6 REPORT—1874. 
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 considered 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 
history of any of those sciences which have been hitherto regarded as lying wholly 
without our Section ? 
And first, what shall we say of Seetion B? Does chemical science show any 
indications pointing to a future union with the group already collected under the 
genus (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 hesitation, being conscious that I am no longer on familiar 
ground. Still there are signs which even an outside spectator may read. And we 
may, I think, speak confidently of their direction, although the goal to which they 
point is far distant and may perhaps be unattainable. 
One of these signs is the appearance of time as one of the elements of a che- 
mical problem. And in recognizing the necessity of a certain time for the produc- 
tion of a chemical effect, chemists are now pointing not obscurely to the analo 
of mechanical science. “Time,” says Berthelot, “is necessary for the accomplish- 
ment of chemical reactions, as it is for all the other mechanical phenomena.” This 
might not in itself be very significant ; but chemists have not merely recognized the 
necessity of time as a condition for the production of chemical phenomena, they 
have also undertaken to measure it; or rather, taking the converse problem, they 
have undertaken to measure the amount of chemical effect produced in the unit of 
time ; and the law of this phenomenon announced by Berthelot takes (necessarily, 
indeed) a mathematical form quite analogous to equations which present them- 
selves in dynamical science. The next step has followed as a matter of course, 
and chemists now speak as familiarly of the velocity of chemical reactions as engi- 
neers do of the velocity of a cannon-ball. 
Still more important in its bearing on the future of chemistry, and tending 
distinctly in the same direction, is the theory of Chemical Combination, which 
science owes to Prof. Williamson, and according to which this phenomenon, like so 
many others, ought to be regarded as in great measure a mode of motion. We 
suppose the normal condition of the atomic constituents of a body to be motion, not 
rest; and when we say that a molecule of one substance enters into combination 
with a molecule of another substance, we do not mean that the same molecules 
constantly adhere together, but that the union between the molecules, whatever 
be its nature, is continually dissolved and as continually re-formed. According to 
this theory, chemical equilibrium does not denote molecular rest, but a system of 
molecular motion, in which these decompositions and recompositions balance each 
other. 
If I may venture to add any thing to that which comes from such an authority, 
I would say that this theory leads us naturally to regard the chemical properties 
of bodies as, if not wholly modes of motion, yet largely dependent upon the nature 
of the movements which take place among their constituent atoms. Hence, if two 
bodies incapable of chemical action are brought into chemical presence of each 
other, we may suppose that their atomic movements, and therefore their properties, 
remain unaltered. If, on the other hand, these bodies be capable of acting che- 
mically on each other, their atomic movements are modified by their mutual 
chemical presence ; and therefore the chemical properties of the compound, as we 
call it, may be wholly different from those of either of the bodies which have 
entered into combination. 
Now we are not yet prepared to consider chemical combination as a problem of 
molecular dynamics. We have not sufficiently clear ideas (even hypothetical 
ideas) of these atomic moyements, and of the modifications which are caused by 
the chemical presence of another body, to place the investigation of these phe- 
