of its vibrations gradually, until it settles again in its original position AB. 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 C D, 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 L G.

The angle of incidence is that which is contained between B C and C F; 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 planoconcave, 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 x.

They are said to converge when considered as flowing from z towards C. And to be parallel as flowing from z towards a and b. Ca 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 m n, 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 DE. If the object be in C, the image and object will be equal and coincide.

Fig. 37. P is a prism. A is a ray of light, which is refracted on entering the prism, and also on leaving it. A B is the spectrum, on which are exhibited the variously coloured rays.

LESSON 36.

Structure of the Eye. Fig. 28. aa a aa, is called the sclerotica: bb, the cornea: ccc, the choroid: dd, the pupil: ee, the iris: ff, the aqueous humour: gg, the crystalline humour: hh, the vitreous humour: ii, the retina ; which proceeds from the brain and enters the eye at n.

LESSON 37.

Single Microscope, fig. 35. E F is the object to be viewed: A B a double convex lens: c the pupil of the eye: D the crystalline humour: the rays are converged to a focus on the retina at R R. Compound Microscope, fig. 34. with which we do not see the object A B, but a magnified image of it a b. Two lenses are employed; the one L M, for the purpose of magnifying the object, is called the object glass; the other N O, acts on the principle of the single microscope, and is called the eye glass.

LESSON 39.

To obtain an idea of the Newtonian Telescope, look at fig. 27. and consider the concave mirror A B as placed at the end of a tube, and rays of light falling upon it from the object DE: then suppose a plane mirror placed a little below e, so that the rays, being reflected from it, shall pass out through a lens at d, where the eye of the observer looks down on the image.

LESSON 41.

Solar System. Engr. IV. Fig. 38 exhibits the order in which the planets move round the sun. Fig. 39 shows their comparative magnitudes. On the left hand side of the Engr. are represented the proportional distances of the planets from the sun.

Table of the distances, rotations, periods, &c. of the

second 2×24 times less, or, at the third 3×3—9 times 3, the heat and light received at the first is IXI=1, at the distance of one planet be called 1, of another 2, and of a third heat decrease as the square of the distance increases. If the according to the square of their distances, that is, light and NOTE. The planets receive light and heat from the sun

less, or. The following rule may be given; as the square of the distance of any planet from the sun is to 1, which represents the light and heat received at the earth, so is the square of the earth's distance from the sun, to the degree of light and heat received at the planet in question.

The attraction of bodies decreases as the square of the distance increases; the attraction is mutual, and greater or less according to their solid contents.

The following is the rule for finding the distances of the planets from the sun-as the square of the earth's period of revolution round the sun is to the cube of its dis、nce, so is the square of any other planet's annual period of revolution to the cube of its distance; and the cube root of the number thus found will be the planet's distance from the sun. It was ascertained by Kepler and demonstrated by Newton, that from the combined forces of attraction and rectilinear motion, the squares of the periodical times or revolutions of the planets are, as the cubes of their distances. It was ascertained by Kepler also, that if a line were drawn from the sun to the earth, this line would, by the earth's motion, pass over equal spaces, or areas in equal times.

To such pupils as are sufficiently acquainted with Arithmetic, the instructer should explain at large the particulars mentioned in the above note. Questions may easily be proposed, and worked out by the above rules :—for instance, if the period of Mercury be 83 days, what is its distance from the sun?-If the heat and light at the earth be 1, what is the degree of heat and light at Mercury? and so of other planets.

To find how many times one planet is greater than another, the rule is, cube the diameter of each planet, and divide the greater number by the less, the quotient will give the proportional magnitudes, or the number of times the one is greater than the other.

LESSON 44.

the sun, and N S is The white circle-in The dark circular degrees from each

Fig. 40. Engraving V. S represents the earth in different parts of its orbit. the dark space represents the ecliptic. space filled with stars extending eight side of the ecliptic represents the zodiac. The names of the signs of the zodiac and the characters which represent