Chapter IV: Ozone and Hydrogen Peroxide--Dalton's Law (2)

[28 bis] The lower oxides of nitrogen and chlorine and the higher oxides
of manganese are also formed with the absorption of heat, and
therefore, like hydrogen peroxide, act in a powerfully oxidising
manner, and are not formed by the same methods as the majority
of other oxides. It is evident that, being endowed with a richer
store of energy (acquired in combination or by absorption of
heat), such substances, compared with others poorer in energy,
will exhibit a greater diversity of cases of chemical action with
other substances.

[29] If the point of support of a body lies in a vertical line below
the centre of gravity, it is in unstable equilibrium. If the
centre of gravity lies below the point of support; the state of
equilibrium is very stable, and a vibration may take place about
this position of stable equilibrium, as in a pendulum or balance,
when finally the body assumes a position of stable equilibrium.
But if, keeping to the same mechanical example, the body be
supported not on a point, in the geometrical sense of the word,
but on a small plane, then the state of unstable equilibrium may
be preserved, unless destroyed by external influences. Thus a
man stands upright supported on the plane, or several points of
the surfaces of his feet, having the centre of gravity above the
points of support. Vibration is then possible, but it is limited,
otherwise on passing outside the limit of possible equilibrium
another more stable position is attained about which vibration
becomes more possible. A prism immersed in water may have several
more or less stable positions of equilibrium. The same is also
true with the atoms in molecules. Some molecules present a state
of more stable equilibrium than others. Hence from this simple
comparison it will be at once evident that the stability of
molecules may vary considerably, that one and the same elements,
taken in the same number, may give isomerides of different
stability, and, lastly, that there may exist states of equilibria
which are so unstable, so ephemeral, that they will only arise
under particularly special conditions--such, for example, as
certain hydrates mentioned in the first chapter (_see_ Notes
57, 67, and others). And if in one case the instability of a
given state of equilibrium is expressed by its instability with
a change of temperature or physical state, then in other cases
it is expressed by the facility with which it decomposes under
the influence of contact or of the chemical influence of other
substances.

Besides this, hydrogen peroxide presents another side of the subject which is not less important, and is much clearer and more general.

Hydrogen unites with oxygen in two degrees of oxidation: water or hydrogen oxide, and oxygenated water or hydrogen peroxide; for a given quantity of hydrogen, the peroxide contains twice as much oxygen as does water. This is a fresh example confirming the correctness of the law of multiple proportions, to which we have already referred in speaking of the water of crystallisation of salts. We can now formulate this law--_the law of multiple proportions_. _If two substances A and B (either simple or compound), unite together to form several compounds, A_{n}B_{m}, A_{q}B_{r} ..., then having expressed the compositions of all these compounds in such a way that the quantity (by weight or volume) of one of the component parts will be a constant quantity_ A, _it will be observed that in all the compounds_ AB_{a}, AB_{b} _... the quantities of the other component part,_ B, _will always be in commensurable relation: generally in simple multiple proportion--that is, that a : b ..., or m/n is to r/q as whole numbers, for instance as 2 : 3 or 3 : 4...._

The analysis of water shows that in 100 parts by weight it contains 11·112 parts by weight of hydrogen and 88·888 of oxygen, and the analysis of peroxide of hydrogen shows that it contains 94·112 parts of oxygen to 5·888 parts of hydrogen. In this the analysis is expressed, as analyses generally are, in percentages; that is, it gives the amounts of the elements in a hundred parts by weight of the substance. The direct comparison of the percentage compositions of water and hydrogen peroxide does not give any simple relation. But such a relation is immediately apparent if we calculate the composition of water and of hydrogen peroxide, having taken either the quantity of oxygen or the quantity of hydrogen as a constant quantity--for instance, as unity. The most simple proportions show that in water there are contained eight parts of oxygen to one part of hydrogen, and in hydrogen peroxide sixteen parts of oxygen to one part of hydrogen; or one-eighth part of hydrogen in water and one-sixteenth part of hydrogen in hydrogen peroxide to one part of oxygen. Naturally, the analysis does not give these figures with absolute exactness--it gives them within a certain degree of error--but they approximate, as the error diminishes, to that limit which is here given. The comparison of the quantities of hydrogen and oxygen in the two substances above named, taking one of the components as a constant quantity, gives an example of the application of the law of multiple proportions, because water contains eight parts and hydrogen peroxide sixteen parts of oxygen to one part of hydrogen, and these figures are commensurable and are in the simple proportion of 1 : 2.

An exactly similar multiple proportion is observed in the composition of all other well-investigated definite chemical compounds,[30] and therefore the law of multiple proportions is accepted in chemistry as the starting point from which other considerations proceed.

[30] When, for example, any element forms several oxides, they are
subject to the law of multiple proportions. For a given quantity
of the non-metal or metal the quantities of oxygen in the
different degrees of oxidation will stand as 1 : 2, or as 1 : 3,
or as 2 : 3, or as 2 : 7, and so on. Thus, for instance, copper
combines with oxygen in at least two proportions, forming the
oxides found in nature, and called the suboxide and the oxide of
copper, Cu_{2}O and CuO; the oxide contains twice as much oxygen
as the suboxide. Lead also presents two degrees of oxidation,
the oxide and peroxide, and in the latter there is twice as
much oxygen as in the former, PbO and PbO_{2}. When a base and
an acid are capable of forming several kinds of salts, normal,
acid, basic, and anhydro-, it is found that they also clearly
exemplify the law of multiple proportions. This was demonstrated
by Wollaston soon after the discovery of the law in question. We
saw in the first chapter that salts show different degrees of
combination with water of crystallisation, and that they obey the
law of multiple proportions. And, more than this, the indefinite
chemical compounds existing as solutions may, as we saw in the
same chapter, be brought under the law of multiple proportions
by the hypothesis that solutions are unstable hydrates formed
according to the law of multiple proportions, but occurring in
a state of dissociation. By means of this hypothesis the law of
multiple proportions becomes still more general, and all the
aspects of chemical compounds are subject to it. The direction
of the whole contemporary state of chemistry was determined by
the discoveries of Lavoisier and Dalton. By endeavouring to
prove that in solutions we have nothing else than the liquid
products of the dissociation of definite hydrates, it is my aim
to bring also this category of indefinite compounds under the
general principle enunciated by Dalton; just as astronomers have
discovered a proof and not a negation of the laws of Newton in
perturbations.

The law of multiple proportions was discovered at the beginning of this century by John Dalton, of Manchester, in investigating the compounds of carbon with hydrogen. It appeared that two gaseous compounds of these substances--marsh gas, CH_{4}, and olefiant gas, C_{2}H_{4}, contain for one and the same quantity of hydrogen, quantities of carbon which stand in multiple proportion; namely, marsh gas contains relatively half as much carbon as olefiant gas. Although the analysis of that time was not exact, still the accuracy of this law, recognised by Dalton, was further confirmed by more accurate investigations. On establishing the law of multiple proportions, Dalton gave a hypothetical explanation for it. This explanation is based on the atomic theory of matter. In fact, the law of multiple proportions may be very easily understood by admitting the atomic structure of matter.

The essence of the atomic theory is that matter is supposed to consist of an agglomeration of small and indivisible parts--atoms--which do not fill up the whole space occupied by a substance, but stand apart from each other, as the sun, planets, and stars do not fill up the whole space of the universe, but are at a distance from each other. The form and properties of substances are determined by the position of their atoms in space and by their state of motion, whilst the reactions accomplished by substances are understood as redistributions of the relative positions of atoms and changes in their motion. The atomic representation of matter arose in very ancient times,[31] and up to recent times was at variance with the dynamical hypothesis, which considers matter as only a manifestation of forces. At the present time, however, the majority of scientific men uphold the atomic hypothesis, although the present conception of an atom is quite different from that of the ancient philosophers. An atom at the present day is regarded rather as an individual or unit which is indivisible by physical[32] and chemical forces, whilst the atom of the ancients was actually mechanically and geometrically indivisible. When Dalton (1804) discovered the law of multiple proportions, he pronounced himself in favour of the atomic doctrine, because it enables this law to be very easily understood. If the divisibility of every element has a limit, namely the atom, then the atoms of elements are the extreme limits of all divisibility, and if they differ from each other in their nature, the formation of a compound from elementary matter must consist in the aggregation of several different atoms into one whole or system of atoms, now termed _particles or molecules_. As atoms can only combine in their entire masses, it is evident that not only the law of definite composition, but also that of multiple proportions, must apply to the combination of atoms with one another; for one atom of a substance can combine with one, two, or three atoms of another substance, or in general one, two, three atoms of one substance are able to combine with one, two, or three atoms of another; this being the essence of the law of multiple proportions. Chemical and physical data are very well explained by the aid of the atomic theory. The displacement of one element by another follows the law of equivalency. In this case one or several atoms of a given element take the place of one or several atoms of another element in its compounds. The atoms of different substances can be mixed together in the same sense as sand can be mixed with clay. They do not unite into one whole--_i.e._ there is not a perfect blending in the one or other case, but only a juxtaposition, a homogeneous whole being formed from individual parts. This is the first and most simple method of applying the atomic theory to the explanation of chemical phenomena.[33]

[31] Leucippus, Democritus, and especially Lucretius, in the classical
ages, represented matter as made up of atoms--that is, of parts
incapable of further division. The geometrical impossibility of
such an admission, as well as the conclusions which were deduced
by the ancient atomists from their fundamental propositions,
prevented other philosophers from following them, and the atomic
doctrine, like very many others, lived, without being ratified
by fact, in the imaginations of its followers. Between the
present atomic theory and the doctrine of the above-named ancient
philosophers there is naturally a remote historical connection,
as between the doctrine of Pythagoras and Copernicus, but they
are essentially different. For us the atom is indivisible, not
in the geometrical abstract sense, but only in a physical and
chemical sense. It would be better to call the atoms indivisible
_individuals_. The Greek atom = the Latin individual, both
according to the etymology and original sense of the words, but
in course of time these two words have acquired a different
meaning. The individual is mechanically and geometrically
divisible, and only indivisible in a special sense. The earth,
the sun, a man or a fly are individuals, although geometrically
divisible. Thus the 'atoms' of contemporary science, indivisible
in a chemical sense, form those units with which we are concerned
in the investigation of the natural phenomena of matter, just
as a man is an indivisible unit in the investigation of social
relations, or as the stars, planets, and luminaries serve as
units in astronomy. The formation of the vortex hypothesis,
in which, as we shall afterwards see, atoms are entire whirls
mechanically complex, although physico-chemically indivisible,
clearly shows that the scientific men of our time in holding
to the atomic theory have only borrowed the word and form of
expression from the ancient philosophers, and not the essence
of their atomic doctrine. It is erroneous to imagine that the
contemporary conceptions of the atomists are nothing but the
repetition of the metaphysical reasonings of the ancients. To
show the true meaning of the atomism of the ancient philosophers,
and the profound difference between their points of argument
and those of contemporary men of science, I cite the following
fundamental propositions of Democritus (B.C. 470-380) as the best
expounder of the atomic doctrine of the ancients:--(1) Nothing
can proceed from nothing, nothing that exists can disappear or
be destroyed (and hence matter), and every change only consists
of a combination or separation. (2) Nothing is accidental, there
is a reason and necessity for everything. (3) All except atoms
and vacua is reason and not existence. (4) The atoms, which are
infinite in number and form, constitute the visible universe by
their motion, impact, and consequent revolving motion. (5) The
variety of objects depends only upon a difference in the number,
form, and order of the atoms of which they are formed, and not
upon a qualitative difference of their atoms, which only act
upon each other by pressure and impact. (6) The spirit, like
fire, consists of minute, spherical, smooth, and very mobile and
all-penetrating atoms, whose motion forms the phenomenon of life.
These Democritian, chiefly metaphysical, principles of atomism
are so essentially different from the principles of the present
atomic doctrine, which is exclusively applied to explaining
the phenomena of the external world, that it may be useful to
mention the essence of the atomic propositions of Boscovitch,
a Slav who lived in the middle of the eighteenth century, and
who is regarded as the founder of the modern atomic doctrines
which, however, did not take hold upon the minds of scientific
men, and were rarely applied prior to Dalton--_i.e._ until the
beginning of the nineteenth century. The doctrine of Boscovitch
was enunciated by him in 1758-1764 in his '_Philosophiæ naturalis
theoria reducta ad unicam legem virium in natura existentium_.'
Boscovitch considers matter to be composed of atoms, and the
atoms to be the points or centres of forces (just as the stars
and planets may be considered as points of space), acting between
bodies and their parts. These forces vary with the distance, so
that beyond a certain very small distance all atoms, and hence
also their aggregates, are attracted according to Newton's law,
but at less distances, there alternate wave-like spheres of
gradually decreasing attraction and increasing (as the distance
decreases) repulsion, until at last at a minimum distance only
the repellent action remains. Atoms, therefore, cannot merge
into each other. Consequently, the atoms are held at a certain
distance from each other, and therefore occupy space. Boscovitch
compares the sphere of repulsion surrounding the atoms to
the spheres of action of firing of a detachment of soldiers.
According to his doctrine, atoms are indestructible, do not merge
into each other, have mass, are everlasting and mobile under the
action of the forces proper to them. Maxwell rightly calls this
hypothesis the 'extreme' among those existing to explain matter,
but many aspects of Boscovitch's doctrine repeat themselves
in the views of our day, with this essential difference, that
instead of a mathematical point furnished with the properties of
mass, the atoms are endowed with a corporality, just as the stars
and planets are corporal, although in certain aspects of their
interaction they may be regarded as mathematical points. In my
opinion, the atomism of our day must first of all be regarded
merely as a convenient method for the investigation of ponderable
matter. As a geometrician in reasoning about curves represents
them as formed of a succession of right lines, because such a
method enables him to analyse the subject under investigation,
so the scientific man applies the atomic theory as a method of
analysing the phenomena of nature. Naturally there are people
now, as in ancient times, and as there always will be, who apply
reality to imagination, and therefore there are to be found
atomists of extreme views; but it is not in their spirit that
we should acknowledge the great services rendered by the atomic
doctrine to all science, which, while it has been essentially
independently developed, is, if it be desired to reduce all
ideas to the doctrines of the ancients, a union of the ancient
dynamical and atomic doctrines.

[32] Dalton and many of his successors distinguished the atoms of
elements and compounds, in which they clearly symbolised the
difference of their opinion from the representations of the
ancients. Now only the individuals of the elements, indivisible
by physical and chemical forces, are termed atoms, and the
individuals of compounds indivisible under physical changes are
termed molecules; these are divisible into atoms by chemical
forces.

[33] In the present condition of science, either the atomic or the
dynamical hypothesis is inevitably obliged to admit the existence
of an invisible and imperceptible motion in matter, without
which it is impossible to understand either light or heat, or
gaseous pressure, or any of the mechanical, physical, or chemical
phenomena. The ancients saw vital motion in animals only, but
to us the smallest particle of matter, endued with _vis viva_,
or energy in some degree or other, is incomprehensible without
self-existent motion. Thus motion has become a conception
inseparably knit with the conception of matter, and this has
prepared the ground for the revival of the dynamical hypothesis
of the constitution of matter. In the atomic theory there has
arisen that generalising idea by which the world of atoms is
constructed, like the universe of heavenly bodies, with its
suns, planets, and meteors, endued with everlasting force of
motion, forming molecules as the heavenly bodies form systems,
like the solar system, which molecules are only relatively
indivisible in the same way as the planets of the solar system
are inseparable, and stable and lasting as the solar system
is lasting. Such a representation, without necessitating the
absolute indivisibility of atoms, expresses all that science can
require for an hypothetical representation of the constitution
of matter. In closer proximity to the dynamical hypothesis of
the constitution of matter is the oft-times revived _vortex
hypothesis_. Descartes first endeavoured to raise it; Helmholtz
and Thomson (Lord Kelvin) gave it a fuller and more modern form;
many scientific men applied it to physics and chemistry. The idea
of vortex rings serves as the starting point of this hypothesis;
these are familiar to all as the rings of tobacco smoke, and may
be artificially obtained by giving a sharp blow to the sides
of a cardboard box having a circular orifice and filled with
smoke. Phosphuretted hydrogen, as we shall see later on, when
bubbling from water always gives very perfect vortex rings in a
still atmosphere. In such rings it is easy to observe a constant
circular motion about their axes, and to notice the stability the
rings possess in their motion of translation. This unchangeable
mass, endued with a rapid internal motion, is likened to the
atom. In a medium deprived of friction, such a ring, as is shown
by theoretical considerations of the subject from a mechanical
point of view, would be perpetual and unchangeable. The rings
are capable of grouping together, and in combining, without
being absolutely indivisible, remain indivisible. The vortex
hypothesis has been established in our times, but it has not
been fully developed; its application to chemical phenomena is
not clear, although not impossible; it does not satisfy a doubt
in respect to the nature of the space existing between the rings
(just as it is not clear what exists between atoms, and between
the planets), neither does it tell us what is the nature of the
moving substance of the ring, and therefore for the present it
only presents the germ of an hypothetical conception of the
constitution of matter; consequently, I consider that it would
be superfluous to speak of it in greater detail. However, the
thoughts of investigators are now (and naturally will be in the
future), as they were in the time of Dalton, often turned to the
question of the limitation of the mechanical division of matter,
and the atomists have searched for an answer in the most diverse
spheres of nature. I select one of the methods attempted, which
does not in any way refer to chemistry, in order to show how
closely all the provinces of natural science are bound together.
Wollaston proposed the investigation of the _atmosphere of the
heavenly bodies_ as a means for confirming the existence of
atoms. If the divisibility of matter be infinite, then air must
extend throughout the entire space of the heavens as it extends
all over the earth by its elasticity and diffusion. If the
infinite divisibility of matter be admitted, it is impossible
that any portion of the whole space of the universe can be
entirely void of the component parts of our atmosphere. But if
matter be divisible up to a certain limit only--namely, up to
the atom--then there _can exist_ a heavenly body void of an
atmosphere; and if such a body be discovered, it would serve as
an important factor for the acceptation of the validity of the
atomic doctrine. The moon has long been considered as such a
luminary and this circumstance, especially from its proximity to
the earth, has been cited as the best proof of the validity of
the atomic doctrine. This proof is apparently (Poisson) deprived
of some of its force from the possibility of the transformation
of the component parts of our atmosphere into a solid or liquid
state at immense heights above the earth's surface, where the
temperature is exceedingly low; but a series of researches
(Pouillet) has shown that the temperature of the heavenly
space is comparatively not so very low, and is attainable by
experimental means, so that at the low existing pressure the
liquefaction of the gases of the atmosphere cannot he expected
even on the moon. Therefore the absence of an atmosphere about
the moon, if it were not subject to doubt, would be counted as a
forcible proof of the atomic theory. As a proof of the absence of
a lunar atmosphere, it is cited that the moon, in its independent
motion between the stars, when eclipsing a star--that is, when
passing between the eye and the star--does not show any signs
of refraction at its edge; the image of the star does not alter
its position in the heavens on approaching the moon's surface,
consequently there is no atmosphere on the moon's surface capable
of refracting the rays of light. Such is the conclusion by which
the absence of a lunar atmosphere is acknowledged. But this
conclusion is most feeble, and there are even facts in exact
contradiction to it, by which the existence of a lunar atmosphere
may be proved. The entire surface of the moon is covered with a
number of mountains, having in the majority of cases the conical
form natural to volcanoes. The volcanic character of the lunar
mountains was confirmed in October 1866, when a change was
observed in the form of one of them (the crater Linnea). These
mountains must be on the edge of the lunar disc. Seen in profile,
they screen one another and interfere with observations on the
surface of the moon, so that when looking at the edge of the
lunar disc we are obliged to make our observations not on the
moon's surface, but at the summits of the lunar mountains. These
mountains are higher than those on our earth, and consequently at
their summits the lunar atmosphere must he exceedingly rarefied
even if it possess an observable density at the surface. Knowing
the mass of the moon to be eighty-two times less than the mass
of the earth, we are able to determine approximately that our
atmosphere at the moon's surface would be about twenty-eight
times lighter than it is on the earth, and consequently at the
very surface of the moon the refraction of light by the lunar
atmosphere must he very slight, and at the heights of the lunar
mountains it must be imperceptible, and would be lost within the
limits of experimental error. Therefore the absence of refraction
of light at the edge of the moon's disc cannot yet be urged in
favour of the absence of a lunar atmosphere. There is even a
series of observations obliging us to admit the existence of
this atmosphere. These researches are due to Sir John Herschel.
This is what he writes: 'It has often been remarked that during
the eclipse of a star by the moon there occurs a peculiar
optical illusion; it seems as if the star before disappearing
passed over the edge of the moon and is seen through the lunar
disc, sometimes for a rather long period of time. I myself have
observed this phenomenon, and it has been witnessed by perfectly
trustworthy observers. I ascribe it to optical illusion, but it
must be admitted that the star might have been seen on the lunar
disc through some deep ravine on the moon.' Geniller, in Belgium
(1856), following the opinion of Cassini, Eiler, and others,
gave an explanation of this phenomenon: he considers it due to
the refraction of light in the valleys of the lunar mountains
which occur on the edge of the lunar disc. In fact, although
these valleys do not probably present the form of straight
ravines, yet it may sometimes happen that the light of a star
is so refracted that its image might he seen, notwithstanding
the absence of a direct path for the light-rays. He then goes
on to remark that the density of the lunar atmosphere must be
variable in different parts, owing to the very long nights on
the moon. On the dark, or non-illuminated portion, owing to
these long nights, which last thirteen of our days and nights,
there must be excessive cold, and hence a denser atmosphere,
while, on the contrary, on the illuminated portion the atmosphere
must be much more rarefied. This variation in the temperature
of the different parts of the moon's surface explains also the
absence of clouds, notwithstanding the possible presence of air
and aqueous vapour, on the visible portion of the moon. The
presence of an atmosphere round the sun and planets, judging from
astronomical observations, may be considered as fully proved. On
Jupiter and Mars even bands of clouds may be distinguished. Thus
the atomic doctrine, admitting a finite mechanical divisibility
only, must he, as yet at least, only accepted as a means, similar
to that means which a mathematician employs when he breaks up
a continuous curvilinear line into a number of straight lines.
There is a simplicity of representation in atoms, but there is no
absolute necessity to have recourse to them. The conception of
the individuality of the parts of matter exhibited in chemical
elements only is necessary and trustworthy.

A certain number of atoms _n_ of an element A in combining with several atoms _m_ of another element B give a compound A_{_n_} B_{_m_}, each molecule of which will contain the atoms of the elements A and B in this ratio, and therefore the compound will present a _definite composition_, expressed by the formula A_{_n_}B_{_m_}, where A and B are the weights of the atoms and _n_ and _m_ their relative number. If the same elements A and B, in addition to A_{_n_}B_{_m_}, also yield another compound A_{_r_}B_{_q_}, then by expressing the composition of the first compound by A_{_nr_}B_{_mr_} (and this is the same composition as A_{_n_}B_{_m_}), and of the second compound by A_{_rn_}B_{_qn_}, we have the law of multiple proportions, because for a given quantity of the first element, A_{_rn_}, there occur quantities of the second element bearing the same ratio to each other as _mr_ is to _qn_; and as _m_, _r_, _q_, and _n_ are whole numbers, their products are also whole numbers, and this is expressed by the law of multiple proportion. Consequently the atomic theory is in accordance with and evokes the first laws of definite chemical compounds: the law of definite composition and the law of multiple proportions.

So, also, is the relation of the atomic theory to the third law of definite chemical compounds, the _law of reciprocal combining weights_, which is as follows:--If a certain weight of a substance C combine with a weight _a_ of a substance A, and with a weight _b_ of a substance B, then, also, the substances A and B will combine together in quantities _a_ and _b_ (or in multiples of them). This should be the case from the conception of atoms. Let A, B, and C be the weights of the atoms of the three substances, and for simplicity of reasoning suppose that combination takes place between single atoms. It is evident that if the substance gives AC and BC, then the substances A and B will give a compound AB, or their multiple, A_{_n_}B_{_m_}. And so it is in reality in nature.

Sulphur combines with hydrogen and with oxygen. Sulphuretted hydrogen contains thirty-two parts by weight of sulphur to two parts by weight of hydrogen; this is expressed by the formula H_{2}S. Sulphur dioxide, SO_{2}, contains thirty-two parts of sulphur and thirty-two parts of oxygen, and therefore we conclude, from the law of combining weights, that oxygen and hydrogen will combine in the proportion of two parts of hydrogen and thirty-two parts of oxygen, or multiple numbers of them. And we have seen this to be the case. Hydrogen peroxide contains thirty-two parts of oxygen, and water sixteen parts, to two parts of hydrogen; and so it is in all other cases. This consequence of the atomic theory is in accordance with nature, with the results of analysis, and is one of the most important laws of chemistry. It is a law, because it indicates the _relation between_ the weights of substances entering into chemical combination. Further, it is an eminently exact law, and not an approximate one. The law of combining weights is a law of nature, and by no means an hypothesis, for even if the entire theory of atoms be refuted, still the laws of multiple proportions and of combining weights will remain, inasmuch as they deal with facts. They may be guessed at from the sense of the atomic theory, and historically the law of combining weights is intimately connected with this theory; but they are not identical, but only connected, with it. The law of combining weights is formulated with great ease, and is an immediate consequence of the atomic theory; without it, it is even difficult to understand. Data for its evolution existed previously, but it was not formulated until those data were interpreted by the atomic theory, an hypothesis which up to the present time has contradicted neither experiment nor fact, and is useful and of general application. Such is the nature of hypotheses. They are indispensable to science; they bestow an order and simplicity which are difficultly attainable without their aid. The whole history of science is a proof of this. And therefore it may be truly said that it is better to hold to an hypothesis which may afterwards prove untrue than to have none at all. Hypotheses facilitate scientific work and render it consistent. In the search for truth, like the plough of the husbandman, they help forward the work of the labourer.