IN STUDYING QUESTIONS OF CHEMICAL MECHANICS. 301 
With respect to the others, in order that they should produce 
the same results, there must be attributed to them internal mo- 
tions, similar to those which everything leads us to admit in 
real bodies, and to apply to the arbitrarily variable arrangement 
of their active particles the consequences which follow from the 
law of large numbers. In fact, when a polarized ray, infinitely 
thin, traverses a finite thickness of one of these systems, com- 
posed of active molecules all similar, they would doubtless be 
presented to it in all imaginable positions, varying infinitely the 
length of the course which it would pursue in each of them, 
as well as the amplitude of the partial deviation which they would 
individually impress on it. But, on account of their excessive 
minuteness, joined to their almost infinite multitude in every 
finite thickness of the system, the relation of the total thicknesses 
to the total quantities of active matter traversed would only vary 
by excessively small fractions, as hundred-thousandths, mil- 
lionths, or still less; which would produce only inequalities of 
one-hundredth or one-thousandth of a millimetre, or still smaller, 
in a column of one metre in length. Now, all the rotatory powers 
hitherto observed being inappreciable to the senses through such 
small thicknesses, such inequalities will be imperceptible; so 
that the proportionality of the deviations to the total thicknesses 
will appear exact. And these deviations will appear also the 
same, whether the active mass be mechanically agitated, or left 
in apparent repose. For, on agitating it, we merely cause it to 
vary the already infinitely diverse positions of the active mole- 
cules, which, by the same law of large numbers, cannot sensibly 
change their mean effect. I must call to mind that I present - 
this idea not as a necessary reality, but as a simple mathematical 
possibility, which would be logically compatible with all the 
phznomena observed. Without doubt it may be said that this 
is only to avoid the difficulty which we have of conceiving the 
natural and primordial cause of these properties, since we thus 
only transfer to the constituent molecules of the active masses 
the same physical actions which these masses present; but all 
our science consists only of similar reductions which succeed one 
another indefinitely, without term or limit; and the individual 
gravity of the molecules of bodies is established on an exactly 
similar reasoning. 
7. Conceiving then a power of deviation thus exercised suc- 
cessively on the plane of polarization of one and the same simple 
VOL. IV. PART XIV. ¥ 
