These are the rules; an example will make them clearer. We will show you
the methods in exercise; here is an example which combines nearly the
whole of them, namely, Dr. Well's theory of dew. I will give it to you
in Mill's own words, which are so clear that you must have the pleasure
of pondering over them: "We must separate dew from rain and the moisture
of fogs, and limit the application of the term to what is really meant,
which is, the spontaneous appearance of moisture on substances exposed
in the open air when no rain or visible wet is falling."[422] What is
the cause of the phenomena we have thus defined, and how was that cause
discovered?
"'Now, here we have analogous phenomena, in the moisture which bedews a
cold metal or stone when we breathe upon it; that which appears on a
glass of water fresh from the well in hot weather; that which appears on
the inside of windows when sudden rain or hail chills the external air;
that which runs down our walls when, after a long frost, a warm moist
thaw comes on.' Comparing these cases, we find that they all contain the
phenomenon which was proposed as the subject of investigation. Now 'all
these instances agree in one point: the coldness of the object dewed, in
comparison with the air in contact with it.' But there still remains the
most important case of all, that of nocturnal dew: does the same
circumstance exist in this case? 'Is it a fact that the object dewed is
colder than the air? Certainly not, one would at first be inclined to
say; for what is to make it so? But ... the experiment is easy; we have
only to lay a thermometer in contact with the dewed substance, and hang
one at a little distance above it, out of reach of its influence. The
experiment has been therefore made; the question has been asked, and the
answer has been invariably in the affirmative. Whenever an object
contracts dew, it is colder than the air.'
"Here then is a complete application of the Method of Agreement,
establishing the fact of an invariable connection between the deposition
of dew on a surface, and the coldness of that surface, compared with the
external air. But which of these is cause, and which effect? or are they
both effects of something else? On this subject the Method of Agreement
can afford us no light: we must call in a more potent method. 'We must
collect more facts, or, which comes to the same thing, vary the
circumstances; since every instance in which the circumstances differ is
a fresh fact: and especially, we must note the contrary or negative
cases, i.e., where no dew is produced': for a comparison between
instances of dew and instances of no dew, is the condition necessary to
bring the Method of Difference into play.
"'Now, first, no dew is produced on the surface of polished metals, but
it is very copiously on glass, both exposed with their faces upwards,
and in some cases the under side of a horizontal plate of glass is also
dewed.' Here is an instance in which the effect is produced, and another
instance in which it is not produced; but we cannot yet pronounce, as
the canon of the Method of Difference requires, that the latter instance
agrees with the former in all its circumstances except one: for the
differences between glass and polished metals are manifold, and the only
thing we can as yet be sure of is, that the cause of dew will be found
among the circumstances by which the former substance is distinguished
from the latter."
To detect this particular circumstance of difference, we have but one
practicable method, that of Concomitant Variations:
"'In the cases of polished metal and polished glass, the contrast shows
evidently that the substance has much to do with the phenomenon;
therefore let the substance alone be diversified as much as possible, by
exposing polished surfaces of various kinds. This done, a scale of
intensity becomes obvious. Those polished substances are found to be
most strongly dewed which conduct heat worst, while those which conduct
well resist dew most effectually....'
"The conclusion obtained is, that _cœteris paribus_ the deposition of
dew is in some proportion to the power which the body possesses of
resisting the passage of heat; and that this, therefore (or something
connected with this), must be at least one of the causes which assist in
producing the deposition of dew on the surface.
"'But if we expose rough surfaces instead of polished, we sometimes find
this law interfered with. Thus, roughened iron, especially if painted
over or blackened, becomes dewed sooner than varnished paper: the kind
of surface, therefore, has a great influence. Expose, then, the same
material in very diversified states as to surface' (that is, employ the
Method of Difference to ascertain concomitance of variations),' and
another scale of intensity becomes at once apparent; those surfaces
which part with their heat most readily by radiation, are found to
contract dew most copiously....'
"The conclusion obtained by this new application of the method is, that
_cœteris paribus_ the deposition of dew is also in some proportion to
the power of radiating heat; and that the quality of doing this
abundantly (or some cause on which that quality depends) is another of
the causes which promote the deposition of dew on the substance.
"'Again, the influence ascertained to exist of substance and surface,
leads us to consider that of texture; and here, again, we are presented
on trial with remarkable differences, and with a third scale of
intensity, pointing out substances of a close firm texture, such as
stones, metals, etc., as unfavourable, but those of a loose one, as
cloth, velvet, wool, eiderdown, cotton, etc., as eminently favourable to
the contraction of dew.' The Method of Concomitant Variations is here,
for the third time, had recourse to; and, as before, from necessity,
since the texture of no substance is absolutely firm or absolutely
loose. Looseness of texture, therefore, or something which is the cause
of that quality, is another circumstance which promotes the deposition
of dew; but this third cause resolves itself into the first, viz., the
quality of resisting the passage of heat: for substances of loose
texture 'are precisely those which are best adapted for clothing, or for
impeding the free passage of heat from the skin into the air, so as to
allow their outer surfaces to be very cold, while they remain warm
within....'
"It thus appears that the instances in which much dew is deposited,
which are very various, agree in this, and, so far as we are able to
observe, in this only, that they either radiate heat rapidly or conduct
it slowly: qualities between which there is no other circumstance of
agreement than that by virtue of either, the body tends to lose heat
from the surface more rapidly than it can be restored from within. The
instances, on the contrary, in which no dew, or but a small quantity of
it, is formed, and which are also extremely various, agree (so far as we
can observe) in nothing except in not having this same property....
"This doubt we are now able to resolve. We have found that in every such
instance, the substance must be one which, by its own properties or
laws, would, if exposed in the night, become colder than the surrounding
air. The coldness, therefore, being accounted for independently of the
dew, while it is proved that there is a connection between the two, it
must be the dew which depends on the coldness; or, in other words, the
coldness is the cause of the dew.
"This law of causation, already so amply established, admits, however,
of efficient additional corroboration in no less than three ways. First,
by deduction from the known laws of aqueous vapour when diffused through
air or any other gas, and though we have not yet come to the Deductive
Method, we will not omit what is necessary to render this speculation
complete. It is known, by direct experiment, that only a limited
quantity of water can remain suspended in the state of vapour at each
degree of temperature, and that this maximum grows less and less, as the
temperature diminishes. From this it follows deductively, that if there
is already as much vapour suspended as the air will contain at its
existing temperature, any lowering of that temperature will cause a
portion of the vapour to be condensed, and become water. But, again, we
know deductively, from the laws of heat, that the contact of the air
with a body colder than itself, will necessarily lower the temperature
of the stratum of air immediately applied to its surface; and will
therefore cause it to part with a portion of its water, which
accordingly will, by the ordinary laws of gravitation or cohesion,
attach itself to the surface of the body, thereby constituting dew. This
deductive proof, it will have been seen, has the advantage of proving at
once causation as well as coexistence; and it has the additional
advantage that it also accounts for the exceptions to the occurrence of
the phenomenon, the cases in which, although the body is colder than the
air, yet no dew is deposited, by showing that this will necessarily be
the case when the air is so under-supplied with aqueous vapour,
comparatively to its temperature, that even when somewhat cooled by the
contact of the colder body, it can still continue to hold in suspension
all the vapour which was previously suspended in it: thus, in a very dry
summer there are no dews, in a very dry winter no hoar frost....
"The second corroboration of the theory is by direct experiment,
according to the canon of the Method of Difference. We can, by cooling
the surface of any body, find in all cases some temperature (more or
less inferior to that of the surrounding air, according to its
hygrometric condition) at which dew will begin to be deposited. Here,
too, therefore, the causation is directly proved. We can, it is true,
accomplish this only on a small scale; but we have ample reason to
conclude that the same operation, if conducted in Nature's great
laboratory, would equally produce the effect.
"And, finally, even on that great scale we are able to verify the
result. The case is one of those rare cases, as we have shown them to
be, in which nature works the experiment for us in the same manner in
which we ourselves perform it; introducing into the previous state of
things a single and perfectly definite new circumstance, and manifesting
the effect so rapidly that there is not time for any other material
change in the pre-existing circumstances. 'It is observed that dew is
never copiously deposited in situations much screened from the open sky,
and not at all in a cloudy night; but if the clouds withdraw even for a
few minutes, and leave a clear opening, a deposition of dew presently
begins, and goes on increasing.... Dew formed in clear intervals will
often even evaporate again when the sky becomes thickly overcast.' The
proof, therefore, is complete, that the presence or absence of an
uninterrupted communication with the sky causes the deposition or
non-deposition of dew. Now, since a clear sky is nothing but the absence
of clouds, and it is a known property of clouds, as of all other bodies
between which and any given object nothing intervenes but an elastic
fluid, that they tend to raise or keep up the superficial temperature of
the object by radiating heat to it, we see at once that the
disappearance of clouds will cause the surface to cool; so that Nature,
in this case, produces a change in the antecedent by definite and known
means, and the consequent follows accordingly: a natural experiment
which satisfies the requisitions of the Method of Difference."