4 AC, 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

The Wedge, fig. 6.—A BCD may be divided into two inclined planes, ADC and BDC, 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. 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= an inch. If the lever A = 36 inches, then the circle described by its end a 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, therefore, 72×3.1416 the circumference 226 inches or 452 half inches.]

LESSON 23.

Pressure of Fluids. In the vessel A B, 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 CD balances the large quantity in AB. 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. Hydrostatic Balance, fig. 14. Engr. I. If a body x, 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,what the body loses of its weight in the fluid.

-or it is

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.

The Common Pump, fig. 21. Engr. II. AB the barrel. P the piston. R the rod. V the valve in the moveable piston. y a valve fixed in the body of the pump. S the spout. The Forcing Pump, fig. 22. AB 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. RR 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 ís 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 A CB, 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 ACB 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

of its vibrations gradually, until it settles again in its original position A B. According to the laws of pendulums, those of equal length move in equal times, though they pass through different arcs, or portions of a circle. If the pendulums A B, fig. 18. and CD, fig. 19. be equal, the time of passing through EF is equal to that of passing through G H. Thus the vibration of the string AB, fig. 17. is considered as a double pendulum, vibrating from the points A and B, the respective vibrations of which, from the greatest to the least, are performed in the same time: this is the reason why a musical string has the same tone from the beginning of the vibrations to the end.

LESSON 31.

Optics. Reflection and Refraction of Light. If LG, fig. 29. Engr. III. be a reflecting surface, as a looking glass, then BC is the incident ray, and CE is the reflected ray. The line FC is a perpendicular to the reflecting surface LG. The angle of incidence is that which is contained between B C and CF, and the angle of reflection is that contained between EC and CF: and the angle of incidence is equal to the angle of reflection, that is, the angle BCF is equal to the angle ECF. (It is usual to call every angle by three letters, and that at the angular point must be always the middle letter of the three.)

Let BC, fig. 29. be a ray of light passing out of air into water or glass LG at the point C, the ray B C, instead of proceeding along C H, will be bent, or refracted towards the perpendicular CK, as along C I. But if CI be supposed to be a ray of light passing out of glass or water into air, that is, out of a denser into a rarer medium, it will not proceed in the direction of the line Cx, but in the direction C B, farther from the perpendicular FC than Cx. [NOTE. On the subject of optics the instructer should be particular in giving his pupils a correct idea of angles, parallel lines, &c.]

LESSON 32.

Lenses. Fig. 30. A is a plano-convex lens, B plano concave, C double convex, D double concave, E a meniscus. F G is the axis of all the five lenses.

Fig. 36. A candle at C diverges rays of light towards z.

They are said to converge when considered as flowing from x towards C. And to be parallel as flowing from z towards a and b. C is the focus of the converging rays, and the imaginary focus of the diverging rays. The lens here being plano-convex, the focus, as is manifest, is at the distance of the diameter of the sphere, of which the convex surface of the lens forms a portion. The distance from the middle of the glass to the focus is called the focal distance.

Fig. 32. The focal distance of a double convex lens is situated at the centre of the sphere, of which the surface of the lens forms a portion ;-of the lens A B, for instance, ƒ is the focus, and the distance from f to the circumference of the circle is the focal distance, which is equal to half the diameter of the sphere. If another double convex lens FG be placed in the rays at the same distance from the focus, it will so refract the rays, that they shall go out of it parallel to one another. It is evident that all the rays except the middle one, cross each other in the focus f; of course the ray DA, which is uppermost in going in, is the lowest in going out, as G.c.

Fig. 33. If the rays a bc, &c. pass through A B, and C be the centre of concavity, then the ray a, after passing through the glass, will go in the direction kl, as if it had come from C, and no glass in the way the ray b will go on in the direction mn, and so on. The point C is called the imaginary focus.

LESSON 33.

In fig. 27. A B is a concave mirror, C is the centre of concavity. The rays, which proceed from any remote terrestrial object, as DE, will be converged at a little greater distance than half way between the mirror and C, and the image will be inverted with respect to the object, as de. When the object is more remote than the centre of concavity, or C, the image is less than the object, and is between the object and the mirror, as de between DE and BC. When the object is nearer than C, the image will be more remote and larger than the object, as D E. If the object be in C, the image and object will be equal and coincide.