CHAPTER XVIII.

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.