APPENDIX. No. I.-Page 50. [Extracted, by permission, from the Preliminary Treatise of the Library of Useful Knowledge; On the Objects, Advantages, and Pleasures of Science.] THE illustrations of the argument which it is the object of this part of the author's Address to exhibit, which may be deduced from the consideration of the organic structures and habits of animals, &c. have been so concisely and excellently stated in the very useful treatise above cited, that I am truly gratified in having obtained permission to enrich my Address with the following extract; being fully persuaded that thereby I shall greatly increase its utility to the collegiate class to which it is essentially and principally dedicated*. "For the purpose of further illustrating the advantages of Philosophy, its tendency to enlarge the mind, as well as to interest it agreeably, and afford pure and solid gratification, a few instances may be given of the singular truths brought to * On the same subject I would particularly recommend to the attention of the class the very interesting Treatise on Animal Mechanics by Dr. Olinthus Gregory, which forms a part of the series of publications by the same Society. light by the application of mathematical, mechanical, and chemical knowledge to the habits of animals and plants; and some examples may be added of the more ordinary and easy, but scarcely less interesting observations, made upon those habits, without the aid of the profounder sciences. "We may remember the curve line which mathematicians call a cycloid. It is the path which any point of a circle, moving along a plane, and round its centre, traces in the air; so that the nail on the felly of a cart-wheel moves in a cycloid, as the cart goes along, and as the wheel itself both turns round its axle, and is carried along the ground. Now this curve has certain properties of a peculiar and very singular kind with respect to motion. One is, that if any body whatever moves in a cycloid by its own weight or swing, together with some other force acting upon it, it will go through all distances of the same curve in exactly the same time; and, accordingly, pendulums are contrived to swing in such a manner, that they shall describe cycloids, or curves very near cycloids, and thus move in equal times, whether they go through a long or a short part of the same curve. Again, if a body is to descend from any one point to another, not in the perpendicular, by means of some force acting on it together with its weight, the line in which it will go the quickest of all will be the cycloid, not the straight line, though that is the shortest of all lines which can be drawn between the two points; nor any other curve whatever, though many are much flatter, and therefore shorter than the cycloid, but the cycloid, which is longer than they, is yet of all curves or straight lines which can be drawn, the one the body will move through in the shortest time. Suppose the body is to move from one point to another, by its weight and some other force acting together, but to go through a certain space, as a hundred yards, the way it must take to do this in the shortest time possible is by moving in a cycloid; or the length of a hundred yards must be drawn into a cycloid, and then the body will descend through the hundred yards in a shorter time than it could go the same distance in any other path whatever. Now, it is believed that birds which build in the rocks, drop or fly down from height to height in this course. It is impossible to make very accurate observations on their flight and path; but there is a general resemblance certainly between the course they take and the cycloid, which has led ingenious men to adopt this opinion. "If we have a certain quantity of any substance, a pound of wood, for example, and would fashion it in the shape to take the least room, we must make a globe of it; it will in this figure have the smallest surface. But suppose we want to form the pound of wood, so that in moving through the air or water it shall meet with the least possible resistance, then we must lengthen it out for ever, till it becomes not only like a long-pointed pin, but thinner and thinner, longer and longer, till it is quite a straight line, and has no perceptible breadth or thickness at all. If we would dispose of the given quantity of matter so that it shall have a certain length only, say a foot, and a certain breadth at the thickest part, say three inches, and move through the air or water with the smallest possible resistance which a body of those dimensions can meet, then we must form it into a figure of a peculiar kind, called the Solid of least resistance, because of all the shapes that can be given to the body, its length and breadth remaining the same, this is the one which will make it move with the least resistance through the air, or water, or other fluid. A very difficult chain of mathematical reasoning, by means of the highest branches of algebra, leads to a knowledge of the curve, which by revolving on its axis makes a solid of this shape, in the same way that a circle by so revolving makes a sphere or globe; and the curve certainly resembles closely the face or head part of a fish. Nature, therefore (by which we always mean the Divine Author of nature), has fashioned these fishes so, that, according to mathematical principles, they swim the most easily through the element they live and move in. 66 Suppose upon the face part of one of these fishes a small insect were bred, endowed with faculties sufficient to reason upon its condition, and upon the motion of the fish it belonged to, but never to have discovered the whole size and shape of the face part, it would certainly complain of the form as clumsy, and fancy that it could have made the fish so as to move with less resistance. Yet if the whole shape were disclosed to it, and it could discover the principle on which that shape was preferred, it would at once perceive, not only that what had seemed clumsy was skilfully contrived, but that if any other shape whatever had been taken, there would have been an error committed; nay, that there must of necessity have been an error; and that the very best possible arrangement had been adopted. So it may be with man in the Universe, where, seeing only a part of the great system, he fancies there is evil; and yet, if he were permitted to survey the whole, what had seemed imperfect might appear to be necessary for the general perfection, insomuch that any other arrangement, even of that seemingly imperfect part, must needs have rendered the whole less perfect. The common objection is, that what seems evil might have been avoided; but in the case of the fish's shape it could not have been avoided. "It is found by optical inquiries, that the rays or particles of light, in passing through transparent substances of a certain form, are bent to a point where they make an image or picture of the shin ing bodies they come from, or of the dark bodies they are reflected from. Thus, if a pair of spectacles be held between a candle and the wall, they make two images of the candle upon it; and if they be held between the window and a sheet of paper when the sun is shining, they will make a picture on the paper of the houses, trees, fields, sky, and clouds. The eye is found to be composed of several natural magnifiers which make a picture on a membrane at the back of it, and from this membrane there goes a nerve to the brain, conveying the impression of the picture, by means of which we see it. Now, white light was discovered by Newton to consist of different-coloured parts, which are differently bent in passing through transparent substances, so that the lights of dif |