three components of rotation, instead of the motion 

 of each element of its mass. With the number of independent coordinates thus 

 diminished, when the initial state of the motion is specified the subsequent course of 

 the complete system can be traced ; but the course of the changes in any part of 

 it can only be treated in relation to the motion of the system as a whole. It is just 

 this mode of treatment of a system as a whole that is the main characteristic of 

 modern physical analysis. The way in which Maxwell analysed the interactions 

 of a system of linear electric currents, previously treated as if each were made up 

 of small independent pieces or elements, and accumulated the evidence that they 

 formed a sing-le dynamical system, is a trenchant example. The interactions of 

 vortices in fluid form a very similar problem, which is of special note in that the 

 constitution of the system is there completely known in advance, so that the two 

 modes of dynamical exposition can be compared. In this case the older method 

 forms independent equations for the motion of each material element of the fluid, 

 aud so requires the introduction of the stress— here the fluid pressure— by which 



