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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 ainong 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 leit, by the analogy of the law of reflection, to search for the relation, beiween the angles of incidence and refraction, (in the case of light passing froin one medium into another,) in the angles themselves; and that some of them, finding this inquiry unsuccessful, took the trouble to determine, by experiinents, (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 froin 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 endeavored to show 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 a comparatively sınall 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 facilitale the recollection of facts, in the same manner in which the

* It was in this manner undoubtedly, that the Chaldean Saros was discovered. This period brings back the moon alınost 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," says Pliny, is ducentis vis inti et tribus inensibus redire in orbem, compertum est. Modern astronomers i ave pointed out some small correction that this cycle requires; but if only the more considerable eclipses were attended to, a cycle of 223 lunations mighi maintain its credit long enough to be thought perpetual.

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 froin facts, that we can venture, with safety, to deduce consequences by reasoning à 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 difierent 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 eartli'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 pressure of a column of mercury twenty-eight inches high. Hence we obtain an algebraical equation, which affords an easy solution of the problem. It is further evident, that my knowledge of the physical laws which are here combined, puts it in my power to foretel the result, not only in this case, but in all the cases of a similar nature which can be supposed. The problem, in any particular instance, might be solved by making the experiment; but the result would be of no use to me if the slightest alteration were made on the data.

It is in this manner that philosophy, by putting us in possession of a few general facts, enables us to determine, by reasoning, what will be the result of any supposed combination of them, and thus to comprehend an infinite variety of particulars, which no memory, however vigorous, would have been able to retain. In consequence of the knowledge of such general facts, the philosopher is relieved from the necessity of treasuring up in bis inind all those truths which are involved in his principles, and which may be deduced fron thein by reasoning; and he can often prosecute his discoveries synthetically in those parts of the universe which he has no access to examine by immediate observation. There is, therefore, this important difference between the hypothetical theory and a theory obtained by induction; that the latter not only enables us to remember the facts we already know, but to ascertain, by reasoning, many facts which we have never had an opportunity of examining : whereas when we reason from a hypothesis à priori, we are almost certain of running into error; and, consequently, whatever may be its use to the memory, it can never be trusted to in judging of cases which have not previously fallen within our experience.

There are some sciences, in which hypothetical theories are more useful than in others; those sciences, to wit, in which we have occasion for an extensive knowledge and a ready recollection of facts, and which, at the sanie time, are yet in too imperfect a state to allow us to obtain just theories by the method of induction. This is particularly the case in the science of medicine, in which we are under a necessiiy to apply our knowledge, such as it is, to practice. It is also, in some degree, the case in agriculture. In the merely speculative parts of physic and chemistry, we may go on patiently accumulating facts, without forming any one conclusion, farther than our facts authorize us: and leave to posterity the credit of establishing the theory to which our labors are subservient. But in medicine, in which it is of consequence to have our knowledge at command, it seems reasonable to think, that hypothetical theories may be used with advantage; provided always, that they are considered merely in the light of artificial memories, and that the student is prepared to lay them aside, or to correct them, in proportion as his knowledge of nature becomes more extensive. I am, indeed, ready to confess, that this is a caution which it is more easy to give than to follow: for it is painful to change any of our habits of arrangement, and to relinquish those systems in which we have been educated, and which have long flattered us with an idea of our own wisdom. Dr. Gregory mentions (Lectures on the Duties and Qualifications of a Physician) it as a striking and distinguishing circumstance in the character of Sydenham, that, although full of hypothetical reasoning, it did not render him the less attentive to observation ; and that his hypotheses seems to have sat so loosely about him, that either they did not influence his practice at all, or he could easily abandon them, whenever they would not bend to his experience.

SECTION V.

Continuation of the same subject.Effects produced on the Memory

by committing to Writing our acquired Knowledge.

Having treated at considerable length of the improvement of memory, it may not be improper, before leaving this part of the subject, lo consider what effects are likely to be produced on the mind by the practice of committing to writing our acquired knowledge. That such a practice is unfavorable, in some respects, to the faculty of memory, by superseding, to a certain degree, the necessity of its exertions, has been often remarked, and I believe is true; but the advantages with which it is attended in other respects, are so iinportant, as to overbalance greatly this trifling inconvenience.

It is not my intention at present tu examine and compare together the different methods which have been proposed, of keeping a common place book. In this, as in other cases of a similar kind, it may be difficult, perhaps, or impossible, to establish any rules which will apply universally. Individuals must be left to judge for themselves, and to adapt their contrivances to the particular nature of their literary pursuits, and to their own peculiar habits of association and arrangement. The remarks which I am to offer are very general, and are intended merely to illustrate a few of the advantages which the art of writing affords to thie philosopher, for recording, in the course of his progress through life, the results of his speculations, and the fruits of his experience.

The utility of writing, in enabling one generation to transmit its discoveries to another, and in thus giving rise to a gradual progress in the species, has been sufficiently illustrated by many authors. Lilile attention, however, has been paid to another of its effects, which is no less important; I mean to the foundation which inlays for a perpetual progress in the intellectual powers of the individual.

It is to experience, and to our own reflections, that we are indebted for by far the most valuable part of our knowledge ; and hence it is, that although in youth the imagination may be more vigorous, and the genius more original, than in advanced years; yet, in the case of a man of observation and inquiry, the judgment may be expected, at least as long as his faculties remain in perfection, to become every day sounder and more enlightened. It is, however, only by the constant practice of writing, that the results of our experience, and the progress of our ideas, can be accurately recorded. If they are trusted merely to the memory, they will gradually vanish from it like a dream, or will come in tine to be so blended with the suggestions of imagination, that we shall not be able to reason from them with any degree of confidence. What improvements in science might we not flatter ourselves with the hopes of accomplishing, had we only activity and indusiry to treasure up every plausible bint that occurs 10 us! Hardly a day passes, when many such do not occur to ourselves, or are suggested by others; and detached and insulated as they may appear at present, some of them may perhaps afierwards, at the distance of years, furnish the key-stone of an important system.

But it is not only in this point of view that the philosopher derives advantage from the practice of writing. Without iis assistance he could seldom be able to advance beyond those simple elementary truths which are current in the world, and which forin,

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