which he is unable to account, of the uniformity of the laws of nature. There are, however, two important refpects, which diftinguifh the knowledge he poffeffes from that of ordinary men. In the firft place, it is far more extensive, in confequence of the affiftance which fcience gives to his natural powers of invention and difcovery. Secondly, it is not only more easily retained in the memory, and more conveniently applied to use, in confequence of the manner in which his ideas are arranged; but it enables him to ascertain, by a process of reasoning, all those truths which may be fynthetically deduced from his general principles. The illuftration of these particulars will lead to fome useful remarks; and will at the fame time fhew, that, in difcuffing the fubject of this Section, I have not loft fight of the inquiry which occafioned it.

I. 1. It was already remarked, that the natural powers of Memory, together with an inftinctive anticipation of the future from the paft, which forms one of the original principles of the mind, are fufficient to enable infants, after a very fhort experience, to preserve their animal existence. The laws of nature, which it is not fo important for us to know, and which are the objects of philofophical curiofity, are not fo obviously exposed to our view, but are, in general, brought to light by means of experiments which are made for the purpose of discovery; or, in other words, by artificial combinations of circumftances, which we have no opportunity of feeing conjoined in the course of our ordinary experience. In this manner, it is evident, that many connexions may be ascertained, which would never have occurred fpontaneously to our observation.

2. There are, too, fome inftances, particularly in the cafe of the aftronomical phenomena, in which event, that appear to common obfervers to be altogether anomalous, are found, upon a more accurate

and continued examination of them, to be fubjected to a regular law. Such are those phenomena in the heavens, which we are able to predict by means of Cycles. In the cases formerly described, our knowledge of nature is extended by placing her in new fituations. In these cafes, it is extended by continuing our obfervations beyond the limits of ordinary curiofity.

3. In the cafe of human affairs, as long as we confine our attention to particulars, we do not obferve the fame uniformity, as in the phenomena of the material world. When, however, we extend our views to events which depend on a combination of different circumftances, fuch a degree of uniformity appears, as enables us to establish general rules, from which probable conjectures may often be formed with respect to futurity. It is thus, that we can pronounce, with much greater confidence, concèrning the proportion of deaths which fhall happen in a certain period among a given number of men, than we can predict the death of any individual; and that it is more reasonable to employ our fagacity, in fpeculating concerning the probable determinations of a uumerous fociety, than concerning events which depend on the will of a fingle perfon.

In what manner this uniformity in events depending on contingent circumftances is produced, I fhall not inquire at prefent. The advantages which we derive from it are obvious, as it enables us to collect, from our past experience, many general rules, both with refpect to the hiftory of political focieties, and the characters and conduct of men in private life.

4. In the laft place; the knowledge of the philof opher is more extensive than that of other men, in confequence of the attention which he gives, not merely to objects and to events, but to the relations which different objects and different events bear to each other.

The obfervations and the experience of the vulgar are almost wholly limited to things perceived by the fenfes. A fimilarity between different objects, or between different events, roufes their curiofity, and leads them to claffification, and to general rules. But a fimilarity between different relations, is feldom to be traced without previous habits of philofophical inquiry. Many fuch familiarities or connections, however, are to be found in nature; and when once they are ascertained, they frequently lead to important discoveries; not only with refpect to other relations, but with refpect to the objects or to the events which are related. These remarks it will be neceffary to illuftrate more particularly.

The great object of Geometry is to afcertain the relations which exift between different quantities, and the connections which exift between different relations. When we demonftrate, that the angle at the centre of a circle is double of the angle at the circumference on the fame base, we afcertain a relation between two quantities. When we demonftrate, that triangles of the fame altitude are to each other as their bafes, we afcertain a connection between two relations. It is obvious, how much the mathematical sciences must contribute to enlarge our knowledge of the universe, in confequence of fuch difcoveries. In that fimpleft of all proceffes of practical geometry, which teaches us to meafure the height of an acceffible tower, by comparing the length of its shadow with that of a staff fixed vertically in the ground, we proceed on the principle, that the relation between the fhadow of the staff and the height of the ftaff is the fame with the relation between the fhadow of the tower and the height of the tower. But the former relation we can afcertain by actual measurement; and, of confequence, we not only obtain the other relation; but, as we can measure one of the A Aa

related quantities, we obtain also the other quantity. In every cafe in which mathematics aflifts us in meaturing the magnitudes or the diftances of objects, it proceeds on the fame principle; that is, it begins with ascertaining conections among different relations, and thus enables us to carry our inquiries from facts which are exposed to the examination of our fenfes, to the most remote parts of the universe. I obferved also, that there are various relations exifting among physical events, and various connections exifting among these relations. It is owing to this circumftance, that mathematics is so useful an inftrument in the hands of the phyfical inquirer. In that beautiful theorem of Huyghens, which demonstrates, that the time of a complete oscillation of a pendulum in the cycloid, is to the time in which a body would fall through the axis of the cycloid, as the circumference of a circle is to its diameter, we are made acquainted with a very curious and unexpected connection between two relations; and the knowledge of this connexion facilitates the determination of a moft important fact with refpect to the descent of heavy bodies near the earth's surface, which could not be afcertained conveniently by a direct experiment.

In examining, with attention, the relations among different phyfical events, and the connexions among different relations, we fometimes are led by mere induction to the discovery of a general law; while, to ordinary obfervers, nothing appears but irregularity. From the writings of the earlier opticians we learn, that, in examining the firft principles of dioptrics, they were led, by the analogy of the law of reflexion, to fearch for the relation between the angles of incidence and refraction, (in the cafe of light paffing from one medium into another,) in the angles themselves; and that fome of them, finding this inquiry unfuccefsful, took the trouble to deter

mine, by experiments, (in the cafe of the media which most frequently fall under confideration,) the angle of refraction correfponding to every minute of incidence. Some very laborious tables, deduced from fuch experiments, are to be found in the works of Kircher. At length, Snelius difcovered what is now called the law of refraction, which comprehends their whole contents in a single sentence.

The law of the planetary motions, deduced by Kepler, from the obfervations of Tycho Brahe, is another ftriking illuftration of the order, which an attentive enquirer is fometimes able to trace, among the relations of phyfical events, when the events themselves appear, on a fuperficial view, to be perfectly anomalous.

Such laws are, in fome refpects, analogous to the cycles which I have already mentioned; but they differ from them in this, that a cycle is, commonly, deduced from obfervations made on physical events which are obvious to the fenfes: whereas the laws we have now been confidering, are deduced from an examination of relations which are known only to men of science. The moft celebrated aftronomical cycles, accordingly, are of a very remote antiquity, and were probably discoverd at a period, when the study of aftronomy confifted merely in accumulating and recording the more ftriking appearances of the heavens.

II. Having now endeavored to fhew, how much philofophy contributes to extend our knowledge of facts, by aiding our natural powers of invention and discovery, I proceed to explain, in what manner it fupercedes the neceffity of studying particular truths, by putting us in poffeffion of a comparatively fmall number of general principles in which they are involved.

I already remarked the affiftance which philofophy gives to the memory, in confequence of the ar