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.6
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.7 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 1843,8 and as only about 800 comets altogether have been recorded, the proportion of hyperbolic ones is quite as large as should be expected.
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