vitiated, the limits of possible error may themselves be assigned. But, in the simplest applications of mathematics to mechanics or to physics, the abstractions which are necessary in the theory, must always leave out circumstances which are essentially connected with the effect. In demonstrating, for example, the property of the lever, we abstract entirely from its own weight, and consider it as an inflexible mathematical line;-suppositions with which the fact cannot possibly correspond; and for which, of course, allowances (which nothing but physical experience can enable us to judge of,) must be made in practice*.

Next to practical geometry, properly so called, one of the easiest applications of mathematical theory occurs in those branches of optics which are distinguished by the name of catoptrics and dioptrics. In these, the physical principles from which we reason are few and precisely definite, and the rest of the process is as purely geometrical as the Elements of Euclid,

In that part of astronomy, too, which relates solely to the phenomena, without any consideration of physical causes, our reasonings are purely geometrical. The data indeed on which we proceed must have been previously ascertained by observation; but the inferences we draw from these are connected with them by mathematical demonstration, and are accessible to all who are acquainted with the theory of spherics.

• See Note (H.)

In physical astronomy, the law of gravitation becomes also a principle or datum in our reasonings; but as in the celestial phenomena, it is disengaged from the effects of the various other causes which are combined with it near the surface of our planet, this branch of physics, as it is of all the most sublime and comprehensive in its objects, so it seems, in a greater degree than any other, to open a fair and advantageous field for mathematical ingenuity.

In the instances which have been last mentioned, the evidence of our conclusions resolves ultimately not only into that of sense, but into another law of belief formerly mentioned; that which leads us to expect the continuance, in future, of the established order of physical phenomena. A very striking illustration of this presents itself in the computations of the astronomer; on the faith of which he predicts, with the most perfect assurance, many centuries before they happen, the appearances which the heavenly bodies are to exhibit. The same fact is assumed in all our conclusions in natural philosophy; and something extremely analogous to it in all our conclusions concerning human affairs. They relate, in both cases, not to necessary connections, but to probable or contingent events; of which (how confidently soever we may expect them to take place), the failure is by no means perceived to be impossible. Such conclusions, therefore, differ essentially from those to which we are led by the demonstrations of pure mathematics, which not only command our assent to the theorems they establish, but satisfy us that the contrary suppositions are absurd.

These examples may suffice to convey a general idea of the distinction between demonstrative and probable evidence; and I purposely borrowed them from sciences where the two are brought into immediate contrast with each other, and where the authority of both has hitherto been equally undisputed.

Before prosecuting any farther the subject of probable evidence, some attention seems to be due, in the first place, to the grounds of that fundamental supposition on which it proceeds, the stability of the order of nature. Of this important subject, accordingly, I propose to treat at some length.

II.

Continuation of the Subject. Of that Permanence or Stability in the Order of Nature, which is presupposed in our Reasonings concerning Contingent Truths.

I HAVE already taken notice of a remarkable principle of the mind, (whether coëval with the first exercise of its powers, or the gradual result of habit, it is not at present material to inquire), in consequence of which, we are irresistibly led to apply to future events, the results of our past experience. In again resuming the subject, I do not mean to add any thing to what was then stated concerning the origin or the nature of this principle; but shall confine myself to a few reflections on that established order in the succession of events, which it unconsciously assumes

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as a fact; and which, if it were not real, would render human life a continued series of errors and disappointments. In any incidental remarks that may occur on the principle itself, I shall consider its existence as a thing universally acknowledged, and shall direct my attention chiefly to its practical effects ;-effects which will be found to extend equally to the theories of the learned, and to the prejudices of the vulgar. The question with regard to its origin is, in truth, a problem of mere curiosity; for of its actual influence on our belief, and on our conduct, no doubts have been suggested by the most sceptical writers.

Before entering, however, upon the following argument, it may not be superfluous to observe, with respect to this expectation, that, in whatever manner it at first arises, it cannot fail to be mightily confirmed and strengthened by habits of scientific research; the tendency of which is to familiarize us more and more with the simplicity and the uniformity of physical laws, by gradually reconciling with them, as our knowledge extends, those phenomena which we had previously been disposed to consider in the light of exceptions. It is thus that, when due allowances 'are made for the different circumstances of the two events, the ascent of smoke appears to be no less a proof of the law of gravitation than the fall of a stone. This simplification and generalization of the laws of nature is one of the greatest pleasures which philosophy yields; and the growing confidence with which it is anticipated, forms one of the chief incentives to philosophical pursuits. Few experiments perhaps, in physics, af ford more exquisite delight to the novice, or throw a stronger

light on the nature and object of that science, than when he sees, for the first time, the guinea and the feather drop together in the exhausted receiver.

In the language of modern science, the established order in the succession of physical events is commonly referred (by a sort of figure or metaphor) to the general laws of nature. It is a mode of speaking extremely convenient from its conciseness, but is apt to suggest to the fancy a groundless, and indeed absurd analogy between the material and the moral worlds. As the order of society results from the laws prescribed by the legislator, so the order of the universe is conceived to result from certain laws established by the Deity. Thus, it is customary to say, that the fall of heavy bodies towards the earth's surface, the ebbing and flowing of the sea, and the motions of the planets in their orbits, are consequences of the law of gravitation. But although, in one sense, this may be abundantly accurate, it ought always to be kept in view, that it is not a literal but a metaphorical statement of the truth; a statement somewhat analogous to that poetical expression in the sacred writings, in which God is said "to have given his decree to the seas, that they should not pass his commandment." In those political associations from which the metaphor is borrowed, the laws are addressed to rational and voluntary agents, who are able to comprehend their meaning, and to regulate their conduct accordingly; whereas, in the material universe, the subjects of our observation are understood by all men to be unconscious and passive, (that is, are understood to be unchangeable in their state, without the influence of some foreign and external

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