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gether anomalous, are-found, upon a more accurate and continued examination of them, to be subjected 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 situations. In these cases, it is extended by continuing our observations beyond the limits of ordinary curiosity.
3. In the case of human affairs, as long as we confine cur 'attention to particulars, we do not observe 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 circumstances, such a degree of uniformity appears, as enables us to establish general rules, from which probable conjectures may often be formed with refpect to futurity. It is thus, that we can pronounce, with much greater confidence, concerning the proportion of deaths which shall happen in a certain pe. riod among a given number of men, than we can predict the death of any individual ; and that it is more reasonable to employ our sagacity, in speculating concerning the probable determinations of a numerous society, than concerning events which depend on the will of a single person.
In what manner this uniformity in events depend. ing on contingent circumstances is produced, I shall not inquire at present. The advantages which we derive from it are obvious, as it enables us to collect, from our past experience, many general rules, both with respect to the history of political societies, and the characters and conduct of men in private life.
4. In the last place; the knowledge of the philosopher is more extensive than that of other men, in consequence of the attention which he gives, not merely to objects and events, but to the relations which different objects and different events bear to each other.
The observations and the experience of the vulgar are almost wholly limited to things perceived by the senses. A similarity between different objects, or between different events, rouses their curiosity, and leads them to classification, and to general rules. But a similarity between different relations, is feldom to be traced without previous habits of philosophical inquiry. Many such similarities or connexions, how. ever, are to be found in nature ; and when once they are ascertained, they frequently lead to important discoveries ; not only with respect to other relations, but with respect to the objects or to the events which are related. These remarks it will be necessary to illustrate more particularly.
The great object of Geometry is to ascertain the relations which exist between different quantities, and the connexions which exist between different rela. tions. When we demonstrate, that the angle at the centre of a circle is double of the angle at the cir, cumference on the same base, we ascertain a relation between two quantities. When we demonftrate, that triangles of the same altitude are to each other as their bases, we ascertain a connexion between two relations. It is obvious, how much the mathematical sciences must contribute to enlarge our knowledge of the universe, in consequence of such discoveries. In
that simplest of all processes of practical geometry, which teaches us to measure the height of an accelfible tower, by comparing the length of its fhadow with that of a staff fixed vertically in the ground, we proceed on the principle, that the relation between the shadow of the staff and the height of the staff is the same with the relation between the shadow of the tower and the height of the tower. But the former relation we can ascertain by actual measurement; and, of consequence, we not only obtain the other relation ; but, as we can measure one of the related quantities, we obtain also the other quantity. In every case in which mathematics assists us in measuring the magnitudes or the distances of objects, it proceeds on the same principle; that is, it begins with ascertaining connexions among different relations, and thus enables us to carry our inquiries from facts which are exposed to the examination of our senses, to the most remote parts of the universe.
I observed also, that there are various relations ex. isting among physical events, and various connexions existing among these relations. It is owing to this circumstance, that mathematics is so useful an instrument in the hands of the physical 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 connexion between two relations; and the knowledge of this connexion facilitates the determination of a most
important fact with respect to the descent of heavy bodies near the earth's surface, which could not be ascertained conveniently by a direct experiment.
In examining, with attention, the relations among different physical events, and the connexions among different relations, we sometimes are led by mere induction to the discovery of a general law; while, to ordinary observers, nothing appears but irregularity. From the writings of the earlier opticians we learn, that, in examining the first principles of dioptrics, they were led, by the analogy of the law of reflexion, to search for the relation between the angles of incidence and refraction, in the case of light pafling from one medium into another,) in the angles themselves ; and that some of them, finding this inquiry unsuccessful, took the trouble to determine, by expe. riments, (in the case of the media which most frequently fall under consideration,) the angle of refraction corresponding to every minute of incidence. Some very laborious tables, deduced from such experiments, are to be found in the works of Kircher. At length, Snellius discovered 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 observations of Tycho Brahe, is another striking illustration of the order, which an attentive inquirer is sometimes able to trace, among the relations of physical events, when the events them. selves appear, on a superficial view, to be perfectly anomalous.
Such laws are, in some respects, analogous to the cycles which I have already mentioned; but they differ from them in this, that a cycle is, commonly, deduced from observations made on physical events which are obvious to the senses; whereas the laws we have now been considering, are deduced from an examination of relations which are known only to men of science. The most celebrated astronomical cycles, accordingly, are of a very remote antiquity, and were probably discovered at a period, when the study of astronomy consisted merely in accumulating and recording the more striking appearances of the heavens.
II. Having now endeavoured to shew, how much philosophy contributes to extend our knowledge of facts, by aiding our natural powers of invention and discovery, I proceed to explain, in what manner it supersedes the necessity of studying particular truths, by putting us in possession of fa comparatively small number of general principles in which they are involved.
I already remarked the assistance which philosophy gives to the memory, in consequence of the arrangement it introduces among our ideas. In this respect even a hypothetical theory may facilitate the recol. lection of facts; in the same manner in which the memory is aided in remembering the objects of natural history by artificial classifications.
The advantages, however, we derive from true philosophy, are incomparably greater than what are to be expected from any hypothetical theories. These, indeed, may assist us in recollecting the particulars