brought forward on many occafions, in the course of thefe Lectures.

That the action of oblique forces may be more ftrongly impreffed on your minds, I fhall exhibit two or three experiments, which you may extend at leisure. To this purpose here is a round table, to the edge of which you may fix any number of pullies, varying their direction at pleasure. By this I fhall now illuftrate the following propofition.

Two forces acting at once on a body in the direction of, and in quantity proportional to, the fides of the parallelogram, will be kept at rest, or counterpoifed, by a force oppofed to them in the direction of, and proportional to, the diagonal.

I place a circular paper upon the round table, fig. 5, pl. 3, fo that it's center may coincide with that of the table. Upon this paper a triangle, ABC, is delineated, whofe fides are to one another as 2, 3, and 4. Draw CE parallel to A B, and continue A C towards D.

I take three ftrings, which are joined in one point by a knot; and placing the point over C, I ftretch the ftrings over CD, CE, CB, and place the pullies T, T, T, to coincide with the direction of the ftrings: then putting the ftrings over their refpective pullies, at the end of the thread CD I fufpend a weight of four pounds, to CE three pounds, and to CF two pounds. Thefe weights will remain in equilibrio while the knot remains over C; but if it be removed out of that point, they will not be at reft.

It is evident from this experiment, as well as from what I have before mentioned to you, that power is always loft in the compofition of forces; for here a weight of three pounds, and another of two, only counterpoife a weight of four; confequently no motion produced by a compofition of

forces

forces can be lafting, unless thofe forces are perpe→ tually renewed.

With the fame apparatus you may perform a variety of experiments, with three, four, or five forces acting at once.

To illuftrate further the nature and application of this article, let A B, fig. 10, pl. 1, reprefent an artificial kite, kept up by the wind, blowing in the direction W C; by drawing the ftring AÏBIH, fixed at A and B, the kite will gain fuch a position, that HI produced will pafs through the center of gravity at C.

Draw CO perpendicular to BA, and DO perpendicular to the horizon HO. Then OC is the direction of the force of the wind that acts against the kite; and the force by which it is kept up, is as the fquare of the fine of the angle A CW, or COD. Now if DO reprefent the given weight of the kite, CO will be the force of the wind acting against it, and C D the force pulling at the ftring. The tail, EF, which generally has a small weight at E, keeps the head of the kite always towards the wind.

As the direction of the ftring always paffes through C, the angle, A CH, and confequently HCO, will be the fame at all altitudes, and the kite can never afcend fo high as to make the angle CHO equal to A CH. Hence it follows, that the smaller the angle H CO is made, the higher fhe will rife: the greater the wind, or the lighter the kite, the higher alfo it will rife.

The wings of a bird are fo conftructed, that in ftriking downwards they expand to their greatest, and become almoft two planes, being fomewhat hollow on the under fide. Thefe planes are not then horizontal, the back part, K, fig. 11, pl. 1, being higher than the fore part, DFG; but in moving the wings upward, to fetch a new ftroke,

they

they go with the edge, D, F, G, foremost, and the wings contract, and become hollow. Their bodies are fpecifically lighter than that of men and beafts; their bones and feathers extremely porous, hollow, and light; the mufcles which move the wing downwards are exceeding large, and have been estimated, in fome inftances, to be not lefs than a fixth part of the weight of the whole body. When a bird is on the ground, and intends to fly, he takes a large leap, and ftretches his wings right from the body, and strikes them downwards with great force, by which they are put into an oblique pofition; and the refiftance of the air acting ftrongly against them from the ftroke, impels them and the bird in a direction perpendicular to their planes; which is in an oblique direction, partly upwards, and partly horizontally forward. That part of the force tending upwards is destroyed by the weight of the bird; the horizontal force ferves to carry him forward. The ftroke being over, he moves his wings; which being contracted, and turning their edges upwards, meet with very little refiftance from the air. When they are fufficiently elevated, he takes a fecond stroke downwards, and the impulfe of the air again moves him forwards; and fo from one ftroke to another, which are only as fo many leaps taken in the air. When the bird wants to turn to the right or left, he ftrikes ftrongly with the oppofite wing, which impels him to the contrary fide. The tail a&ts like the rudder of a hip; except only that it moves them upwards or downwards, inftead of fideways. If the bird wants to rife, he puts the tail in the position IH; if to fall, in the pofition I I.: whilft in an horizontal pofition, it keeps him fteady. A bird can, by fpreading his wings, continue to move horizontally for fome time, without ftriking the air, because he has acquired a fufficient velocity and his wings being VOL. III. parallel

K

parallel to the horizon, meet with but a fmall re fiftance; and when he begins to fall, he can easily fleer himself upwards by his tail, till the motion he had acquired is nearly fpent, when he must renew it by two or three more ftrokes with his wings. On alighting, he expands his wings and tail full against the air, that they may meet with all the refiftance poffible. The center of gravity of a bird is rather behind the wings: to counterballance this, they thrust out their head and neck in flying.

It is impoffible, as already obferved, for men to fly by the strength of their arms. For their pectoral muscles are vaftly too weak: in a man, they are not one-fixtieth part of the muscles of the body; in a bird, they are more than all the others put together.

Some birds are faid to fly a thoufand yards in a minute.

A fif fwims by the help of his fins and tail, and fishes are nearly of the fame fpecific gravity with water. The mufcular force of the tail is very great their direct motion is obtained by moving the tail from one fide to the other with a vibrating motion. When going to move it, the fish turns the end oblique to the water, and moves it through it in that pofition. The water re-acts obliquely againft the tail, and moves him partly forward and partly laterally. The lateral motion is corrected by the next ftroke the contrary way, while the progreffive motion is continued. They exert a very great force with their tail. By the help of the tail they alfo turn on one fide; ftriking ftrongly with it on that fide, and keeping it bent, it acts like the rudder of a fhip. The fins of a fifh keep it upright, especially the belly fins, which act like two feet without these he would fwim with his belly upwards, as the center of gravity lies near the

back.

back. By contracting or expanding the fins, they alfo affift him in afcending and defcending: by inclining his tail obliquely, and turning it a little from an erect pofition to one fide, it helps him to rife and fall. Fish swim but flow, and foon tire; yet fome are faid to fwim feventy or eighty yards in a minute.

Brutes swim naturally; for they are fpecifically lighter than water, and require but a fmall part of their head out for breathing. It is also easy to them; for they use their legs in fwimming after the fame manner as they do in walking.

Men do not swim naturally, though they are fpecifically lighter than water; for their heads are very large, and require to be almoft out of the water for breathing, and their way of striking has no analogy to walking. Men attain the art of fwimming by practice and induftry. The art confifts in ftriking the water alternately with the feet and hands; which, like oars, row him forward. When he strikes with his hands, he neither keeps the palm parallel, nor perpendicular to the horizon, but inclined; and his hands ftriking the water obliquely, the refiftance of the water moves him partly upward and partly forward. Whilft his hands are ftriking, he gradually draws up his feet; and when the stroke of his hands is over, he strikes with his feet, by extending his legs, and pushing the foles of his feet against the water; and while he ftrikes with his legs, he brings about his arms for a new ftroke, and fo on alternately; keeping the body fomewhat oblique, that he may more easily erect his head, and keep his mouth above water.