of this Section, I have not lost sight of the inquiry which occasioned it.

I.-1. It was already remarked, that the natural powers of Memory, together with that instinctive anticipation of the future from the past, which forms one of the original principles of the mind, are sufficient to enable infants, after a very short experience, to preserve their animal existence. The laws of nature, which it is not so important for us to know, and which are the objects of philosophical curiosity, are not so 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 circumstances, which we have no opportunity of seeing 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 spontaneously to our observation.

2. There are, too, some instances, particularly in the case of the astronomical phenomena, in which events that appear to common observers to be altogether 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 our attention to particulars, we do not observe the same 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 respect to futurity. It is thus that we can pronounce, with much greater confidence, concerning the proportion of deaths which shall 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 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 depending 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 seldom to be traced without previous habits of philosophical inquiry. Many such similarities or connexions, however, 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 relations. When we demonstrate that the angle at the centre of a circle is double of the angle at the circumference on the same base, we ascertain a relation between two quantities. When we demonstrate 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 accessible 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 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 existing 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 Huygens, 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 reflection, to search for the relation between the angles of incidence and refraction, (in

the case of light passing from one medium into another,) in the angles themselves; and that some of them, finding this inquiry unsuccessful, took the trouble to determine, by experiments, (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 themselves 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.1

II. Having now endeavoured to shew how much philosophy contributes to extend our knowledge of facts, by aiding our

1 [It was in this manner, undoubtedly, that the Chaldean Saros was discovered. This period brings back the moon almost exactly into the same situation with respect to the sun, her node, and her apogee; and, of consequence, the phenomena which depend on the combined motions of these two bodies are nearly repeated over again in the same order. "Defectus solis ac lunæ,"

VOL. II.

says Pliny, "ducentis viginti et tribus mensibus redire in orbem compertum est." Modern astronomers have pointed out some small corrections that this cycle requires; but if only the more considerable eclipses were attended to, a cycle of 223 lunations might maintain its credit long enough to be thought perpetual.]

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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 a 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 recollection 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 we are already acquainted with, but it is only from the laws of nature which have been traced analytically from facts, that we can venture with safety to deduce consequences by reasoning a priori. An example will illustrate and confirm this observation.

Suppose that a glass tube, thirty inches long, is filled with mercury, excepting eight inches, and is inverted as in the Torricellian experiment, so that the eight inches of common air may rise to the top, and that I wish to know at what height the mercury will remain suspended in the tube, the barometer being at that time twenty-eight inches high. There is here a combination of different laws, which it is necessary to attend to, in order to be able to predict the result:-1. The air is a heavy fluid, and the pressure of the atmosphere is measured by the column of mercury in the barometer. 2. The air is an elastic fluid, and its elasticity at the earth's surface (as it resists the pressure of the atmosphere) is measured by the column of mercury in the barometer. 3. In different states, the elastic force of the air is reciprocally as the spaces which it occupies. But, in this experiment, the mercury which remains suspended in the tube, together with the elastic force of the air in the top of the tube, is a counterbalance to the pressure of the atmosphere, and therefore their joint effect must be equal to the