sistence and the safety of mankind. It is by the modern improvements in agriculture and navigation, added to the invention of gunpowder, that the barbarous have ceased to be formidable to the civilized nations; and that the race of Europeans, or rather of Britons, promises to extend itself over the fairest portions of the habitable globe.

I mentioned Mathematics as a third branch of knowledge. Strictly speaking, perhaps it can scarcely be accounted a branch of science, or a department of the study of Nature; being rather an art which is subservient to the acquisition of physical science. It is the art of comparing dexterously, or, as it is called, of measuring the quantities of bodies. This art of comparing the magnitude, weight, and number of bodies, was brought to considerable perfection at a very early period; because mankind have daily occasion to exercise a certain degree of it, and because very little knowledge of Nature is necessary for the study of it. After the first steps, it is carried on by imagining new figures and quantities, and by contemplating their resemblance or difference, and the ways in which they may be compared. The object, therefore, which a mathematician studies is not truth, or things actually existing in Nature, but imaginary objects, contrived to resemble and to facilitate the comparison of those that really exist.

From misunderstanding the object of mathema tics, and the points about which they are conver sant, it has become a sort of fashion to speak of mathematical certainty, mathematical accuracy; and mathematical precision; as if truth were ascertained with greater correctness in this than in any other branch of human inquiry-a supposition which is altogether erroneous. A mathematician imagines or supposes the existence of perfect circles, perfect globes, squares, cubes, and triangles; though Nature never produced any such objects. His whole facts are imaginary. When he reasons concerning a lever, he means a straight line, which is perfectly inflexible, and which is of no breadth or thickness. His ropes are straight lines, which are perfectly flexible. He argues about the properties of his imaginary figures, and the operations of his imaginary instruments; and he no doubt forms conclusions or inferences which are perfectly correct: for this reason, that he has got the premisses of his own making, and is not hampered by the consideration of the irregular figures which Nature has produced. When mathematicians, however, come to reduce their speculations to practice, their art is found to have no higher certainty than any other; for let a dozen of them in succession be turned into a field which is surrounded by irregular lines, and no two of them will give the

same precise report of its dimensions. Of this the courts of law have ample experience. I have known a piece of work measured by judicial authority six several times by as many artists, whose probity was not impeached, before the amount of the tradesman's account could be fixed. After all no certainty was obtained: But the judges, who were bound by their duty to bring the dispute to a close, adopted the last measurement; because it happened to correspond tolerably with the first, and no two others had such a resemblance. In like manner, when applied to mechanics, the rules of mathematics are equally defective. The ropes which human skill produces are found to be very different from the imaginary flexible lines of the mathematician. They are stiff and bulky; and the operation of the lever is, in like manner, in practice obstructed by friction; so that, without the aid of experience, nothing can be done. Were men of science in other departments to proceed like mathematicians, they also could form conclusions, which would be equally precise and certain. A moralist, for example, might imagine or suppose the existence of a man possessed of perfect wisdom and perfect self-command; he might suppose this wise man engaged in a most important pursuit, upon the result of which depended the welfare of thousands; he might next suppose that somebody

should be idle enough to to this perfect being a bribe of L. 100 to desist from his purpose-it is evident, that no conclusion in all mathematics is more certain than that which the moralist might here make; and that it would be as impossible to move his imaginary virtuous being by a bribe of L. 100, as to bend an inflexible lever with the force of a pound weight. In short, where reasoners have the premises of their own making, it is their own fault if their conclusions are incorrect.

By speculating, however, about the properties of imaginary figures, such as globes, cylinders, and cubes, men become better qualified for comparing or measuring the less perfect figures which actually exist in Nature, or can be fashioned by human art. Thus the mathematics form a very valuable but subordinate and artificial branch of knowledge, from which great aid is derived in transacting business, and in arranging, comparing, and recollecting, the objects of Nature. The study of mathematics produces a considerable degree of command over the train of our ideas, as well as of acuteness of discrimination; and so far is attended with direct moral advantage. In other respects, however, this study is to be regarded rather as a step towards acquiring a knowledge of physical science, and a capacity for doing business with facility, than as forming any part of the investigation of what actually exists in the universe.

CHAP. VII.

OF INTELLECTUAL FATIGUE AND AMUSEMENT.

As it is impossible to do justice to the intellectual character of man, without occupying in its improvement as much as possible of the opportunity allotted by Providence for that purpose, that is, of our existence in this world, I shall here take some notice of the degree in which a suspension of the useful exertion of the intellectual powers seems necessary to the general welfare of the human constitution.

Those parts of our constitution which do not require the exertion of the will, never become weary or require rest: the heart beats, the blood and the aliment circulate, and the chest alternately expands and contracts to admit of breathing, without any necessity of rest; but the arms, the legs, the eyes, and all the organs of sense and of voluntary motion require periodical repose. A painful sensation, called Weariness, is, on such occasions produced; the proper reVOL. I.

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