in many respects, we must expect to find them alike in other respects. He even enters into an inquiry whether the inhabitants of other planets would possess reason and knowledge of the same sort as ours, concluding in the affirmative. Although the power of intellect might be different, he considers that they would have the same geometry if they had any at all, and that what is true with us would be true with them.2 As regards the sun, he wisely observes that every conjecture fails. Laplace entertained a strong belief in the existence of inhabitants on other planets. The benign influence of the sun gives birth to animals and plants upon the surface of the earth, and analogy induces us to believe that his rays would tend to have a similar effect elsewhere. It is not probable that matter which is here so fruitful of life would be sterile upon so great a globe as Jupiter, which, like the earth, has its days and nights and years, and changes which indicate active forces. Man indeed is formed for the temperature and atmosphere in which he lives, and, so far as appears, could not live upon the other planets. But there might be an infinity of organisations relative to the diverse constitutions of the bodies of the universe. The most active imagination cannot form any idea of such various creatures, but their existence is not unlikely.3

We now know that many metals and other elements never found in organic structures are yet capable of forming compounds with substances of vegetable or animal origin. It is therefore just possible that at different temperatures creatures formed of different yet analogous compounds might exist, but it would seem indispensable that carbon should form the basis of organic structures. We have no analogies to lead us to suppose that in the absence of that complex element life can exist. Could we find globes surrounded by atmospheres resembling our own in temperature and composition, we should be almost forced to believe them inhabited, but the probability of any analogical argument decreases rapidly as the condition of a globe diverges from that of our own. The Cardinal Nicholas de Cusa held long ago that the moon was

1 Cosmotheoros (1699), p. 17.

3 System of the World, vol. ii. p. 326.

2 Ibid. p. 36. Essai Philosophique, p. 87.

inhabited, but the absence of any appreciable atmosphere renders the existence of inhabitants highly improbable. Speculations resting upon weak analogies hardly belong to the scope of true science, and can only be tolerated as an antidote to the far worse dogmas which assert that the thousand million of persons on earth, or rather a small fraction of them, are the sole objects of care of the Power which designed this limitless Universe.

Failures of Analogy.

So constant is the aid which we derive from the use of analogy in all attempts at discovery or explanation, that it is most important to observe in what cases it may lead us into difficulties. That which we expect by analogy to

exist

(1) May be found to exist;

(2) May seem not to exist, but nevertheless may really exist;

(3) May actually be non-existent.

In the second case the failure is only apparent, and arises from our obtuseness of perception, the smallness of the phenomenon to be noticed, or the disguised character in which it appears. I have already pointed out that the analogy of sound and light seems to fail because light does not apparently bend round a corner, the fact being that it does so bend in the phenomena of diffraction, which present the effect, however, in such an unexpected and minute form, that even Newton was misled, and turned from the correct hypothesis of undulations which he had partially entertained.

In the third class of cases analogy fails us altogether, and we expect that to exist which really does not exist. Thus we fail to discover the phenomena of polarisation in sound travelling through the atmosphere, since air is not capable of any appreciable transverse undulations. These failures of analogy are of peculiar interest, because they make the mind aware of its superior powers. There have been many philosophers who said that we can conceive nothing in the intellect which we have not previously received through the senses. This is true in the sense that we cannot image them to the mind in the concrete

TT

form of a shape or a colour; but we can speak of them and reason concerning them; in short, we often know them in everything but a sensuous manner. Accurate investigation shows that all material substances retard the motion of bodies through them by subtracting energy by impact. By the law of continuity we can frame the notion of a vacuous space in which there is no resistance whatever, nor need we stop there; for we have only to proceed by analogy to the case where a medium should accelerate the motion of bodies passing through it, somewhat in the mode which Aristotelians attributed falsely to the air. Thus we can frame the notion of negative density, and Newton could reason exactly concerning it, although no such thing exists.1

In every direction of thought we may meet ultimately with similar failures of analogy. A moving point generates a line, a moving line generates a surface, a moving surface generates a solid, but what does a moving solid generate? When we compare a polyhedron, or manysided solid, with a polygon, or plane figure of many sides, the volume of the first is analogous to the area of the second; the face of the solid answers to the side of the polygon; the edge of the solid to the point of the figure; but the corner, or junction of edges in the polyhedron, is left wholly unrepresented in the plane of the polygon. Even if we attempted to draw the analogies in some other manner, we should still find a geometrical notion embodied in the solid which has no representative in the figure of two dimensions.2

Faraday was able to frame some notion of matter in a fourth condition, which should be to gas what gas is to liquid. Such substance, he thought, would not fall far short of radiant matter, by which apparently he meant the supposed caloric or matter assumed to constitute heat, according to the corpuscular theory. Even if we could frame the notion, matter in such a state cannot be known to exist, and recent discoveries concerning the continuity

1 Principia, bk. ii. Section ii. Prop. x.

2 De Morgan, Cambridge Philosophical Transactions vol. xi. Part ii. p. 246.

3 Life of Faraday, vol. i. p. 216.

of the solid, liquid, and gaseous states remove the basis of the speculation.

From these and many other instances which might be adduced, we learn that analogical reasoning leads us to the conception of many things which, so far as we can ascertain, do not exist. In this way great perplexities have arisen in the use of language and mathematical symbols. All language depends upon analogy; for we join and arrange words so that they may represent the corresponding junctions or arrangements of things and their equalities. But in the use of language we are obviously capable of forming many combinations of words to which no corresponding meaning apparently exists. The same difficulty arises in the use of mathematical signs, and mathematicians have needlessly puzzled themselves about the square root of a negative quantity, which is, in many applications of algebraic calculation, simply a sign without any analogous meaning, there being a failure of analogy

CHAPTER XXIX.

EXCEPTIONAL PHENOMENA.

IF science consists in the detection of identity and the recognition of uniformity existing in many objects, it follows that the progress of science depends upon the study of exceptional phenomena. Such new phenomena are the raw material upon which we exert our faculties of observation and reasoning, in order to reduce the new facts beneath the sway of the laws of nature, either those laws already well known, or those to be discovered. Not only are strange and inexplicable facts those which are on the whole most likely to lead us to some novel and important discovery, but they are also best fitted to arouse our attention. So long as events happen in accordance with our anticipations, and the routine of every-day observation is unvaried, there is nothing to impress upon the mind the smallness of its knowledge, and the depth of mystery, which may be hidden in the commonest sights and objects. In early times the myriads of stars which remained in apparently fixed relative positions upon the heavenly sphere, received less notice from astronomers than those few planets whose wandering and inexplicable motions formed a riddle. Hipparchus was induced to prepare the first catalogue of stars, because a single new star had been added to those nightly visible; and in the middle ages two brilliant but temporary stars caused more popular interest in astronomy than any other events, and to one of them we owe all the observations of Tycho Brahe, the mediæval Hipparchus.

In other sciences, as well as in that of the heavens,