xvi INTRODUCTORY DISCOURSE OF THE 



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 move in a cycloid by its own weight or 

 swing, together with some other force acting upon it all the while, it will go through all distances of the 

 same curve in exactly the same time; and, accordingly, pendulums have sometimes been 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 il< 

 from any one poiut to any other, 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 ninny are much flatter, and therefore shorter than the cycloid but the cycloid, which ia longer than 

 many of them, is yet, of all curved or straight lines which can be drawn, the one the body will move through 

 in the shortest time. Suppose, again, that 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, ia 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, as the 

 Eagle, which build in the rocks, drop or fly down from height to height in this course. It is impossible to 

 make very accurate observations of their flight and path ; but there is a general resemblance 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, aud 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 inehen, 

 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 aud 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.* 



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. Tet 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 bo with man in the 

 universe, where, seeing only a part of the great system, he fancies there is evil; and yet, if he wore 

 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 particles or rays 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 shining 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 make a picture on the paper of the houses, trees, field*, 

 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, convevim; 

 the impression of the picture, by means of which we see. Now, white light was discovered by .Newton 

 * 'Hie feathers of the wings of birds are found to be placed at the belt pottiblt angle for helping on the bird by their action on 



