OBSERVATION.
ALL knowledge proceeds originally from experience. Using the name in a
wide sense, we may say that experience comprehends all that we *feel*,
externally or internally--the aggregate of the impressions which we
receive through the various apertures of perception--the aggregate
consequently of what is in the mind, except so far as some portions
of knowledge may be the reasoned equivalents of other portions. As
the word experience expresses, we *go through* much in life, and the
impressions gathered intentionally or unintentionally afford the
materials from which the active powers of the mind evolve science.
No small part of the experience actually employed in science is
acquired without any distinct purpose. We cannot use the eyes without
gathering some facts which may prove useful. A great science has in
many cases risen from an accidental observation. Erasmus Bartholinus
thus first discovered double refraction in Iceland spar; Galvani
noticed the twitching of a frog’s leg; Oken was struck by the form of
a vertebra; Malus accidentally examined light reflected from distant
windows with a double refracting substance; and Sir John Herschel’s
attention was drawn to the peculiar appearance of a solution of quinine
sulphate. In earlier times there must have been some one who first
noticed the strange behaviour of a loadstone, or the unaccountable
motions produced by amber. As a general rule we shall not know in what
direction to look for a great body of phenomena widely different from
those familiar to us. Chance then must give us the starting point; but
one accidental observation well used may lead us to make thousands of
observations in an intentional and organised manner, and thus a science
may be gradually worked out from the smallest opening.
*Distinction of Observation and Experiment.*
It is usual to say that the two sources of experience are Observation
and Experiment. When we merely note and record the phenomena which
occur around us in the ordinary course of nature we are said *to
observe*. When we change the course of nature by the intervention
of our muscular powers, and thus produce unusual combinations and
conditions of phenomena, we are said *to experiment*. Herschel justly
remarked[300] that we might properly call these two modes of experience
*passive and active observation*. In both cases we must certainly
employ our senses to observe, and an experiment differs from a mere
observation in the fact that we more or less influence the character
of the events which we observe. Experiment is thus observation *plus*
alteration of conditions.
[300] *Preliminary Discourse on the Study of Natural Philosophy*,
p. 77.
It may readily be seen that we pass upwards by insensible gradations
from pure observation to determinate experiment. When the earliest
astronomers simply noticed the ordinary motions of the sun, moon, and
planets upon the face of the starry heavens, they were pure observers.
But astronomers now select precise times and places for important
observations of stellar parallax, or the transits of planets. They make
the earth’s orbit the basis of a well arranged *natural experiment*,
as it were, and take well considered advantage of motions which they
cannot control. Meteorology might seem to be a science of pure
observation, because we cannot possibly govern the changes of weather
which we record. Nevertheless we may ascend mountains or rise in
balloons, like Gay-Lussac and Glaisher, and may thus so vary the points
of observation as to render our procedure experimental. We are wholly
unable either to produce or prevent earth-currents of electricity,
but when we construct long lines of telegraph, we gather such strong
currents during periods of disturbance as to render them capable of
easy observation.
The best arranged systems of observation, however, would fail to give
us a large part of the facts which we now possess. Many processes
continually going on in nature are so slow and gentle as to escape
our powers of observation. Lavoisier remarked that the decomposition
of water must have been constantly proceeding in nature, although its
possibility was unknown till his time.[301] No substance is wholly
destitute of magnetic or diamagnetic powers; but it required all the
experimental skill of Faraday to prove that iron and a few other
metals had no monopoly of these powers. Accidental observation long
ago impressed upon men’s minds the phenomena of lightning, and the
attractive properties of amber. Experiment only could have shown that
phenomena so diverse in magnitude and character were manifestations of
the same agent. To observe with accuracy and convenience we must have
agents under our control, so as to raise or lower their intensity,
to stop or set them in action at will. Just as Smeaton found it
requisite to create an artificial and governable supply of wind for
his investigation of windmills, so we must have governable supplies of
light, heat, electricity, muscular force, or whatever other agents we
are examining.
[301] Lavoisier’s *Elements of Chemistry*, translated by Kerr, 3rd
ed. p. 148.
It is hardly needful to point out too that on the earth’s surface we
live under nearly constant conditions of gravity, temperature, and
atmospheric pressure, so that if we are to extend our inferences to
other parts of the universe where conditions are widely different, we
must be prepared to imitate those conditions on a small scale here.
We must have intensely high and low temperatures; we must vary the
density of gases from approximate vacuum upwards; we must subject
liquids and solids to pressures or strains of almost unlimited amount.
*Mental Conditions of Correct Observation.*
Every observation must in a certain sense be true, for the observing
and recording of an event is in itself an event. But before we proceed
to deal with the supposed meaning of the record, and draw inferences
concerning the course of nature, we must take care to ascertain that
the character and feelings of the observer are not to a great extent
the phenomena recorded. The mind of man, as Francis Bacon said, is
like an uneven mirror, and does not reflect the events of nature
without distortion. We need hardly take notice of intentionally false
observations, nor of mistakes arising from defective memory, deficient
light, and so forth. Even where the utmost fidelity and care are used
in observing and recording, tendencies to error exist, and fallacious
opinions arise in consequence.
It is difficult to find persons who can with perfect fairness register
facts for and against their own peculiar views. Among uncultivated
observers the tendency to remark favourable and forget unfavourable
events is so great, that no reliance can be placed upon their supposed
observations. Thus arises the enduring fallacy that the changes of the
weather coincide in some way with the changes of the moon, although
exact and impartial registers give no countenance to the fact. The
whole race of prophets and quacks live on the overwhelming effect of
one success, compared with hundreds of failures which are unmentioned
and forgotten. As Bacon says, “Men mark when they hit, and never mark
when they miss.” And we should do well to bear in mind the ancient
story, quoted by Bacon, of one who in Pagan times was shown a temple
with a picture of all the persons who had been saved from shipwreck,
after paying their vows. When asked whether he did not now acknowledge
the power of the gods, “Ay,” he answered; “but where are they painted
that were drowned after their vows?”
If indeed we could estimate the amount of *bias* existing in any
particular observations, it might be treated like one of the forces
of the problem, and the true course of external nature might still be
rendered apparent. But the feelings of an observer are usually too
indeterminate, so that when there is reason to suspect considerable
bias, rejection is the only safe course. As regards facts casually
registered in past times, the capacity and impartiality of the observer
are so little known that we should spare no pains to replace these
statements by a new appeal to nature. An indiscriminate medley of
truth and absurdity, such as Francis Bacon collected in his *Natural
History*, is wholly unsuited to the purposes of science. But of course
when records relate to past events like eclipses, conjunctions,
meteoric phenomena, earthquakes, volcanic eruptions, changes of sea
margins, the existence of now extinct animals, the migrations of
tribes, remarkable customs, &c., we must make use of statements however
unsatisfactory, and must endeavour to verify them by the comparison of
independent records or traditions.
When extensive series of observations have to be made, as in
astronomical, meteorological, or magnetical observatories,
trigonometrical surveys, and extensive chemical or physical researches,
it is an advantage that the numerical work should be executed by
assistants who are not interested in, and are perhaps unaware of, the
expected results. The record is thus rendered perfectly impartial.
It may even be desirable that those who perform the purely routine
work of measurement and computation should be unacquainted with the
principles of the subject. The great table of logarithms of the
French Revolutionary Government was worked out by a staff of sixty or
eighty computers, most of whom were acquainted only with the rules of
arithmetic, and worked under the direction of skilled mathematicians;
yet their calculations were usually found more correct than those of
persons more deeply versed in mathematics.[302] In the Indian Ordnance
Survey the actual measurers were selected so that they should not have
sufficient skill to falsify their results without detection.
[302] Babbage, *Economy of Manufactures*, p. 194.
Both passive observation and experimentation must, however, be
generally conducted by persons who know for what they are to look. It
is only when excited and guided by the hope of verifying a theory that
the observer will notice many of the most important points; and, where
the work is not of a routine character, no assistant can supersede the
mind-directed observations of the philosopher. Thus the successful
investigator must combine diverse qualities; he must have clear notions
of the result he expects and confidence in the truth of his theories,
and yet he must have that candour and flexibility of mind which enable
him to accept unfavourable results and abandon mistaken views.
*Instrumental and Sensual Conditions of Observation.*
In every observation one or more of the senses must be employed, and
we should ever bear in mind that the extent of our knowledge may be
limited by the power of the sense concerned. What we learn of the world
only forms the lower limit of what is to be learned, and, for all that
we can tell, the processes of nature may infinitely surpass in variety
and complexity those which are capable of coming within our means of
observation. In some cases inference from observed phenomena may make
us indirectly aware of what cannot be directly felt, but we can never
be sure that we thus acquire any appreciable fraction of the knowledge
that might be acquired.
It is a strange reflection that space may be filled with dark wandering
stars, whose existence could not have yet become in any way known to
us. The planets have already cooled so far as to be no longer luminous,
and it may well be that other stellar bodies of various size have
fallen into the same condition. From the consideration, indeed, of
variable and extinguished stars, Laplace inferred that there probably
exist opaque bodies as great and perhaps as numerous as those we
see.[303] Some of these dark stars might ultimately become known to
us, either by reflecting light, or more probably by their gravitating
effects upon luminous stars. Thus if one member of a double star
were dark, we could readily detect its existence, and even estimate
its size, position, and motions, by observing those of its visible
companion. It was a favourite notion of Huyghens that there may exist
stars and vast universes so distant that their light has never yet
had time to reach our eyes; and we must also bear in mind that light
may possibly suffer slow extinction in space, so that there is more
than one way in which an absolute limit to the powers of telescopic
discovery may exist.
[303] *System of the World*, translated by Harte, vol. ii. p. 335.
There are natural limits again to the power of our senses in detecting
undulations of various kinds. It is commonly said that vibrations of
more than 38,000 strokes per second are not audible as sound; and
as some ears actually do hear sounds of much higher pitch, even two
octaves higher than what other ears can detect, it is exceedingly
probable that there are incessant vibrations which we cannot call sound
because they are never heard. Insects may communicate by such acute
sounds, constituting a language inaudible to us; and the remarkable
agreement apparent among bodies of ants or bees might thus perhaps be
explained. Nay, as Fontenelle long ago suggested in his scientific
romance, there may exist unlimited numbers of senses or modes of
perception which we can never feel, though Darwin’s theory would render
it probable that any useful means of knowledge in an ancestor would
be developed and improved in the descendants. We might doubtless have
been endowed with a sense capable of feeling electric phenomena with
acuteness, so that the positive or negative state of charge of a body
could be at once estimated. The absence of such a sense is probably due
to its comparative uselessness.
Heat undulations are subject to the same considerations. It is now
apparent that what we call light is the affection of the eye by certain
vibrations, the less rapid of which are invisible and constitute the
dark rays of radiant heat, in detecting which we must substitute
the thermometer or the thermopile for the eye. At the other end of
the spectrum, again, the ultra-violet rays are invisible, and only
indirectly brought to our knowledge in the phenomena of fluorescence or
photo-chemical action. There is no reason to believe that at either end
of the spectrum an absolute limit has yet been reached.
Just as our knowledge of the stellar universe is limited by the
power of the telescope and other conditions, so our knowledge of the
minute world has its limit in the powers and optical conditions of
the microscope. There was a time when it would have been a reasonable
induction that vegetables are motionless, and animals alone endowed
with power of locomotion. We are astonished to discover by the
microscope that minute plants are if anything more active than
minute animals. We even find that mineral substances seem to lose
their inactive character and dance about with incessant motion when
reduced to sufficiently minute particles, at least when suspended
in a non-conducting medium.[304] Microscopists will meet a natural
limit to observation when the minuteness of the objects examined
becomes comparable to the length of light undulations, and the extreme
difficulty already encountered in determining the forms of minute marks
on Diatoms appears to be due to this cause. According to Helmholtz the
smallest distance which can be accurately defined depends upon the
interference of light passing through the centres of the bright spaces.
With a theoretically perfect microscope and a dry lense the smallest
visible object would not be less than one 80,000th part of an inch in
red light.
[304] This curious phenomenon, which I propose to call *pedesis*, or
the *pedetic movement*, from πηδόω, to jump, is carefully described
in my paper published in the *Quarterly Journal of Science* for
April, 1878, vol. viii. (N.S.) p. 167. See also *Proceedings of the
Literary and Philosophical Society of Manchester*, 25th January,
1870, vol. ix. p. 78, *Nature*, 22nd August, 1878, vol. xviii.
p. 440, or the *Quarterly Journal of Science*, vol. viii. (N.S.)
p. 514.
Of the errors likely to arise in estimating quantities by the senses I
have already spoken, but there are some cases in which we actually see
things differently from what they are. A jet of water appears to be a
continuous thread, when it is really a wonderfully organised succession
of small and large drops, oscillating in form. The drops fall so
rapidly that their impressions upon the eye run into each other, and in
order to see the separate drops we require some device for giving an
instantaneous view.
One insuperable limit to our powers of observation arises from the
impossibility of following and identifying the ultimate atoms of
matter. One atom of oxygen is probably undistinguishable from another
atom; only by keeping a certain volume of oxygen safely inclosed in a
bottle can we assure ourselves of its identity; allow it to mix with
other oxygen, and we lose all power of identification. Accordingly
we seem to have no means of directly proving that every gas is in a
constant state of diffusion of every part into every part. We can only
infer this to be the case from observing the behaviour of distinct
gases which we can distinguish in their course, and by reasoning on the
grounds of molecular theory.[305]
[305] Maxwell, *Theory of Heat*, p. 301.
*External Conditions of Correct Observation.*
Before we proceed to draw inferences from any series of recorded facts,
we must take care to ascertain perfectly, if possible, the external
conditions under which the facts are brought to our notice. Not only
may the observing mind be prejudiced and the senses defective, but
there may be circumstances which cause one kind of event to come more
frequently to our notice than another. The comparative numbers of
objects of different kinds existing may in any degree differ from the
numbers which come to our notice. This difference must if possible be
taken into account before we make any inferences.
There long appeared to be a strong presumption that all comets moved
in elliptic orbits, because no comet had been proved to move in any
other kind of path. The theory of gravitation admitted of the existence
of comets moving in hyperbolic orbits, and the question arose whether
they were really non-existent or were only beyond the bounds of easy
observation. From reasonable suppositions Laplace calculated that
the probability was at least 6000 to 1 against a comet which comes
within the planetary system sufficiently to be visible at the earth’s
surface, presenting an orbit which could be discriminated from a very
elongated ellipse or parabola in the part of its orbit within the reach
of our telescopes.[306] In short, the chances are very much in favour
of our seeing elliptic rather than hyperbolic comets. Laplace’s views
have been confirmed by the discovery of six hyperbolic comets, which
appeared in the years 1729, 1771, 1774, 1818, 1840, and 1843,[307] and
as only about 800 comets altogether have been recorded, the proportion
of hyperbolic ones is quite as large as should be expected.
[306] Laplace, *Essai Philosophique*, p. 59. Todhunter’s *History*,
pp. 491–494.
[307] Chambers’ *Astronomy*, 1st ed. p. 203.
When we attempt to estimate the numbers of objects which may have
existed, we must make large allowances for the limited sphere of our
observations. Probably not more than 4000 or 5000 comets have been seen
in historical times, but making allowance for the absence of observers
in the southern hemisphere, and for the small probability that we see
any considerable fraction of those which are in the neighbourhood of
our system, we must accept Kepler’s opinion, that there are more comets
in the regions of space than fishes in the depths of the ocean. When
like calculations are made concerning the numbers of meteors visible to
us, it is astonishing to find that the number of meteors entering the
earth’s atmosphere in every twenty-four hours is probably not less than
400,000,000, of which 13,000 exist in every portion of space equal to
that filled by the earth.
Serious fallacies may arise from overlooking the inevitable conditions
under which the records of past events are brought to our notice.
Thus it is only the durable objects manufactured by former races of
men, such as flint implements, which can have come to our notice as a
general rule. The comparative abundance of iron and bronze articles
used by an ancient nation must not be supposed to be coincident with
their comparative abundance in our museums, because bronze is far the
more durable. There is a prevailing fallacy that our ancestors built
more strongly than we do, arising from the fact that the more fragile
structures have long since crumbled away. We have few or no relics of
the habitations of the poorer classes among the Greeks or Romans, or in
fact of any past race; for the temples, tombs, public buildings, and
mansions of the wealthier classes alone endure. There is an immense
expanse of past events necessarily lost to us for ever, and we must
generally look upon records or relics as exceptional in their character.
The same considerations apply to geological relics. We could not
generally expect that animals would be preserved unless as regards the
bones, shells, strong integuments, or other hard and durable parts. All
the infusoria and animals devoid of mineral framework have probably
perished entirely, distilled perhaps into oils. It has been pointed
out that the peculiar character of some extinct floras may be due to
the unequal preservation of different families of plants. By various
accidents, however, we gain glimpses of a world that is usually lost
to us--as by insects embedded in amber, the great mammoth preserved in
ice, mummies, casts in solid material like that of the Roman soldier at
Pompeii, and so forth.
We should also remember, that just as there may be conjunctions of the
heavenly bodies that can have happened only once or twice in the period
of history, so remarkable terrestrial conjunctions may take place.
Great storms, earthquakes, volcanic eruptions, landslips, floods,
irruptions of the sea, may, or rather must, have occurred, events of
such unusual magnitude and such extreme rarity that we can neither
expect to witness them nor readily to comprehend their effects. It is
a great advantage of the study of probabilities, as Laplace himself
remarked, to make us mistrust the extent of our knowledge, and pay
proper regard to the probability that events would come within the
sphere of our observations.
*Apparent Sequence of Events.*
De Morgan has excellently pointed out[308] that there are no less than
four modes in which one event may seem to follow or be connected with
another, without being really so. These involve mental, sensual, and
external causes of error, and I will briefly state and illustrate them.
[308] *Essay on Probabilities*, Cabinet Cyclopædia, p. 121.
Instead of A causing B, it may be *our perception of A that causes B*.
Thus it is that prophecies, presentiments, and the devices of sorcery
and witchcraft often work their own ends. A man dies on the day which
he has always regarded as his last, from his own fears of the day. An
incantation effects its purpose, because care is taken to frighten the
intended victim, by letting him know his fate. In all such cases the
mental condition is the cause of apparent coincidence.
In a second class of cases, *the event A may make our perception of
B follow, which would otherwise happen without being perceived*.
Thus it was believed to be the result of investigation that more
comets appeared in hot than cold summers. No account was taken of
the fact that hot summers would be comparatively cloudless, and
afford better opportunities for the discovery of comets. Here the
disturbing condition is of a purely external character. Certain ancient
philosophers held that the moon’s rays were cold-producing, mistaking
the cold caused by radiation into space for an effect of the moon,
which is more likely to be visible at a time when the absence of clouds
permits radiation to proceed.
In a third class of cases, *our perception of A may make our perception
of B follow*. The event B may be constantly happening, but our
attention may not be drawn to it except by our observing A. This case
seems to be illustrated by the fallacy of the moon’s influence on
clouds. The origin of this fallacy is somewhat complicated. In the
first place, when the sky is densely clouded the moon would not be
visible at all; it would be necessary for us to see the full moon in
order that our attention should be strongly drawn to the fact, and this
would happen most often on those nights when the sky is cloudless. Mr.
W. Ellis,[309] moreover, has ingeniously pointed out that there is a
general tendency for clouds to disperse at the commencement of night,
which is the time when the full moon rises. Thus the change of the sky
and the rise of the full moon are likely to attract attention mutually,
and the coincidence in time suggests the relation of cause and effect.
Mr. Ellis proves from the results of observations at the Greenwich
Observatory that the moon possesses no appreciable power of the kind
supposed, and yet it is remarkable that so sound an observer as Sir
John Herschel was convinced of the connection. In his “Results of
Observations at the Cape of Good Hope,”[310] he mentions many evenings
when a full moon occurred with a peculiarly clear sky.
[309] *Philosophical Magazine*, 4th Series (1867), vol. xxxiv. p. 64.
[310] See *Notes to Measures of Double Stars*, 1204, 1336, 1477,
1686, 1786, 1816, 1835, 1929, 2081, 2186, pp. 265, &c. See also
Herschel’s *Familiar Lectures on Scientific Subjects*, p. 147, and
*Outlines of Astronomy*, 7th ed. p. 285.
There is yet a fourth class of cases, in which *B is really the
antecedent event, but our perception of A, which is a consequence
of B, may be necessary to bring about our perception of B*. There
can be no doubt, for instance, that upward and downward currents are
continually circulating in the lowest stratum of the atmosphere during
the day-time; but owing to the transparency of the atmosphere we have
no evidence of their existence until we perceive cumulous clouds, which
are the consequence of such currents. In like manner an interfiltration
of bodies of air in the higher parts of the atmosphere is probably in
nearly constant progress, but unless threads of cirrous cloud indicate
these motions we remain ignorant of their occurrence.[311] The highest
strata of the atmosphere are wholly imperceptible to us, except when
rendered luminous by auroral currents of electricity, or by the passage
of meteoric stones. Most of the visible phenomena of comets probably
arise from some substance which, existing previously invisible, becomes
condensed or electrified suddenly into a visible form. Sir John
Herschel attempted to explain the production of comet tails in this
manner by evaporation and condensation.[312]
[311] Jevons, *On the Cirrous Form of Cloud*, Philosophical Magazine,
July, 1857, 4th Series, vol. xiv. p. 22.
[312] *Astronomy*, 4th ed. p. 358.
*Negative Arguments from Non-observation.*
From what has been suggested in preceding sections, it will plainly
appear that the non-observation of a phenomenon is not generally to
be taken as proving its non-occurrence. As there are sounds which we
cannot hear, rays of heat which we cannot feel, multitudes of worlds
which we cannot see, and myriads of minute organisms of which not the
most powerful microscope can give us a view, we must as a general rule
interpret our experience in an affirmative sense only. Accordingly
when inferences have been drawn from the non-occurrence of particular
facts or objects, more extended and careful examination has often
proved their falsity. Not many years since it was quite a well credited
conclusion in geology that no remains of man were found in connection
with those of extinct animals, or in any deposit not actually at
present in course of formation. Even Babbage accepted this conclusion
as strongly confirmatory of the Mosaic accounts.[313] While the opinion
was yet universally held, flint implements had been found disproving
such a conclusion, and overwhelming evidence of man’s long-continued
existence has since been forthcoming. At the end of the last century,
when Herschel had searched the heavens with his powerful telescopes,
there seemed little probability that planets yet remained unseen
within the orbit of Jupiter. But on the first day of this century such
an opinion was overturned by the discovery of Ceres, and more than a
hundred other small planets have since been added to the lists of the
planetary system.
[313] Babbage, *Ninth Bridgewater Treatise*, p. 67.
The discovery of the Eozoön Canadense in strata of much greater age
than any previously known to contain organic remains, has given a shock
to groundless opinions concerning the origin of organic forms; and
the oceanic dredging expeditions under Dr. Carpenter and Sir Wyville
Thomson have modified some opinions of geologists by disclosing the
continued existence of forms long supposed to be extinct. These and
many other cases which might be quoted show the extremely unsafe
character of negative inductions.
But it must not be supposed that negative arguments are of no force and
value. The earth’s surface has been sufficiently searched to render it
highly improbable that any terrestrial animals of the size of a camel
remain to be discovered. It is believed that no new large animal has
been encountered in the last eighteen or twenty centuries,[314] and
the probability that if existent they would have been seen, increases
the probability that they do not exist. We may with somewhat less
confidence discredit the existence of any large unrecognised fish, or
sea animals, such as the alleged sea-serpent. But, as we descend to
forms of smaller size negative evidence loses weight from the less
probability of our seeing smaller objects. Even the strong induction in
favour of the four-fold division of the animal kingdom into Vertebrata,
Annulosa, Mollusca, and Cœlenterata, may break down by the discovery
of intermediate or anomalous forms. As civilisation spreads over the
surface of the earth, and unexplored tracts are gradually diminished,
negative conclusions will increase in force; but we have much to learn
yet concerning the depths of the ocean, almost wholly unexamined as
they are, and covering three-fourths of the earth’s surface.
[314] Cuvier, *Essay on the Theory of the Earth*, translation, p. 61,
&c.
In geology there are many statements to which considerable probability
attaches on account of the large extent of the investigations already
made, as, for instance, that true coal is found only in rocks of a
particular geological epoch; that gold occurs in secondary and tertiary
strata only in exceedingly small quantities,[315] probably derived
from the disintegration of earlier rocks. In natural history negative
conclusions are exceedingly treacherous and unsatisfactory. The utmost
patience will not enable a microscopist or the observer of any living
thing to watch the behaviour of the organism under all circumstances
continuously for a great length of time. There is always a chance
therefore that the critical act or change may take place when the
observer’s eyes are withdrawn. This certainly happens in some cases;
for though the fertilisation of orchids by agency of insects is proved
as well as any fact in natural history, Mr. Darwin has never been
able by the closest watching to detect an insect in the performance
of the operation. Mr. Darwin has himself adopted one conclusion on
negative evidence, namely, that the *Orchis pyramidalis* and certain
other orchidaceous flowers secrete no nectar. But his caution and
unwearying patience in verifying the conclusion give an impressive
lesson to the observer. For twenty-three consecutive days, as he tells
us, he examined flowers in all states of the weather, at all hours, in
various localities. As the secretion in other flowers sometimes takes
place rapidly and might happen at early dawn, that inconvenient hour
of observation was specially adopted. Flowers of different ages were
subjected to irritating vapours, to moisture, and to every condition
likely to bring on the secretion; and only after invariable failure of
this exhaustive inquiry was the barrenness of the nectaries assumed to
be proved.[316]
[315] Murchison’s *Siluria*, 1st ed. p. 432.
[316] Darwin’s *Fertilisation of Orchids*, p. 48.
In order that a negative argument founded on the non-observation of
an object shall have any considerable force, it must be shown to be
probable that the object if existent would have been observed, and it
is this probability which defines the value of the negative conclusion.
The failure of astronomers to see the planet Vulcan, supposed by some
to exist within Mercury’s orbit, is no sufficient disproof of its
existence. Similarly it would be very difficult, or even impossible, to
disprove the existence of a second satellite of small size revolving
round the earth. But if any person make a particular assertion,
assigning place and time, then observation will either prove or
disprove the alleged fact. If it is true that when a French observer
professed to have seen a planet on the sun’s face, an observer in
Brazil was carefully scrutinising the sun and failed to see it, we have
a negative proof. False facts in science, it has been well said, are
more mischievous than false theories. A false theory is open to every
person’s criticism, and is ever liable to be judged by its accordance
with facts. But a false or grossly erroneous assertion of a fact
often stands in the way of science for a long time, because it may be
extremely difficult or even impossible to prove the falsity of what has
been once recorded.
In other sciences the force of a negative argument will often depend
upon the number of possible alternatives which may exist. It was long
believed that the quality of a musical sound as distinguished from
its pitch, must depend upon the form of the undulation, because no
other cause of it had ever been suggested or was apparently possible.
The truth of the conclusion was proved by Helmholtz, who applied a
microscope to luminous points attached to the strings of various
instruments, and thus actually observed the different modes of
undulation. In mathematics negative inductive arguments have seldom
much force, because the possible forms of expression, or the possible
combinations of lines and circles in geometry, are quite unlimited in
number. An enormous number of attempts were made to trisect the angle
by the ordinary methods of Euclid’s geometry, but their invariable
failure did not establish the impossibility of the task. This was shown
in a totally different manner, by proving that the problem involves an
irreducible cubic equation to which there could be no corresponding
plane geometrical solution.[317] This is a case of *reductio ad
absurdum*, a form of argument of a totally different character.
Similarly no number of failures to obtain a general solution of
equations of the fifth degree would establish the impossibility of the
task, but in an indirect mode, equivalent to a *reductio ad absurdum*,
the impossibility is considered to be proved.[318]
[317] Peacock, *Algebre*, vol. ii. p. 344.
[318] Ibid, p. 359. Serret, *Algèbre Supérieure*, 2nd ed. p. 304.