APPENDIX. EXPLANATION OF THE ENGRAVINGS. . LESSON 17. Centre of Gravity. Engraving 1.—If the centres of gravity of two bodies, A and B, fig. 12. be connected with the right line A B, then the common centre of gravity, C, will be as much nearer to A than to B, as the ball A is heavier than the ball B. If the ball A weigh 12 pounds, and the ball B only 4 pounds, and the length A B be 20 inches, then, because the ball A is three times heavier than the ball B, the distance AC will be three times less than the distance B C, that is, A C will be 5 inches and B C 15 inches; the point C, therefore, is the common centre of gravity of the two bodies A and B, and if supported by this point they will balance each other. As 12+4=16 is to 20, so is 4 to 5, or so is 12 to 15. The inclining body A B C D, fig. 4. whose centre of gravity is E, stands firmly, because the line of direction EF falls within the base. But if the body A B G H be placed upon it, the centre of gravity will be raised to L, and then the line of direction LD will fall out of the base towards I: the centre of gravity, therefore, is not supported, and the whole body must fall. LESSON 19. Compound Motion.—The body A, fig. 1. acted upon by a force in the direction A B, and at the same time by another force in the direction A C, will move in the direction A D. If the lines A B and A C be made in proportion to the forces, and C D and D B be drawn parallel to them, then A D, the diagonal, will represent the force with which the body will move; and this force will be as much greater than either of the two forces by which it was impelled as A D is longer than A C, or any other single side of the parallelogram. This is called the composition and resolution of motion. [Note. Several things in this Lesson may be obscure to some students: the teacher should explain and illustrate them by familiar “verbal instructions, and by such figures and diagrams as he may have in his possession, or may easily draw upon paper or a slate.] LESSON 20. Levers.--First kind, fig. 7. CE is the lever, and B the prop. A the stone to be raised = 1000 pounds, and the strength of a man at C = 100 pounds. Since the strength of the man is only one tenth the weight of the stone, that the power and weight may balance each other, the arm of the lever B C must be ten times as long as the arm B E. Second kind, fig. 9. If the hand C be nine times as far from A as the point X, then one pound at C will balance nine pounds at B. Fig. 5. a burden on a pole. Weight W three times nearer to a than to b, a then will bear three times as much of the weight as b. Third kind, fig. 10. Distance PF 3 inches; W F 12:—then 20 pounds at W will require the force of 80 at P. in order to balance it, for 12 is four times 3. Fig. 2. man's arm,--D centre of motion,--the power is the muscle inserted at C, A the weight:--now as the distance D C is one tenth part of C A, the muscle, therefore, must exert a power equal to 100 pounds in order to raise 10 pounds LESSON 21. Pulley.--Fig. 13. single moveable,-in order to raise the weight W one inch, the power P must draw the strings B and C one inch each : the whole string, therefore, is shortened two inches, while the weight is raised only one. Fig. 15. System of pullies. While the weight W rises one inch, each of the four ropes must be shortened an inch, and P, therefore, must move four inches : 5 pounds at P will balance 20 at W. Wheel and Axle, Fig. 11. If the diameter of the wheel be 4 feet, and that of the axis only 8 inches, then the power P of 100 pounds will balance the weight W of 600 pounds; for 6X8=48 inches which make 4 feet, the diameter of the wheel. Inclined Plane. Fig. 8. If B C 4 A C, then W will be supported by a power = of its weight. Example. If a wagon with its load weigh 40. cwt. and may be drawn on level ground by a force equal to 8 cwt., in drawing it to the top of a hill which rises 20 yds. in a 100, the horses will have to pull with an additional force of 40 cwt., that is, 8 cwt. more than on level ground, or with double their former force. LESSON 22. The Wedge, fig. 6.-ABCD may be divided into two inclined planes, A DC and B DC, which may be used separately, and will gain advantage as such ; therefore, when united at DC, the advantage gained will be in the same proportion as when they were used in different parts. The Screw, fig. 3. A must turn once round before the resistance can be moved from one spiral winding to another, as from x to z = - į an inch. If the lever A 36. inches, then the circle described by its end will be about 226 inches or 452 half inches; therefore one pound at a will balance a resistance of 452 pounds. [Note. Since the lever = 36 inches, the diameter of the circle will be 72 inches, and the circumference of a circle is 3.1416 times the diameter, there: fore, 72X3.1416 = the circumference = 226 inches or 452 half inches.] LESSON 23. Pressure of Fluids.-In the vessel AB, fig. 25. Engr. II. the bottom C B does not sustain a pressure equal to the quantity of the whole fluid, but only of a column, whose base is C B, and height CF. In the vessel F G, fig. 24. the bottom sustains a pressure equal to what it would if the vessel were as wide at the top as bottom. If to the wide vessel A B, fig. 23. a tube CD be attached, and water poured into either of them, it will stand at the same height in both; of course the small quantity in C D balances the large quantity in A B. This has been called the hydrostatical paradox, because any quantity, however small, may be made to counterpoise any quantity, however large, but it is no paradox, when we consider that the particles of a fluid press against each other in every direction, not only downwards, but upwards and sideways. Specific Gravity. Hydrostàtic Balance, fig. 14. Engr. I. If a body , suspended under the scale, be first counterpoised in air by weights in the opposite scale, and then immersed in water, the equilibrium will be destroyed, then if a weight be put into the scale from which the body hangs, to restore the equilibrium, that weight will be equal to the weight of water as large as the immersed body,-or it is what the body loses of its weight in the fluid. The Hydrometer consists of a thin glass ball, with a graduated tube : a smaller ball is attached to the instrument below, containing a little mercury, for the purpose of making it remain upright in the liquid under trial. The specific gravity of the liquid is estimated by the depth to which the instrument sinks. LESSON 25. ton. The Common Pump, fig. 21. Engr. II. A B the barrel. P the piston. R the rod. V the valve in the moveable pis y a valve fixed in the body of the pump. S the spout. The Forcing Pump, fig. 22. A B the barrel. P a solid piston. D the pipe joined to the barrel. V a fixed valve. When P descends it shuts the valve y, and forces the water into D through V. When P is raised the valve y opens and the valve V shuts, and the water ascends through y. The forcing pump described in the Lesson differs a little from this figure. We may suppose an air vessel to be placed above V, and a pipe descending through it nearly to V, and the elastic pressure of the air upon the surface of the water, confined in the vessel, will force the water upwards through the pipe. LESSON 27. The Air Pump, fig. 16. DE the base or wooden frame. A A the two brass cylinders. B the head. CC the columns holding down the head. K the receiver. I a hole in the brass plate, through which the air passes in a brass tube to the cylinders. R R toothed rods. H handle or winch. Na nut, on turning which the air may be excluded from, or admitted to the receiver. M a quicksilver gage with a small receiver over it: this is designed to show the different densities of the air in the large receiver, when the machine is at work. There is a communication between this and the hole I by a brass pipe. This is not an essential part of an air pump, though it is convenient, as showing the degree of exhaustion : the more the air is exhausted the higher will the mercury rise in the gage. Artificial Fountain, fig. 26. A is a strong copper vessel, , having a tube that screws into the neck of it, so as to be air tight, and so long as nearly to reach to the bottom : x is the handle of a stop. Having poured some water into the vessel, and screwed in the tube, the condensing syringe is to be adapted, and the air condensed. The stop is to be shut while the syringe is unscrewed, then, on opening the stop, the air, by its great density acting upon the water in the vessel, will force it out in a jet to a considerable height, LESSON 29. Sound. Speaking Trumpet, fig. 20. The voice instead of being diffused in the open air, is confined within the trumpet, and the vibrations which spread and fall against the sides of the instrument, are reflected according to the angle of incidence, and fall into the direction of the vibrations which proceed straight forwards. The whole of the vibrations are thus collected into a focus, and if the ear be situated in or near the spot, the sound is prodigiously increased. The reflected rays are distinguished from those of incidence, by being dotted, and they are brought to a focus at F. LESSON 30. Musical Sounds.—The line AB, fig. 17. represents a musical string fastened at both ends. Drawn out in the situation ACB, and then let go, it will, in consequence of its elasticity, not only come back to its position A B, but go to the situation A D B, or nearly as far from A B as A CB was on the other side. All the motion one way is called one vibration ; after this, the string will go again nearly as far as C, making a second vibration, then nearly as far as D, making a third vibration, and so on, diminishing the extent |