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,coo, of which 13,000 exist in every portion of space equal to that filled by the earth's globe.

Most 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 always 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 It is thus that 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 indefinite expanse of past events necessarily lost to us for ever, and we must generally look upon records or relics as exceptional in their character.

away.

Exactly 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 must

probably have 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 may 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 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.

Instead of A causing B, it may be our perception of A that causes B. Thus it is that prophecies, presentiments,

6

1 Essay on Probabilities,' Cabinet Cyclopædia, p. 121.

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 fatem. 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 seriously believed as 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 becomes visible at the 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 was cloudless. Mr. W. Ellis, moreover, has ingeniously

Philosophical Magazine,' 4th Series (1867), vol. xxxiv. p. 64.

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 acute and sound an observer as the late Sir John Herschel was convinced of the connection. In his Results of Observations at the Cape of Good Hope'r, he mentions many evenings when a full moon occurred with a peculiarly clear sky.

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 wholly ignorant of their occurrence. The highest strata of the atmosphere are wholly imperceptible to us, except when rendered

P SeeNotes 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.

a Jevons, On the Cirrous Form of Cloud,' Philosophical Magazine, July, 1857, 4th Series, vol. xiv. p. 22.