fellow men, which the most renowned destroyer of his race might envy. The counsels of such a man, in his retirement and meditation, are worth listening to. I am sure you will think I bring this lecture to the best conclusion, by repeating a sentence from one of his moral works: : "I envy," says he, "no quality of the mind or intellect in others; not genius, power, wit or fancy; but if I could choose what would be most delightful, and I believe most useful to me, I should prefer A FIRM RELIGIOUS BELIEF to every other blessing." *12* OBJECTS, ADVANTAGES, AND PLEASURES OF SCIENCE. I. Mathematical Science. INTRODUCTION. In order fully to understand the advantages and the pleasures which are derived from an acquaintance with any science, it is necessary to become acquainted with that science, and it would therefore be impossible to convey a complete knowledge of the benefits conferred by a study of the various sciences which have hitherto been chiefly cultivated by philosophers, without teaching all the branches of them. But a very distinct idea may be given of those benefits, by explaining the nature and objects of the different sciences; it may be shown by examples how much use and gratification there is in learning a part of any one oranch of knowledge; and it may thus be inferred, how great reason there is to learn the whole. It may be easily demonstrated, that there is an advantage in learning, both for the usefulness and the pleasure of it. There is something positively agreeable to all men, to all at least whose nature is not most grovelling and base, in gaining knowledge for its own sake. When you see any thing for the first time, you at once derive some gratification from the sight being new; your attention is awakened, and you desire to know more about it. If it is a piece of workmanship, as an instrument, a machine of any kind, you wish to know how it is made; how it works; and what use it is of. If it is an animal, you desire to know where it comes from; how it lives; what are its dispositions, and, generally, its nature and habits. This desire is felt, too, without at all considering that the machine or the animal may ever be of the least use to yourself practically; for, in all probability, you may never see them again. But you feel a curiosity to learn all about them, because they are new and unknown to you. You accordingly make inquiries; you feel a gratification in getting answers to your questions, that is, in receiving information, and in knowing more,-in being better informed than you were before. If you ever happen again to see the same instrument or animal, you find it agreeable to recollect having seen it before, and to think that you know something about it. If you see another instrument or animal, in some respects like, but differing in other particulars, you find it pleasing to compare them together, and to note in what they agree, and in what they differ. Now, all this kind of gratification is of a pure and disinterested nature, and has no reference to any of the common purposes of life; yet it is a pleasure-an enjoyment. You are nothing the richer for it; you do not gratify your palate or any other bodily appetite; and yet it is so pleasing that you would give something out of your pocket to obtain it, and would forego some bodily enjoyment for its sake. The pleasure derived from science is exactly of the like nature, or, rather, it is the very same. For what has just been referred to is in fact Science, which in its most comprehensive sense only means Knowledge, and in its ordinary sense means Knowledge reduced to a system; that is, arranged in a regular order so as to be conveniently taught, easily remembered, and readily applied. The practical uses of any science or branch of knowledge are undoubtedly of the highest importance; and there is hardly any man who may not gain some positive advantage in his worldly wealth and comforts, by increasing his stock of information. But there is also a pleasure in seeing the uses to which knowledge may be applied, wholly independent of the share we ourselves may have in those practical benefits. It is pleasing to examine the nature of a new instrument, or the habits of an unknown animal, without considering whether they may be of use to ourselves or to any body. It is another gratification to extend our inquiries, and find that the instrument or animal is useful to man, even although we have no chance ourselves of ever benefitting by the information; as, to find that the natives of some distant country employ the animal in travelling;-nay, though we have no desire of benefitting by the knowledge; as, for example, to find that the instrument is useful in performing some dangerous surgical operation. The mere gratification of curiosity; the knowing more today than we knew yesterday; the understanding what before seemed obscure and puzzling; the contemplation of general truths, and the comparing together of different things, is an agreeable occupation of the mind; and, beside the present enjoyment, elevates the faculties above low pursuits, purifies and refines the passions, and helps our reason to assuage their violence. It is very true, that the fundamental lessons of philosophy may to many at first sight wear a forbidding aspect, because to comprehend them requires an effort of the mind somewhat, though certainly not much, greater than is wanted for understanding more ordinary matters; and the most important branches of philosophy, those which are of the most general application, are for that very reason the less easily followed, and the less entertaining when apprehended, presenting as they do few particulars and individual objects to the mind. In discoursing of them, moreover, no figures will be at present used to assist the imagination; the appeal is made to reason, without help from the senses. But be not therefore prejudiced against the doctrine, that the pleasure of learning the truths which philosophy unfolds is truly above all price. Lend but a patient attention to the principles explained, and giving us credit for stating nothing which has not some practical use belonging to it, or some important doctrine connected with it, you will soon perceive the value of the lessons you are learning, and begin to interest yourselves in comprehending and recollecting them; you will find that you have actually learnt something of science, while "merely engaged in seeing what its end and purpose is; you will be enabled to calculate for yourselves, how far it is worth the trouble of acquiring, by examining samples of it; you will, as it were, taste a little to try whether or not you relish it, and ought to seek after more; you will enable yourselves to go on, and enlarge your stock of it; and after having first mastered a very little, you will proceed so far as to look back with wonder at the distance you have reached beyond your earliest acquirements. The Sciences may be divided into three great classes: those which relate to Number and Quantity, those which relate to Matter, and those which relate to Mind. The first are called the Mathematics, and teach the properties of numbers and of figures; the second are called Natural Philosophy, and teach the properties of the various bodies which we are acquainted with by means of our senses; the third are called Intellectual or Moral Philosophy, and teach the nature of the mind, of the existence of which we have the most perfect evidence in our own reflections; or, in other words, the moral nature of man, both as an individual and as a member of society. Connected with all the sciences, and subservient to them, though not one of their number, is History, or the record of facts relating to all kinds of knowledge. I. The two great branches of the Mathematics, or the two mathematical sciences, are Arithmetic, the science of |