SIR WILLIAM HAMILTON ON INERTIA AND WEIGHT.
In a preceding chapter I have spoken of Sir William Hamilton as the
expositor, to English readers, of modern German systems, and especially
of the so-called "Philosophy of the Unconditioned." But the same writer
is also noticeable as a continuator of the speculations of English and
Scottish philosophers concerning primary and secondary qualities; and
these speculations bear so far upon the philosophy of science that it
is proper to notice them here.
1. In our survey of the sciences, we have spoken of a class which we
have termed the Secondary Mechanical Sciences; these being the sciences
which explain certain sensible phenomena, as sound, light, and heat, by
means of a medium interposed between external bodies and our organs of
sense. In these cases, we ascribe to bodies certain qualities: we call
them resonant, bright, red or green, hot or cold. But in the sciences
which relate to these subjects, we explain these qualities by the
figure, size and motions of the parts of the medium which intervenes
between the object and the ear, eye, or other sensible organ. And those
former qualities, sound, warmth and colour, are called _secondary
qualities_ of the bodies; while the latter, figure, size and motion,
are called the _primary qualities_ of body.
2. This distinction, in its substance, is of great antiquity. The
atomic theory which was set up at an early period of Greek philosophy
was an attempt to account for the secondary qualities of bodies by
means of their primary qualities. And this is really the scientific
ground of the distinction. _Those_ are primary qualities or attributes
of body by means of which we, in a scientific view, explain and derive
their other qualities. But the explanation of the sensible qualities
of bodies by means of their operation through a medium has till now
been very defective, and is so still. We have to a certain extent
theories of Sound, Light and Heat, which reduce these qualities to
scales and standards, and in some measure account mechanically for
their differences and gradations. But we have as yet no similar theory
of Smells and Tastes. Still, we do not doubt that fragrance and flavour
are perceived by means of an aerial medium in which odours float, and
a fluid medium in which sapid matters are dissolved. And the special
odour and flavour which are thus perceived must depend upon the size,
figure, motion, number, &c. of the particles thus conveyed to the
organs of taste and smell: that is, _those_ secondary qualities, as
well as the others, must depend upon the primary qualities of the parts
of the medium.
3. In this way the distinction of primary and secondary qualities is
definite and precise. But when men attempt to draw the distinction
by guess, without any scientific principle, the separation of
the two classes is vague and various. I have, in the _History of
Scientific Ideas_[303], pointed out some of the variations which
are to be found on this subject in the writings of philosophers.
Sir William Hamilton[304] has given an account of many more which
he has compared and analysed with great acuteness. He has shown how
this distinction is treated, among others, by the ancient atomists,
Leucippus and Democritus, by Aristotle, Galen, Galileo, Descartes,
Boyle, Malebranche, Locke, Reid, Stewart, Royer-Collard. He then
proceeds to give his own view; which is, that we may most properly
divide the qualities of bodies into _three_ classes, which he calls
_Primary_, _Secundo-primary_, and _Secondary_. The former he enumerates
as 1, Extension; 2, Divisibility; 3, Size; 4, Density or Rarity; 5,
Figure; 6, Incompressibility absolute; 7, Mobility; 8, Situation.
The Secundo-primary are Gravity, Cohesion, Inertia, Repulsion. The
Secondary are those commonly so called, Colour, Sound, Flavour,
Savour, and Tactical Sensation; to which he says may be added the
muscular and cutaneous sensation which accompany the perception of the
Secundo-primary qualities. "Such, though less directly the result of
foreign causes, are Titillation, Sneezing, Horripilation, Shuddering,
the feeling of what is called Setting-the-teeth-on-edge, &c."
The Secundo-primary qualities Sir William Hamilton traces in further
detail. He explains that with reference to Gravity, bodies are _heavy_
or _light_. With reference to Cohesion, there are many coordinate
pairs, of which he enumerates these:--_hard_ and _soft_; _firm_
and _fluid_,--the fluid being subdivided into _thick_ and _thin_;
_viscid_ and _friable_; _tough_ and _brittle_; _rigid_ and _flexible_;
_fissile_ and _infissile_; _ductile_ and _inductile_; _retractile_
and _irretractile_; _rough_ and _smooth_; _slippery_ and _tenacious_.
With reference to Repulsion he gives these qualities:--_compressible_
and _incompressible_; _elastic_ and _inelastic_. And with reference to
Inertia he mentions only _moveable_ and _immoveable_.
I do not see what advantage is gained to philosophy by such an
enumeration of qualities as this, which, after all, does not pretend
to completeness; nor do I see anything either precise or fundamental
in such distinctions as that of elasticity, a mode of cohesion, and
elasticity, a mode of repulsion. But a question in which our philosophy
is really concerned is how far any of these qualities are _universal_
qualities of matter. Sir W. Hamilton holds that they are none of them
necessary qualities of matter, and therefore of course not universal,
and argues this point at some length. With regard to one of his
Secundo-primary qualities, I will make some remarks.
4. _Inertia._--In discussing the Ideas which enter into the Mechanical
Sciences[305], I have stated that the Idea of Force and Resistance to
Force, that is, of _Force_ and _Matter_, are the necessary foundations
of those sciences. Force cannot act without matter to act on; Matter
cannot exist without Force to keep its parts together and to keep it in
its place. But Force acting upon matter may either be Force producing
rest, or Force producing motion. If we consider Force producing motion,
the motion produced, that is, the velocity produced, must depend upon
the quantity of matter moved. It cannot be that the same power, acting
in the same way, shall produce the same velocity by pushing a small
pebble and a large rock. If this were so, we could have no science on
such matters. It must needs be that the same force produces a smaller
velocity in the larger body; and this according to some measure of
its largeness. The measure of the degree in which the body thus
resists this communication of motion is _inertia_. And the inertia is
necessarily supposed to be proportional to the quantity of matter,
because it is by this inertia that this existence and quantity of the
matter is measured. If therefore any Science concerning Force and
Matter is to exist, matter must have inertia, and the inertia must be
proportional to the quantity of matter.
5. Sir W. Hamilton, in opposition to this, says, that we can conceive
a body occupying space, and yet without attraction or repulsion for
another body, and wholly indifferent to this or that position, in
space, to motion and to rest. He infers thence that inertia is not a
necessary quality of bodies.
To this I reply, that even if we can conceive such bodies, (which in
fact man, living in a world of matter cannot conceive,) at any rate
we cannot conceive any _science_ about such bodies. If bodies were
indifferent to motion and rest, Forces could not be measured by their
effects; nor could be measured or known in any way. Such bodies might
float about like clouds, visible to the eye, but intangible, and
governed by no laws of motion. But if we have any science about bodies,
they must be tangible, and governed by laws of motion. Not, then, from
any observed properties of bodies, but from the possibility of any
science about bodies, does it follow that all bodies have inertia.
6. _Gravity._--Reasoning of the same kind may be employed about weight.
We can conceive, it is urged, matter without weight. But I reply,
we cannot conceive a _science_ which deals with matter that has no
weight:--a science, I mean, which deals with the quantity of matter of
bodies, as arising from the sum of their elements. For the quantity of
matter of bodies is and must be measured by those sensible properties
of matter which undergo quantitative addition, subtraction and
division, as the matter is added, subtracted, and divided. The quantity
of matter cannot be known in any other way. But this mode of measuring
the quantity of matter, in order to be true at all, must be universally
true. If it were only partially true--if some kinds of matter had
weight and others had not--the limits of the mode of measuring matter
by weight would be arbitrary: and therefore the whole procedure
would be arbitrary, and as a mode of obtaining philosophical truth,
altogether futile. But we suppose truth respecting the composition of
bodies to be attainable; therefore we must suppose the rule, which is
the necessary basis of such truth, to be itself true.
Sir W. Hamilton has replied to these arguments, but, as I conceive,
without affecting the force of them. I will repeat here the answer
which I have already given[306], and will reprint in the Appendix the
Memoir by which his objections were occasioned.
He says, (1), that our reasoning assumes that we must necessarily have
it in our power to ascertain the Quantity of Matter; whereas this may
be a problem out of the reach of human determination.
To this I reply, that my reasoning _does_ assume that there is a
science, or sciences, which make assertions concerning the Quantity
of Matter: Mechanics and Chemistry are such sciences. My assertion
is, that to make such sciences possible, Quantity of Matter must
be proportional to Weight. If my opponent deny that Mechanics and
Chemistry can exist as science, he may invalidate my proof; but not
otherwise.
(2) He says that there are two conceivable ways of estimating the
Quantity of Matter: by the Space occupied, and by the Weight or
Inertia; and that I assume the second measure gratuitously.
To which I reply, that the most elementary steps in Mechanics and
in Chemistry contradict the notion that the Quantity of Matter is
proportionate to the Space. They proceed necessarily on a distinction
between Space and Matter:--between mere Extension and material
Substance.
(3) He allows that we cannot make the Extension of a body the
measure of the Quantity of Matter, because, he says, we do not
know if "the compressing force" is such as to produce "the closest
compression." That is, he assumes a compressing force, assumes a
"closest compression," assumes a peculiar (and very improbable) atomic
hypothesis; and all this, to supply a reason why we are not to believe
the first simple principle of Mechanics and Chemistry.
(4) He speaks of "a series of apparent fluids (as Light or its vehicle,
the Calorific, the Electro-galvanic, and Magnetic agents) which we can
neither denude of their character of substance, nor clothe with the
attribute of weight."
To which my reply is, that precisely because I cannot "clothe" these
agents with the attribute of Weight, I _do_ "denude them of the
character of Substance." They are not substances, but agencies. These
Imponderable Agents are not properly called "Imponderable Fluids." This
I conceive that I have proved; and the proof is not shaken by denying
the conclusion without showing any defect in the reasoning.
(5) Finally, my critic speaks about "a logical canon," and about "a
criterion of truth, subjectively necessary and objectively certain;"
which matters I shall not waste the reader's time by discussing.
FOOTNOTES:
[Footnote 303: B. iv. c. i.]
[Footnote 304: Reid's _Works_, Supplementary Dissertation D.]
[Footnote 305: _Hist. Sc. Id._ b. iii.]
[Footnote 306: _Hist. Sc. Id._ b. vi. c. iii.]