though very rarely. The symbols may recur once in a thousand times exactly, but one could not say the same of dice, or of human beings, if we fixed upon a given event, and had even actually observed it to so occur in that number of instances. In a population of so many millions a great poet, sculptor, and statesman might be successively produced once in five thousand years, or more, according to history, but any practical or predictive application of a pretty mathematical theory of such an order would be either useless or impossible. The deduction is too extravagant and remote for our strictly keeping to the correspondences, and we have to choose between mere ideality and experience. Either we go over to the mathematics, and so lose all right of discussion about the things; or we take part with the things and so defy the mathematics.' It is from the selection of examples of cards, dice, &c., that Mr. Venn thinks the à priori tendency that has infected the whole science is due, and the expression of certain events being equally likely, which is so frequently met with, is either purely of this character, which experience contradicts, or is an expectation of the mind arising out of past experience. Mathematics themselves being unlimited, time is often of no account in treating of probability, although experience must determine the extent of their application, so that we have only to put a finite limit upon the number of ways in which a thing can be done, and in time, letters and words being themselves limited, a genius like Shakespeare might be produced by chance! We have to suppose a bag filled with the simple letters of the alphabet on pieces of card, one of which shall be drawn out at a time and then replaced. 'If the letters were written down one after the other as they occurred, it would commonly be expected that they would be found to make mere nonsense, and would never arrange themselves into any language known to men. No more they would in general, but it is a commonly accepted result of the theory, and one which we may assume the reader to be ready to admit without further discussion, that, if the process were continued long enough, words making sense would appear; nay, more, that any book we chose to mention-Milton or Shakespeare, for example-would be produced in this way at last. It might take more years than we have space in this volume to represent in figures to obtain such works, but come they would at last.' Such a chance Shakespeare, and a chance world constructed on the same scheme, is a fine specimen of mathematical subtlety, but little else. It serves, however, to illustrate how mathematics may be applied, and how they may not, which is our excuse for quoting it.

Mr.

Mr. Venn's treatise takes him over a much larger field of inquiry than concerns us here. He discusses the rules of probability, and the fallacies arising either from their perverted application, or from the inferential reasoning being from a purely fictitious series, or one in which there is really no experience at hand to work upon. He points out the common confusions made between probability and induction, ably criticises the teaching of Dr. Whewell and Mr. Mill upon the latter, and cleverly shows the interaction of the two. His definition of inductive logic as concerned with universal propositions, and of probability as concerned with proportional ones, is very simple and clear. He defends the science of probability from the charge of attributing events to chance, because it makes no assumption whatever as to whether events are brought to pass by causation or without it, although frequently using the word to express the relative probability of an event occurring or not. Nor has it more to do with natural theology than either the principles of logic or induction have, probability being simply a body of rules for drawing inferences about classes of events which are distinguished by a certain quality. In fine, his treatment of the subject is concise, clear, cautious, and exhaustive. The style of his book is easy, unaffected, and not without a certain grace and vigour.

Thus shorn of its terror, the doctrine or science of probability will cease to alarm any but the most timid and hesitating minds, and no longer terrorise over any but those who wilfully and hopelessly entangle themselves in their own mathematical meshes. An average need no more terrify a reformer or a philanthropist than Chat Moss did Stephenson. It should inspire him with a stronger faith; it should flame before him. like a warning flash in the sky; it should be the majesty of his hope and not the measure of his despair. Statistics do not teach us to believe in fate. We are part and parcel of our own statistics; we are flesh and blood, and intellect and will, before which all things are plastic and transparent. Our fatalism is but selfishness, and our idleness its excuse. We can make more crime if we choose, and surely less if we will. We are living and breathing experiments, and scarcely know ourselves. We can build ourselves up into beauty and goodness, or downwards into darkness and despair. If we are links in a chain, it is to receive truth and power and flash it on, and if there be necessity in life it ranges up from the dulness of the clod to the divinity of duty. We have our choice. This fear of numbers and proportions and probabilities is but a confession of weakness; it is intelligence that has got a-head of morality,

the

the speculation of science beyond the truer art and science of life. Let us hear no more of it; let us be more lofty and brave. When we have piled up a succession of noble efforts and bright deeds, it is not a pyramid that will stop us; and when we have ceased to play with law, and it streams from our wills with bright and buoyant energy, we shall learn the true secrets of life, reject its casual forms, despise its failures, and joyfully find ourselves working parallel with the movements of the world.

ART. II. THE UNIVERSALITY OF MOTION.

OTION, say the school books, and after them the school

boys, is the changing of place, or the opposite of rest. The same authorities teach, and we all learn of them, the 'laws of motion,' the doctrine of inertia,' and some few facts by way of illustration. We do not think about it, or not more than we must for the purpose of the hour, that is to say,— knowing the lesson; not always so much as that, even. And when we pass from the schoolroom to the workshop-whatever it may be we are most of us too hard pressed by the daily necessity of personal action and movement, for the obtaining of daily bread, to have leisure, or inclination, perhaps, for recalling to mind and pondering definitions, laws, or illustrations of motion. And so, like the grammars of dead languages, or the books of arithmetic, the facts and the science are shelved and practically forgotten.

The truth is that this first introduction to science is, in most cases, a bringing us acquainted with words and formulæ only, by no means with things. And herein lies the explanation of the common want of interest and consequent forgetfulness. The mind is only impressed by things, never by mere words or propositions. The possibility of familiar acquaintance with words and propositions, without any distinct conceptions of the things they are designed to set forth, is, when we reflect on it, one of the strangest facts of human experience, and one of the most fruitful sources of error and mischief.

For example: We learnt at school that the earth turns on its axis daily, and that this rotation is the real cause of the phenomena which we call the rising and setting of the sun. We understood the terms of the proposition, and accepted it without doubting; but it was not until we reached manhood and applied ourself with genuine desire to the getting of knowledge, that even this simple fact revealed itself to us as a

fact,

fact, and impressed our imagination. We can never forget the glow of indescribable joy we felt when the beautiful vision first dawned on us. It was indeed, as Jean Paul says, an exchanging of counters for coins, of creeds for enjoyments.

Of all the results of intellectual culture, and especially of scientific studies, there is, perhaps, none more startling, none more impressive, none more powerfully tending to change the whole mode of thought in the student than this-the discovery of motion everywhere in nature beneath apparent repose. Startling, we said, but that is hardly the word. It would be so if the fact could suddenly become apparent to us while we still continued seeing and conceiving with the vulgar and untaught. But it is a composite, complex fact, which can only present itself element by element. The mind approaches it by many separate paths of observation and reflection, obtaining glimpses now of one portion, now of another; gaining from time to time richer knowledge and fuller experience, until at last, raised above the capacity of mere ignorant surprise, we find ourselves face to face with a glorious revelation which fills. us with silent wonder, and inspires some of us, perhaps, with reverence and adoration.

Then the fascinating task is proposed to us, and the pains will not be ill-bestowed, to measure our gain by the contrasts discernible between the conceptions of things with which we started on our path of scientific inquiry, and those at which we have at length arrived.

The earth, for example, on which we stand, to the unscientific eye the firm-set earth, with its great calm features of natural beauty seen day after day, season after season, age after age, as if, like its Maker, it were 'the same yesterday, to-day, and for ever,' the same broad still landscapes and oceans, the ever-during hills, the vast silent deserts of sand and ice, so solid, still, and permanent, what has it become to us? A tiny, fragile sphere, in swift complex movement through space; a 'round, rushing earth,' says Bailey; spinning round on its ideal axis every twenty-four hours, with a velocity at the surface of a thousand miles an hour; advancing at the same time in a vast but measurable orbit round the sun, at the enormous but certainly ascertained velocity of sixty-eight thousand miles an hour, or nineteen miles in every second. Perhaps, also, as science not wildly dreams, borne on with the sun along some still vaster orbit as yet unmeasured, immeasurable, and beyond the reach of imagination.

Solid, is it? What, then, is the meaning of the term 'Seismology,' one of the latest additions to the vocabulary of Vol- 9.-No. 36.

V

science?

science? The volcano and the earthquake, by their terrible protest perpetually repeated, have made that popular belief untenable. There is nothing left for us but to admit the strange fact, and reconcile our fancy to it as well as we may, that the earth is very much like a huge egg, or even a bombshell. It is even so. This 'crust' as we call it, bears, as far as we know, about the same proportion to the entire diameter as the shell of an egg does to its whole bulk. And it yields, and curves, and even splits under the pressure of the awful unknown forces that act beneath. So that we come at last to look upon our Alps, Andes, and Himalaya, merely as huge hardened ripples of the rock-sea, at long intervals rising and sinking, shaken, convulsed, shattered by tremendous forces for which we have at present no name.

Even the greatest physical features of our planet, the divisions of land and water, are not absolutely fixed, but only fixed by comparison with the brief period of man's existence upon it. Science, prying into the rock-beds beneath our feet, discerning a certain order among them, deciphering with exemplary patience the strange records she finds written. there,-records of an antiquity compared with which the date of Assyrian sculptures and Babylonian cuneiform inscriptions is but of to-day,-has discovered and unfolded to us the evidences of a series of changes,-movements, formations, elevations, depressions, disruptions, displacements, on the vastest scale, which must have occupied periods of time so immense, so completely beyond our power of computation, as to be virtually infinite. So that we can no longer say to the deep and dark blue ocean,' as it rolls round our continents and islands of to-day,

'Such as Creation's dawn beheld, thou rollest now.'

Its fair aspect, and its living, musical motion may be the same, but its place has been changed, not once or twice, but over and over again. In choicest words has the poet already interpreted to the world this testimony of the rocks:

There rolls the deep where grew the tree.

O Earth, what changes hast thou seen!

There where the long street roars, hath been

The silence of the central sea.

The hills are shadows, and they flow

From form to form, and nothing stands;

They melt like mist, the solid lands,

Like clouds they shape themselves and go.'

The granite mountain that looks to-day so steadfast and so motionless, only looks so. It is even now wearing and

passing