Aug. 20, 1874] 



NATURE 



321 



fail to play ;m imporlant part in llie iulure history of physical 

 science. I shall not then, I hope, be thought to misemploy the 

 time of the Section by offering some observations on the science 

 of molecular dynamics. 



AVhen we have to deal witli a science which professes to be 

 more than a mathematical abstraction — a science which assumes 

 to itself the function of representing, with at least approximate 

 truth, the realities of nature — our first question will naturally be, 

 What is the basis on which it rests ? Is it built upon a pure 

 Iiypothesis, not derived from experiment, but seeking to justify 

 its claim to reality by the truth of the results which may be 

 deduced from it ? 



The word "molecule," as Prof. Maxwell has told us, is modern, 

 embodying an idea deiived from modern chemistry. It denotes 

 a material particle so small as to be incapable of subdivision into 

 parts similar in their nature to itself Thus a drop of water may 

 be divided into smaller drops, each of which is also water ; but a 

 tiioieciile of water is regarded as incapable of such division. Not 

 that we regard it as absolutely indivisible ; but we assume that a 

 further division, could it be effected, would produce molecules, 

 not of water, but of its component gases, hydrogen and oxygen. 



Now this conception of a molecule undoubtedly involves an 

 hypothesis. Are there such ultimate particles of matter, not only 

 resisting all the dividing forces whicii we can command, but 

 absolutely indivisible, by any force, into particles similar to each 

 other, or perhaps into particles of any kind ? Or are we to sup- 

 pose that, if we had instruments of sufficient delicacy, the process 

 of division might be carried on without limit ? Experiment gives 

 us no means of deciding between these alternatives ; and if the 

 exigencies of our method of investigation force us to make a 

 decision, we can make it only by an hypothesis. But we may 

 fairly ask, Does the logic of molecular dj namics absolutely require 

 this decision? And on this point I wish to offer one or two 

 remarks. AVhen we propose to determine the motion of a body, 

 solid or fluid, we ought, as indeed in all scientific problems, to 

 form in the first place a clear conception of the meaning of the 

 question which we propose to our.selves. We wish to discover 

 the laws which govern the motion — of what ? Not certainly of 

 the body taken as a whole. That is, no doubt, part of the infor- 

 mation which we seek, but a very small part of it. When we 

 have learned to determine by a fixed mathematical rule, or formula 

 as we generally call it, the position occupied at any instant by the 

 centre of gravity of the body and by its principal axes, we have 

 learned something, but the investigation is far from being com- 

 plete. There are, as you know, large classes of movements of 

 v.hich such knowledge would tell us nothing. Thus, to take a 

 familiar instance, you see a man (to use our ordinary language) 

 " sitting quiet." He is at rest, so far as the movement of the 

 body, taken as a whole, is concerned. He is neither turning on 

 his chair nor wallung about the room ; and yet there is probably 

 not a single particle of his body which is absolutely quiescent. 

 Vou see, then, how ignorant we are of the vital movements of 

 the human body, if we know only that the individual is " sitting 

 quiet." 



But suppose that we push the inquiry a little further and pro- 

 pose to investigate the motion of the blood. We obtain an 

 answer to this question in one sense by determining the rate at 

 which the blood, taken as a whole, is moving — that is to say, 

 suppose the number of ounces of blood which pass through the 

 mitral valve in the space of one minute ; but having learned this, 

 we are still very far from knowing completely the motion of the 

 blood. But suppose that we are able to assign at any instant the 

 position of each one of the \)lood-globules considered as a unit 

 — that is to say, suppose we could assign for each of these 

 globules the position of its centre of gravity and the positions of 

 its principal axes, we should then know the motion of the blood, 

 not, indeed, perfectly (for we should still be ignorant of the 

 motion of the scrum as well as of the mternal movements which 

 take place in each globule), but very much more completely than 

 before. 



Further (and this is the point to which I wish especially to 

 direct your attention), the results v.'ould be equally true, whetlier 

 the globules were really units, incapable of further subdivision, 

 or really aggregates of still smaller particles. In the former 

 case we should know perfectly the motion of that part of the 

 blood which consists of the red globules ; in the latter, we 

 should know the same motion, but not jierfectly ; that is to say, 

 our results, though true as far as they go, would leave us still in 

 ignorance of one or more classes of motions which are really 

 exhibited by the globules of the ^blood. We should then be 



obliged to imagine a still furllier subdiv.si'jn. If, for example, 

 we divided, in imagination, each globule into a thousand parts, 

 and could determine the motion of each part considered as a 

 unit, our results would still further approximate to completeness; 

 and so on for further subdivisions. The logic of molecular 

 dynamics may then be shortly stated as follows : — 



In seeking to form the equations of motion of a body, solid 

 or fluid, we commence by an imaginary division of the body into 

 elements of any arbitrary magnitude, and we form the equations 

 of motion for each of these elements considered as a unit. The 

 results so obtained are true, but, as long as the elements retain a 

 finite magnitude, incomplete. They do not give us full informa- 

 tion as to the movement of the system. But suppose now, 

 adopting the spirit of the differentia! calculus, that the magnitude 

 of these elements is constantly diminished ; then it will be found 

 that, as in the differential calculus, these equations lend towards 

 a certain limiting form, constantly approaching it as the magni- 

 tude of the elements is continually diminished ; and in this 

 limiting form these equations are not only tiue but complete. 



Stated in this general form, the principles of molecular 

 dynamics are not only perfectly logical, but wholly free from 

 hypothesis. Hypotheses have, no doubt, been freely introduced 

 for the purpose of forming the actual equations in any given 

 case ; but molecular dynamics, as such, is not an hypothetical 

 science. The word molecular is in some respects unfortunate, 

 as tending to identify the science with a particular hypothesis as 

 to the constitution of matter. But molecular dynamics as a 

 science has no necessary connection with the molecular hypo- 

 thesis. In truth, the methods of this science harmonise quite as 

 readily with the supposition of the infinite divisibility of matter 

 as with the supposition of ultimate molecules. 



Molecular dynamics may fairly be called the differential cal- 

 culus of physical science. It is, in its relation to physical 

 science, what the differential calculus is in its relation to 

 geometry. As in geometry, when we would pass from the small 

 and exceptional class of rectilinear figures to the infinite varieties 

 of curve-lines, we must invoke the aid of the differential calculus, 

 so when we would pass from the abstractions of rigid solids and 

 unbending surfaces to the contemplation of bodies as they really 

 exist in nature, must we, if we would fully investigate their phe- 

 nomena, invoke the aid of molecular dynamics. It is the science 

 of that phenomenon which is gradually drawing all others within 

 its sway ; it is the science of that phenomenon which, "changed 

 in all and yet in all the same," we have learned to see in every part 

 of nature. Molecular dynamics is the science of Motion in its 

 widest and truest sense — of the motion which passes along in the 

 sweep of the tempest or the fierce throb of the earthquake — of 

 the motion (no less real) which breathes in the gentlest whisper 

 or thrills along the minutest nerve. 



I have dealt thus long upon the subject of molecular dynamics 

 because the amount of attention which in the present century it 

 has commanded, and the great advance which it has made, mark 

 most distinctly the tendency of scientific thought to the intro- 

 duction of mathematical analysis into all parts of physical science; 

 for molecular dynamics is the key to this introduction. It is to 

 the perfection of this science that we must look for an increased 

 use of the mathematical instrument ; and when we combine the 

 indications afforded by the history of this science with those 

 which we may derive from the history of its principal application 

 (Physical Optics), we have at least this partial answer to our 

 question — Mathematical analysis shows no sign of relaxing its 

 grasp upon any of the sciences which have been hitherto con- 

 sidered to belong to its domain ; nay, more, the desire to extend 

 that domain is indicated by the efforts to perfect the instrument 

 by which that extension must be made. We may now ask. Is 

 this indication confirmed by the liistory of any of those sciences 

 which have been hitherto regarded as lying wholly without our 

 Section ? 



And first, what shall we [say of Section B ? Does chemical 

 science show any indications pointing to a future union with the 

 group already collected under the gc7t!is (if I may so call it) 

 Theoretical Mechanics? Take, for example, the great problem 

 of chemical combination. Does the treatment of this problem 

 now show any signs pointing in the direction of dynamical 

 science ? I desire here to speak with all reserve and even hesi- 

 tation, being conscious that I am no longer on familiar ground. 

 Still there are signs wliich even an outside spectator may read. 

 And we may, I thinly, speak confidently of their direction, 

 although the goal to which they point is far distant >nd may 

 perhaps be unattainable. 



