« הקודםהמשך »
ment when we pass from the mathematics of the one department to the mathematics of the other.
There is, no doubt, in one respect, a very wide transition; when instead of a triangle, whose baseline is taken by a pair of compasses from the Gunter scale, or even measured by a chain on the surface of the earth, we are called to investigate the relations of a triangle whose base-line is the diameter of the earth, or perhaps the diameter of the earth's orbit. There is doubtless a very wide transition from the objects of the terrestrial to those of the celestial physics; when, instead of three indivisible points on the parchment that lies before us, or three signposts of observation that wave on mountain-tops within sight of each other, we have three planetary bodies that, huge though they be in themselves, shrink into atoms when compared with the mighty spaces that lie between them. The fields of observation are wholly different; but it is by the very same trigonometry that we achieve the computation of the resulting triangles. And we again repeat that, sublime as the ascent may be from the facts or data of the one computation to those of the other, there is no gigantic or impracticable stride in their mathematics—that if able to trace certain curves in the page which lies before us, we are further able to scan the cycles of astronomy—that, widely apart as are the revelations of this wondrous science from the conceptions of our first and ordinary experience, yet grant but the facts, and it is by the dint of a familiar and ordinary mathematics, that the mind can ascend to them. It is thus that though in person we never stepped beyond the humble glen of our nativity, we may have that within the depository of our thoughts, which guides us to the certainties that be on the outskirts of creation. Within the little home of our bosom, there lie such principles and powers, as without one mile of locomotion are of as great avail, as if we could have traversed the infinities of space with the plumb-line in our hand, or carried the torch of discovery round the universe. It does look a marvel and a mystery, how man is able to climb the steep and lofty ascent from the terrestrial to the celestial in Natural Philosophy. But it helps to resolve the mystery, when we thus advert to the distinction between the facts or objects of the science, and the mathematics of the science. It at least tells us what that is, wherein the transition from the one department to the other lies; and gives us to understand that, could we in any way ascertain by observation, certain of the motions and magnitudes that belong to the upper regions of astronomy, there is an instrument within our reach, by which we may come to the accurate determination of its laws.
18. And as with Natural, so with Moral, Philosophy. The former hath its objects, whose properties are found by observation; and these objects have their mathematical relations, most of which are found without observation, by an abstract and solitary exercise of mind on the data which have been previously ascertained. There is a great difference between the terrestrial and the celestial physics, in regard to the way by which we arrive at the data. On the one field they are near at
hand; and at all events do not lie beyond the confines of the globe which we inhabit. On the other field they have place and occupancy at an exceeding distance away from us. The eye in quest of them must lift itself above all earthly objects; and often beyond the ken of our natural vision, they would have been for ever unknown_had not the telescope, that powerful instrument of revelation, fetched them to the men of our world, from those far and hidden obscurities in which they had lain for ages. But whatever the difference may be between the terrestrial and the celestial physics, in regard to the way by which we arrive at their data—there is no such difference in regard to the way through which, by a mathematical process of reasoning, truths are educed from these data. It matters not whether they be the elements of some terrestrial survey, or the observed elements of some distant planet that have been committed to a formula, and made over to the investigations of the analyst. It was indeed a far loftier flight, when in the capacity of an observer, he passed from the stations and the objects of a landscape below to those of the upper firmament. But there was no transition, at all corresponding to this when passing from the mathematics of the one contemplation to the mathematics of the other. Even at the time when he labours to determine the form or the periods of some heavenly orbit, his mind is only in contact with the symbols of that formula, or with the lines and spaces of that little diagram, which is before his eyes. It is enough that the triangle which comprehends any portion however small of his paper, hath the same relations and properties with the triangle which comprehends any portion however large of immensity. It is enough that what is predicated of the line which extends but a few inches may also be predicated of the same line when prolonged to the outskirts of creation. And thus it is, that after observation hath done its work and collected what may be styled the facts of Astronomy, there is a capability in the human spirit, and upon no other materials than what may lie within the compass of a table, to unravel the principles of its wondrous mechanism—and in the little chamber of thought, to elaborate a doctrine which shall truly represent the universe and is realized in its most distant processes.
19. Now whence were the mathematics by which he made an achievement so marvellous—whence were these mathematics derived ? For our purpose it is a sufficient answer to this question that he had not to go abroad for them. They may have enabled him to scan the cycles of heavenbut most certainly heaven's lofty concave is not the page from which his geometry was drawn. To obtain the necessary mathematics he has not to travel beyond the limits of his own humble apartment—and though in person he may have never wandered from the secluded valley that bounds his habitation, yet, such is the power of this home instrument, that it can carry him in thought through the remotest provinces of nature, and give him the intellectual mastery over them. He needs not have gone half-a-mile in quest of those conceptions which lie in little room within the receptacle of his
bosom. There may have been some obscurely initial or rudimental business of observation at the outset of his mental history, ere his notions of a line or a number or a quantity were settled; but it is an observation that might have all been carried on within a cell or a hermitage : And the important thing to be remarked is, that these notions, of homeward growth and origin though they be, are available on the field of the celestial as well as on that of the terrestrial Physics—and that when once by observation the respective data of each are ascertained, the same mathematics are applicable to both.
20. And it is just so in Moral Philosophy. This science hath its objects that are ascertained by observation—and, apart from these, it hath its Ethics, in virtue of which it can assign the moral relations that subsist between these objects. The facts of the science are just as distinct from the ethics of the science, as the facts of Natural Philosophy are from the mathematics of Natural Philosophy. By observation we can know of certain particulars in the state, or of certain passages in the history of two human beings—and, not by means of any further observation, but by certain ethical principles and by these alone, we can pronounce on the moral relationship that is between them, and on the proprieties of that relationship. Let us but know of any two men, that the one is a friendly and disinterested benefactor, and that the other is a dependant on his liberalities—or of the one that he is the generous lender, and of the other that he is the debtor who had promised and