SEPTEMBER 18, 1902] 
NATURE 
497 
as of the former ; it is not these gravimetrically expressed inter- 
acting quantities that we are to think of when the formulz 
NaOH and HBr are before us, as we too often strive to do ; it 
is not these, from a chemical point of view, meaningless numbers 
of parts, but quantities which are equal in the sense of chemistry, 
that are expressed as such by these symbolic formulz. The real 
purpose of chemical formulation is not to abbreviate or replace 
language, but to facilitate, if not ensure, abstraction from and 
non-contemplation of gravimetric numbers. 
I have just passed from atomic symbols to the formulz of 
molecules; but this was not without warrant. In the form in 
which I have enunciated the atomic theory, it relates to the 
chemical interaction of substances, whether compound or simple, 
and the equality of the quantities concerned is the equality of 
molecules, since these are the quantities of substances entering 
into or coming out from single chemical interactions. Were it 
not, therefore, for fear of confounding it with the mechanical 
theory of that name, the atomic theory should be called the 
molecular theory of chemistry. It might, indeed, have hap- 
pened to be so called by its author, for Dalton has told us 
that he had in mind both atom and molecule as names for his 
chemically ultimate particles, and chose the former because it 
carried with it the notion of indivisibility. He extended, also, 
as we do, the use of the term ‘‘atom” tochemically compound 
substances, since their combining quantities are chemically 
indivisible. 
Next, I would point out that in the atomic theory the notions 
of indivisibility and equality are inseparably involved. The in- 
divisibility of atom and molecule is not absolute or ultimate, and 
Dalton distinctly guarded himself against being understood to 
claim for the atom more than chemical indivisibility, and chemists 
of to-day assert no more than this. This indivisibility being 
conditioned by the equality of molecules, the importance of em- 
phasising it rests only upon the danger, when it is overlooked, 
of losing sight also of the chemical equality through the gravi- 
metric inequality receiving numerical expression, and thereby 
conveying the notion of divisibility, though only gravimetrically. 
The idea of indivisibility in connection with the atom or mole- 
cule is intrinsically quite subordinate to that of equality ; for 
equality, being unity or oneness brought into relation with itself, 
the conception of it carries with it and includes that of indivisi- 
bility. Any rational hypothesis as to substances consisting 
of ultimate particles will include the notion of their being in- 
divisible particles ; and the import of the hypothesis in chemical 
theory must lie, therefore, not in this indivisibility, but in the 
nature of the equality of the particles. By his atomic theory 
Dalton asserted that where the substances are different this 
equality is chemical instead of gravimetric. 
Molecules are equal in the sense that they are quantities of 
their substances which are interdependent and coordinate in any 
and every single chemical change in which they take part to- 
gether. It is a form of equality for which no close parallel can 
be found ; but as to that it should be remembered that this 
equality relates to the phenomena of the transformations of sub- 
stances into each other, which, though they form so large a part 
of the phenomena of the universe, are fundamentally distinct in 
nature from the rest of the behaviour of bodies throughout which 
the substance remains what it was. In some agreement with it 
there is that of mechanical pressures when these balance or 
neutralise each other, and therefore are opposite and mutually 
destructive though equal. But such pressures when exerted in 
the same direction are also equal in their effect on any body in 
their path, whereas in chemical interactions the effects of mole- 
cules or equal quantities of two unlike substances are only equal 
in the sense that each is that quantity which interacts with the 
same quantity of some third substance, which itself proves to be 
also a chemically equal quantity to them. For the products of 
the interaction in the one case are in part at least not the same 
as those in the other, though all prove chemically equal in further 
interactions. 
To give an example: the molecule of ammonia is equal to 
that of aldehyde in that it combines with it and with it disappears, 
or ceases to exist as such. For the same reason it is equal to 
the molecule of hydrocyanic acid, and molecules of aldehyde and 
hydrocyanic acid equal to each other, because they, too, combine 
and disappear as such in doing so. But the molecule of am- 
monia again equals that of aldehyde in effecting transformation 
of hydrocyanic acid and its own self into something else. And 
lastly, chemically equal or molecular are the products of these 
combinations; aldehyde ammonia, ammonium cyanide and 
NO. 1716, VOL. 66] 
aldehyde-cyanhydrine, not only among themselves, but also 
with the quantities of ammonia, aldehyde and hydrocyanic acid 
from which they come and into which they return in other 
chemical changes. But with all this quantitative equality in 
transforming power, the substances produced are unlike and, each 
to each, peculiar to one of the three acts of chemical combina- 
tion ; and on this account exception may be taken to the treat- 
ment of molecules as equal chemical quantities. Yet the equality 
of molecules here asserted is but an extension of what is meant 
by the equivalence of certain atoms and radicals, since the atom 
and the radical are, nowadays, conceptions entirely dependent 
upon and derived from that of the molecule (apart, of course, 
from the atomic hypothesis); and this universally allowed 
equivalence admittedly does not extend to the identity of the 
products of the replacing activity of the atoms and radicals. 
Quantitative equality and equivalency, it is true, have not 
the same meaning, equivalence being used to denote qualified 
equality, equality in certain specified ways, of quantities not 
equal in all other ways and possibly in no other. (Quantities 
of different substances cannot, strictly speaking, ever be equal, 
and can only be styled so in the sense of being equivalent ; for 
were they equal in every way the substances would obviously be 
the same. But this fact, if it ever strikes one, is ignored by uni- 
versal custom, and quantities of substances, however unlike— 
feathers, air, water, salt, and what not—are taken to be all equal, 
even by chemists as by the world at large, if only they have the 
same weight, notwithstanding the incongruities of the substances. 
I proceed now to show the baselessness of this conviction, but 
only to bring out more strongly the claim of chemical activity to 
equal rights with weight or mass in determining what are equal 
quantities of substances, for I am aware that here I have nothing 
to tell you that you do not already know. Weight being only 
the gravitational measure of mass, which itself is independent of 
it, quantities of substances are held to be equal when their 
masses are equal. Now, mass is quantity of matter. But what 
then is meant by matter? The answer must be either that it is 
a general term for any and all substances, or else that it is the 
common basis of all substances, which presents itself in all the 
different forms which are known to us as such, by virtue of a 
corresponding variety in its intestinal motions. 1 gladly pass 
over the latter answer without discussing it, on the ground that 
it introduces the subject of the intimate constitution of substances, 
which it is my set purpose to keep independent of in this dis- 
course. I will only say of it that it would probably be the 
answer of many physicists and chemists, and yet that it gives 
such a limitation to the nature of matter as makes the common 
expression ‘‘ constitution of matter” devoid of all meaning. 
That expression means, and can only mean, the constitution of 
substances in common ; and this brings me to the first answer, 
that matter is the term standing for all substances in common. 
Now, one thing which all substances possess in common is the 
property of resisting pressures; pressures not only of moving 
bodies, but of the motions of the ether and electrons. Measured 
or quantified, resistance becomes mass, all that can be signified 
by this term being the quantity of the resistance or inertia a 
substance exhibits when tested. It is the measure of a property 
of the substance, that is all; and there is no other way of quanti- 
fying a substance than through some one of its properties. No 
quantities of different substances can, as such, be commensurable 
throughout ; and when compared and measured through some 
common property, such as the possession of mass, the equivalence 
or pseudo-equality found by this means is not the same as that 
found when some other common property is taken as the means 
of measurement. But experience has shown that though there 
are several rational and comprehensive ways of instituting, 
through some common property, comparisons between quantities 
of different substances, they all, with the exception of that of 
weighing, agree more or less exactly in pointing to the same 
order of cquinaience: that of chemical activity ; for with this are 
colligated thos®@ of gaseous volume and the other well-known 
physical activities, which give nearly the same quantities as it 
gives of different substances as being molecularly equivalent. 
There are, therefore, essentially only two measures of quanti- 
tative equivalency or pseudo-equality between substances, the 
dynamical and the chemical or molecular, the one wholly inde- 
pendent of and the other wholly dependent upon the particular 
nature of the substances compared. The former is the measure 
of dynamical phenomena, those of changes of bodies, due to 
their impacts and pressures, which may lead to their deformation 
and disruption, but do not involve transformations of the 
