—_ 
TRANSACTIONS OF THE SECTIONS. 5 
knowing completely the motion of the blood. But suppose that we were able to 
assign at any instant the position of each one of the blood-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 serwm as well as of the internal 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), 
these results would be equally true, whether the globules were really units, inca- 
pable 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 perfectly; 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 further 
subdivision, 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 com- 
mence by an imaginary division of the body into elements of any arbitrary mag- 
nitude, and we form the equations of motion for each of these elements considered 
asaunit. The results so obtained are true, but, as long as the elements retain a 
finite magnitude, incomplete. They do not give us full information as to the 
movement of the system. But suppose now, adopting the spirit of the differential 
calculus, that the magnitude of ieee elements is constantly diminished; then it 
will be found that, as in the differential calculus, these equations tend towards a 
certain limiting form, constantly approaching it as the magnitude of the elements 
is continually diminished ; and in this limiting form these equations are not only 
true but complete. 
Stated in this general form, the principles of molecular dynamics are not only 
peaily logical, but wholly free from hypothesis. Hypotheses have, no doubt, 
een 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 connexion with the molecular hypothesis. In truth 
the methods of this science harmonize 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 calculus 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 curye-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 
phenomena, invoke the aid of molecular dynamics. It is the science of that phe- 
nomenon 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 dwelt 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 introduction 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 
