178 JOURNAL OF THE PLYMOUTH INSTITUTION. 
actual phenomena, and are therefore (at any rate provisionally) 
adopted. Is there then any other hypothesis which may enable 
Mathematics to push its sure methods into other provinces? There. 
is one which is now making rapid progress, and which seems likely 
to have a far-reaching influence. It is that of Molecular Mechanics. 
The molcule is the smallest portion of any substance still retaining 
all the qualities of the substance—the smallest possible drop (for 
instance) of water. It is incapable of further mechanical subdivision, 
though not of chemical; for the molecule of water may be still 
torn asunder into its constituent atoms of Oxygen and Hydrogen. 
Molecular Mechanics, then, is the new science which deals with the 
movements of these ultimate particles of all bodies. Now, since 
motion is always capable of mathematical expression, it is evi- 
dently calculated to extend widely the domain of mathematical’ | 
reasoning ; for motion appears to be more and more that into 
which all forces are ultimately resolvable. Sound is the vibration 
of air, Light is the vibration of ether, Heat is nothing but the 
minute and invisible movements of the particles which make up the 
heated body; and Professor Williamson has almost proved that 
Chemical combination itself is nothing but an incessant union and 
separation of these same minute particles from different bodies. If 
so, Chemistry itself is destined to fall under Mathematical Rule, even 
as Biology has already partially fallen, in consequence of those 
muscular movements which have been recently very ably treated 
by Professor Haughton. But all this, it will be said, rests on the 
molecular hypothesis, and that involves a deep and ancient——and still 
unsettled, controversy whether matter is infinitely divisible, or 
whether it can be separated into ultimate particles beyond which 
further division is impossible. Well, this is not exactly a correct 
statement of the case. Molecular Dynamics, remember, is indepe- 
pendent of this controverted hypothesis. Jts equations are true, 
whatever be the particles it deals with; eg. whether they are 
ultimately particles or not. ‘The only difference is, that in the first 
case its statements are complete and perfect, in the second case they 
are only tending towards completeness. Mathematicians have a 
powerful instrument in the Differential Calculus, which expresses the 
limiting forms to which equations tend, as the quantities which 
compose them are continually diminishing, so that its statements 
are independent of the actual value of these quantities. Molecular 
Dynamics may thus be regarded as the Differential Calculus of 
