§ 1. I shall select, as a first example, an interesting speculation of one
of the most eminent of theoretical chemists, Professor Liebig. The object
in view, is to ascertain the immediate cause of the death produced by
metallic poisons.
Arsenious acid, and the salts of lead, bismuth, copper, and mercury, if
introduced into the animal organism, except in the smallest doses, destroy
life. These facts have long been known, as insulated truths of the lowest
order of generalization; but it was reserved for Liebig, by an apt
employment of the first two of our methods of experimental inquiry, to
connect these truths together by a higher induction, pointing out what
property, common to all these deleterious substances, is the really
operating cause of their fatal effect.
When solutions of these substances are placed in sufficiently close
contact with many animal products, albumen, milk, muscular fibre, and
animal membranes, the acid or salt leaves the water in which it was
dissolved, and enters into combination with the animal substance: which
substance, after being thus acted upon, is found to have lost its tendency
to spontaneous decomposition, or putrefaction.
Observation also shows, in cases where death has been produced by these
poisons, that the parts of the body with which the poisonous substances
have been brought into contact, do not afterwards putrefy.
And, finally, when the poison has been supplied in too small a quantity to
destroy life, eschars are produced, that is, certain superficial portions
of the tissues are destroyed, which are afterwards thrown off by the
reparative process taking place in the healthy parts.
These three sets of instances admit of being treated according to the
Method of Agreement. In all of them the metallic compounds are brought
into contact with the substances which compose the human or animal body;
and the instances do not seem to agree in any other circumstance. The
remaining antecedents are as different, and even opposite, as they could
possibly be made; for in some the animal substances exposed to the action
of the poisons are in a state of life, in others only in a state of
organization, in others not even in that. And what is the result which
follows in all the cases? The conversion of the animal substance (by
combination with the poison) into a chemical compound, held together by so
powerful a force as to resist the subsequent action of the ordinary causes
of decomposition. Now, organic life (the necessary condition of sensitive
life) consisting in a continual state of decomposition and recomposition
of the different organs and tissues; whatever incapacitates them for this
decomposition destroys life. And thus the proximate cause of the death
produced by this description of poisons, is ascertained, as far as the
Method of Agreement can ascertain it.
Let us now bring our conclusion to the test of the Method of Difference.
Setting out from the cases already mentioned, in which the antecedent is
the presence of substances forming with the tissues a compound incapable
of putrefaction, (and _à fortiori_ incapable of the chemical actions which
constitute life,) and the consequent is death, either of the whole
organism, or of some portion of it; let us compare with these cases other
cases, as much resembling them as possible, but in which that effect is
not produced. And, first, “many insoluble basic salts of arsenious acid
are known not to be poisonous. The substance called alkargen, discovered
by Bunsen, which contains a very large quantity of arsenic, and approaches
very closely in composition to the organic arsenious compounds found in
the body, has not the slightest injurious action upon the organism.” Now
when these substances are brought into contact with the tissues in any
way, they do not combine with them; they do not arrest their progress to
decomposition. As far, therefore, as these instances go, it appears that
when the effect is absent, it is by reason of the absence of that
antecedent which we had already good ground for considering as the
proximate cause.
But the rigorous conditions of the Method of Difference are not yet
satisfied; for we cannot be sure that these unpoisonous bodies agree with
the poisonous substances in every property, except the particular one, of
entering into a difficultly decomposable compound with the animal tissues.
To render the method strictly applicable, we need an instance, not of a
different substance, but of one of the very same substances, in
circumstances which would prevent it from forming, with the tissues, the
sort of compound in question; and then, if death does not follow, our case
is made out. Now such instances are afforded by the antidotes to these
poisons. For example, in case of poisoning by arsenious acid, if hydrated
peroxide of iron is administered, the destructive agency is instantly
checked. Now this peroxide is known to combine with the acid, and form a
compound, which, being insoluble, cannot act at all on animal tissues. So,
again, sugar is a well-known antidote to poisoning by salts of copper; and
sugar reduces those salts either into metallic copper, or into the red
suboxide, neither of which enters into combination with animal matter. The
disease called painter’s colic, so common in manufactories of white lead,
is unknown where the workmen are accustomed to take, as a preservative,
sulphuric-acid-lemonade (a solution of sugar rendered acid by sulphuric
acid). Now diluted sulphuric acid has the property of decomposing all
compounds of lead with organic matter, or of preventing them from being
formed.
There is another class of instances, of the nature required by the Method
of Difference, which seem at first sight to conflict with the theory.
Soluble salts of silver, such for instance as the nitrate, have the same
stiffening antiseptic effect on decomposing animal substances as corrosive
sublimate and the most deadly metallic poisons; and when applied to the
external parts of the body, the nitrate is a powerful caustic, depriving
those parts of all active vitality, and causing them to be thrown off by
the neighbouring living structures, in the form of an eschar. The nitrate
and the other salts of silver ought, then, it would seem, if the theory be
correct, to be poisonous; yet they may be administered internally with
perfect impunity. From this apparent exception arises the strongest
confirmation which the theory has yet received. Nitrate of silver, in
spite of its chemical properties, does not poison when introduced into the
stomach; but in the stomach, as in all animal liquids, there is common
salt; and in the stomach there is also free muriatic acid. These
substances operate as natural antidotes, combining with the nitrate, and
if its quantity is not too great, immediately converting it into chloride
of silver; a substance very slightly soluble, and therefore incapable of
combining with the tissues, although to the extent of its solubility it
has a medicinal influence, through an entirely different class of organic
actions.
The preceding instances have afforded an induction of a high order of
conclusiveness, illustrative of the two simplest of our four methods;
although not rising to the maximum of certainty which the Method of
Difference, in its most perfect exemplification, is capable of affording.
For (let us not forget) the positive instance and the negative one which
the rigour of that method requires, ought to differ only in the presence
or absence of one single circumstance. Now, in the preceding argument,
they differ in the presence or absence not of a single _circumstance_, but
of a single _substance_: and as every substance has innumerable
properties, there is no knowing what number of real differences are
involved in what is nominally and apparently only one difference. It is
conceivable that the antidote, the peroxide of iron for example, may
counteract the poison through some other of its properties than that of
forming an insoluble compound with it; and if so, the theory would fall to
the ground, so far as it is supported by that instance. This source of
uncertainty, which is a serious hindrance to all extensive generalizations
in chemistry, is however reduced in the present case to almost the lowest
degree possible, when we find that not only one substance, but many
substances, possess the capacity of acting as antidotes to metallic
poisons, and that all these agree in the property of forming insoluble
compounds with the poisons, while they cannot be ascertained to agree in
any other property whatsoever. We have thus, in favour of the theory, all
the evidence which can be obtained by what we termed the Indirect Method
of Difference, or the Joint Method of Agreement and Difference; the
evidence of which, though it never can amount to that of the Method of
Difference properly so called, may approach indefinitely near to it.
§ 2. Let the object be(78) to ascertain the law of what is termed
_induced_ electricity; to find under what conditions any electrified body,
whether positively or negatively electrified, gives rise to a contrary
electric state in some other body adjacent to it.
The most familiar exemplification of the phenomenon to be investigated, is
the following. Around the prime conductors of an electrical machine, the
atmosphere to some distance, or any conducting surface suspended in that
atmosphere, is found to be in an electric condition opposite to that of
the prime conductor itself. Near and around the positive prime conductor
there is negative electricity, and near and around the negative prime
conductor there is positive electricity. When pith balls are brought near
to either of the conductors, they become electrified with the opposite
electricity to it; either receiving a share from the already electrified
atmosphere by conduction, or acted upon by the direct inductive influence
of the conductor itself: they are then attracted by the conductor to which
they are in opposition; or, if withdrawn in their electrified state, they
will be attracted by any other oppositely charged body. In like manner the
hand, if brought near enough to the conductor, receives or gives an
electric discharge; now we have no evidence that a charged conductor can
be suddenly discharged unless by the approach of a body oppositely
electrified. In the case, therefore, of the electrical machine, it appears
that the accumulation of electricity in an insulated conductor is always
accompanied by the excitement of the contrary electricity in the
surrounding atmosphere, and in every conductor placed near the former
conductor. It does not seem possible, in this case, to produce one
electricity by itself.
Let us now examine all the other instances which we can obtain, resembling
this instance in the given consequent, namely, the evolution of an
opposite electricity in the neighbourhood of an electrified body. As one
remarkable instance we have the Leyden jar; and after the splendid
experiments of Faraday in complete and final establishment of the
substantial identity of magnetism and electricity, we may cite the magnet,
both the natural and the electro-magnet, in neither of which is it
possible to produce one kind of electricity by itself, or to charge one
pole without charging an opposite pole with the contrary electricity at
the same time. We cannot have a magnet with one pole: if we break a
natural loadstone into a thousand pieces, each piece will have its two
oppositely electrified poles complete within itself. In the voltaic
circuit, again, we cannot have one current without its opposite. In the
ordinary electric machine, the glass cylinder or plate, and the rubber,
acquire opposite electricities.
From all these instances, treated by the Method of Agreement, a general
law appears to result. The instances embrace all the known modes in which
a body can become charged with electricity; and in all of them there is
found, as a concomitant or consequent, the excitement of the opposite
electric state in some other body or bodies. It seems to follow that the
two facts are invariably connected, and that the excitement of electricity
in any body has for one of its necessary conditions the possibility of a
simultaneous excitement of the opposite electricity in some neighbouring
body.
As the two contrary electricities can only be produced together, so they
can only cease together. This may be shown by an application of the Method
of Difference to the example of the Leyden jar. It needs scarcely be here
remarked that in the Leyden jar, electricity can be accumulated and
retained in considerable quantity, by the contrivance of having two
conducting surfaces of equal extent, and parallel to each other through
the whole of that extent, with a non-conducting substance such as glass
between them. When one side of the jar is charged positively, the other is
charged negatively, and it was by virtue of this fact that the Leyden jar
served just now as an instance in our employment of the Method of
Agreement. Now it is impossible to discharge one of the coatings unless
the other can be discharged at the same time. A conductor held to the
positive side cannot convey away any electricity unless an equal quantity
be allowed to pass from the negative side: if one coating be perfectly
insulated, the charge is safe. The dissipation of one must proceed _pari
passu_ with that of the other.
The law thus strongly indicated admits of corroboration by the Method of
Concomitant Variations. The Leyden jar is capable of receiving a much
higher charge than can ordinarily be given to the conductor of an
electrical machine. Now in the case of the Leyden jar, the metallic
surface which receives the induced electricity is a conductor exactly
similar to that which receives the primary charge, and is therefore as
susceptible of receiving and retaining the one electricity, as the
opposite surface of receiving and retaining the other; but in the machine,
the neighbouring body which is to be oppositely electrified is the
surrounding atmosphere, or any body casually brought near to the
conductor; and as these are generally much inferior in their capacity of
becoming electrified, to the conductor itself, their limited power imposes
a corresponding limit to the capacity of the conductor for being charged.
As the capacity of the neighbouring body for supporting the opposition
increases, a higher charge becomes possible: and to this appears to be
owing the great superiority of the Leyden jar.
A further and most decisive confirmation by the Method of Difference, is
to be found in one of Faraday’s experiments in the course of his
researches on the subject of induced electricity.
Since common or machine electricity, and voltaic electricity, may be
considered for the present purpose to be identical, Faraday wished to know
whether, as the prime conductor develops opposite electricity upon a
conductor in its vicinity, so a voltaic current running along a wire would
induce an opposite current upon another wire laid parallel to it at a
short distance. Now this case is similar to the cases previously examined,
in every circumstance except the one to which we have ascribed the effect.
We found in the former instances that whenever electricity of one kind was
excited in one body, electricity of the opposite kind must be excited in a
neighbouring body. But in Faraday’s experiment this indispensable
opposition exists within the wire itself. From the nature of a voltaic
charge, the two opposite currents necessary to the existence of each other
are both accommodated in one wire; and there is no need of another wire
placed beside it to contain one of them, in the same way as the Leyden jar
must have a positive and a negative surface. The exciting cause can and
does produce all the effect which its laws require, independently of any
electric excitement of a neighbouring body. Now the result of the
experiment with the second wire was, that no opposite current was
produced. There was an instantaneous effect at the closing and breaking of
the voltaic circuit; electric inductions appeared when the two wires were
moved to and from one another; but these are phenomena of a different
class. There was no induced electricity in the sense in which this is
predicated of the Leyden jar; there was no sustained current running up
the one wire while an opposite current ran down the neighbouring wire; and
this alone would have been a true parallel case to the other.
It thus appears by the combined evidence of the Method of Agreement, the
Method of Concomitant Variations, and the most rigorous form of the Method
of Difference, that neither of the two kinds of electricity can be excited
without an equal excitement of the other and opposite kind: that both are
effects of the same cause; that the possibility of the one is a condition
of the possibility of the other, and the quantity of the one an impassable
limit to the quantity of the other. A scientific result of considerable
interest in itself, and illustrating those three methods in a manner both
characteristic and easily intelligible.(79)
§ 3. Our third example shall be extracted from Sir John Herschel’s
_Discourse on the Study of Natural Philosophy_, a work replete with
happily-selected exemplifications of inductive processes from almost every
department of physical science, and in which alone, of all books which I
have met with, the four methods of induction are distinctly recognised,
though not so clearly characterized and defined, nor their correlation so
fully shown, as has appeared to me desirable. The present example is
described by Sir John Herschel as “one of the most beautiful specimens”
which can be cited “of inductive experimental inquiry lying within a
moderate compass;” the theory of dew, first promulgated by the late Dr.
Wells, and now universally adopted by scientific authorities. The passages
in inverted commas are extracted verbatim from the “Discourse.”(80)
“Suppose _dew_ were the phenomenon proposed, whose cause we would know. In
the first place” we must determine precisely what we mean by dew: what the
fact really is, whose cause we desire to investigate. “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.” This answers to a preliminary operation which will be
characterized in the ensuing book, treating of operations subsidiary to
induction.(81) The state of the question being fixed, we come to the
solution.
“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 connexion 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. But if we could be sure that glass, and the various other
substances on which dew is deposited, have only _one_ quality in common,
and that polished metals and the other substances on which dew is _not_
deposited have also nothing in common but the one circumstance, of _not_
having the one quality which the others have; the requisitions of the
Method of Difference would be completely satisfied, and we should
recognise, in that quality of the substances, the cause of dew. This,
accordingly, is the path of inquiry which is next to be pursued.
“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 complication increases; here is the
Method of Concomitant Variations called to our assistance; and no other
method was practicable on this occasion; for the quality of conducting
heat could not be excluded, since all substances conduct heat in some
degree. The conclusion obtained is, that _cæteris 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.” Here, therefore, are the requisites for a
second employment of the Method of Concomitant Variations; which in this
case also is the only method available, since all substances radiate heat
in some degree or other. The conclusion obtained by this new application
of the method is, that _cæteris 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,
&c., as unfavourable, but those of a loose one, as cloth, velvet, wool,
eiderdown, cotton, &c., 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;” and this last is, therefore, an
induction (from fresh instances) simply _corroborative_ of a former
induction.
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. We seem, therefore, to
have detected the characteristic difference between the substances on
which dew is produced, and those on which it is not produced. And thus
have been realized the requisitions of what we have termed the Indirect
Method of Difference, or the Joint Method of Agreement and Difference. The
example afforded of this indirect method, and of the manner in which the
data are prepared for it by the Methods of Agreement and of Concomitant
Variations, is the most important of all the illustrations of induction
afforded by this interesting speculation.
We might now consider the question, on what the deposition of dew depends,
to be completely solved, if we could be quite sure that the substances on
which dew is produced differ from those on which it is not, in _nothing_
but in the property of losing heat from the surface faster than the loss
can be repaired from within. And though we never can have that complete
certainty, this is not of so much importance as might at first be
supposed; for we have, at all events, ascertained that even if there be
any other quality hitherto unobserved which is present in all the
substances which contract dew, and absent in those which do not, this
other property must be one which, in all that great number of substances,
is present or absent exactly where the property of being a better radiator
than conductor is present or absent; an extent of coincidence which
affords a strong presumption of a community of cause, and a consequent
invariable coexistence between the two properties; so that the property of
being a better radiator than conductor, if not itself the cause, almost
certainly always accompanies the cause, and for purposes of prediction, no
error is likely to be committed by treating it as if it were really such.
Reverting now to an earlier stage of the inquiry, let us remember that we
had ascertained that, in every instance where dew is formed, there is
actual coldness of the surface below the temperature of the surrounding
air; but we were not sure whether this coldness was the cause of dew, or
its effect. 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 connexion 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.
Here, therefore, is an additional condition of the production of dew,
which the methods we previously made use of failed to detect, and which
might have remained still undetected, if recourse had not been had to the
plan of deducing the effect from the ascertained properties of the agents
known to be present.
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.(82)
The accumulated proof of which the Theory of Dew has been found
susceptible, is a striking instance of the fulness of assurance which the
inductive evidence of laws of causation may attain, in cases in which the
invariable sequence is by no means obvious to a superficial view.
§ 4. The last example will have conveyed to any one by whom it has been
duly followed, so clear a conception of the use and practical management
of three of the four methods of experimental inquiry, as to supersede the
necessity of any further exemplification of them. The remaining method,
that of Residues, not having found any place either in this or in the two
preceding investigations, I shall extract from Sir John Herschel some
examples of that method, with the remarks by which they are introduced.
“It is by this process, in fact, that science, in its present advanced
state, is chiefly promoted. Most of the phenomena which Nature presents
are very complicated; and when the effects of all known causes are
estimated with exactness, and subducted, the residual facts are constantly
appearing in the form of phenomena altogether new, and leading to the most
important conclusions.
“For example: the return of the comet predicted by Professor Encke, a
great many times in succession, and the general good agreement of its
calculated with its observed place during any one of its periods of
visibility, would lead us to say that its gravitation towards the sun and
planets is the sole and sufficient cause of all the phenomena of its
orbitual motion: but when the effect of this cause is strictly calculated
and subducted from the observed motion, there is found to remain behind a
_residual phenomenon_, which would never have been otherwise ascertained
to exist, which is a small anticipation of the time of its reappearance,
or a diminution of its periodic time, which cannot be accounted for by
gravity, and whose cause is therefore to be inquired into. Such an
anticipation would be caused by the resistance of a medium disseminated
through the celestial regions; and as there are other good reasons for
believing this to be a _vera causa_,” (an actually existing antecedent,)
“it has therefore been ascribed to such a resistance.
“M. Arago, having suspended a magnetic needle by a silk thread, and set it
in vibration, observed, that it came much sooner to a state of rest when
suspended over a plate of copper, than when no such plate was beneath it.
Now, in both cases there were two _veræ causæ_ (antecedents known to
exist) “why it _should_ come at length to rest, viz. the resistance of the
air, which opposes, and at length destroys, all motions performed in it;
and the want of perfect mobility in the silk thread. But the effect of
these causes being exactly known by the observation made in the absence of
the copper, and being thus allowed for and subducted, a residual
phenomenon appeared, in the fact that a retarding influence was exerted by
the copper itself; and this fact, once ascertained, speedily led to the
knowledge of an entirely new and unexpected class of relations." This
example belongs, however, not to the Method of Residues but to the Method
of Difference, the law being ascertained by a direct comparison of the
results of two experiments, which differed in nothing but the presence or
absence of the plate of copper. To have made it exemplify the Method of
Residues, the effect of the resistance of the air and that of the rigidity
of the silk should have been calculated _à priori_, from the laws obtained
by separate and foregone experiments.”
“Unexpected and peculiarly striking confirmations of inductive laws
frequently occur in the form of residual phenomena, in the course of
investigations of a widely different nature from those which gave rise to
the inductions themselves. A very elegant example may be cited in the
unexpected confirmation of the law of the development of heat in elastic
fluids by compression, which is afforded by the phenomena of sound. The
inquiry into the cause of sound had led to conclusions respecting its mode
of propagation, from which its velocity in the air could be precisely
calculated. The calculations were performed; but, when compared with fact,
though the agreement was quite sufficient to show the general correctness
of the cause and mode of propagation assigned, yet the _whole_ velocity
could not be shown to arise from this theory. There was still a residual
velocity to be accounted for, which placed dynamical philosophers for a
long time in a great dilemma. At length Laplace struck on the happy idea,
that this might arise from the _heat_ developed in the act of that
condensation which necessarily takes place at every vibration by which
sound is conveyed. The matter was subjected to exact calculation, and the
result was at once the complete explanation of the residual phenomenon,
and a striking confirmation of the general law of the development of heat
by compression, under circumstances beyond artificial imitation.”
“Many of the new elements of chemistry have been detected in the
investigation of residual phenomena. Thus Arfwedson discovered lithia by
perceiving an excess of weight in the sulphate produced from a small
portion of what he considered as magnesia present in a mineral he had
analysed. It is on this principle, too, that the small concentrated
residues of great operations in the arts are almost sure to be the lurking
places of new chemical ingredients: witness iodine, brome, selenium, and
the new metals accompanying platina in the experiments of Wollaston and
Tennant. It was a happy thought of Glauber to examine what everybody else
threw away.”(83)
“Almost all the greatest discoveries in Astronomy,” says the same
author,(84) “have resulted from the consideration of residual phenomena of
a quantitative or numerical kind.... It was thus that the grand discovery
of the precession of the equinoxes resulted as a residual phenomenon, from
the imperfect explanation of the return of the seasons by the return of
the sun to the same apparent place among the fixed stars. Thus, also,
aberration and nutation resulted as residual phenomena from that portion
of the changes of the apparent places of the fixed stars which was left
unaccounted for by precession. And thus again the apparent proper motions
of the stars are the observed residues of their apparent movements
outstanding and unaccounted for by strict calculation of the effects of
precession, nutation, and aberration. The nearest approach which human
theories can make to perfection is to diminish this residue, this _caput
mortuum_ of observation, as it may be considered, as much as practicable,
and, if possible, to reduce it to nothing, either by showing that
something has been neglected in our estimation of known causes, or by
reasoning upon it as a new fact, and on the principle of the inductive
philosophy ascending from the effect to its cause or causes.”
The disturbing effects mutually produced by the earth and planets upon
each other’s motions were first brought to light as residual phenomena, by
the difference which appeared between the observed places of those bodies,
and the places calculated on a consideration solely of their gravitation
towards the sun. It was this which determined astronomers to consider the
law of gravitation as obtaining between all bodies whatever, and therefore
between all particles of matter; their first tendency having been to
regard it as a force acting only between each planet or satellite and the
central body to whose system it belonged. Again, the catastrophists, in
geology, be their opinion right or wrong, support it on the plea, that
after the effect of all causes now in operation has been allowed for,
there remains in the existing constitution of the earth a large residue of
facts, proving the existence at former periods either of other forces, or
of the same forces in a much greater degree of intensity. To add one more
example: those who assert, what no one has ever shewn any real ground for
believing, that there is in one human individual, one sex, or one race of
mankind over another, an inherent and inexplicable superiority in mental
faculties, could only substantiate their proposition by subtracting from
the differences of intellect which we in fact see, all that can be traced
by known laws either to the ascertained differences of physical
organization, or to the differences which have existed in the outward
circumstances in which the subjects of the comparison have hitherto been
placed. What these causes might fail to account for, would constitute a
residual phenomenon, which and which alone would be evidence of an
ulterior original distinction, and the measure of its amount. But the
assertors of such supposed differences have not provided themselves with
these necessary logical conditions of the establishment of their doctrine.
The spirit of the Method of Residues being, it is hoped, sufficiently
intelligible from these examples, and the other three methods having been
so aptly exemplified in the inductive processes which produced the Theory
of Dew, we may here close our exposition of the four methods, considered
as employed in the investigation of the simpler and more elementary order
of the combinations of phenomena.(85)