-Less; as a-b, is a less by b.

XMultiplied; as axb, is a multiplied by b; or ab without the sign, is the same.

÷Divided; as a÷b, is a divided by b; or

is the same and more usual.

Equal to; as a=b, is a equal to b.

a

:is to; as thus, ab::c:d; that is, as a is ::Sois; to b, so is c to d. S

Involved; as squared, cubed, &c.

Evolved; or the root extracted.

2

The root; asa b, is the square root of a b. The power, as a2 or b3 is the square of a or the cube of b; that is, a×a, or b×bxb.

560. When an arithmetician wishes to perform his problem algebraically, he writes down the data of his question, as severally equal to a, b, or c, as he please; and the unknown or sought numbers, as x, y, or z; and then adds, subtracts, multiplies, and divides these, by the signs, as his reason directs, till he arrive at a simple result.

Obs. 1.-Suppose the joint ages of Eliza and Emily are 23, and that Eliza is three years older than Emily, and their respective ages are required: put a- 23 and b=3, and call Eliza's unknown age y, and Emily's z, and then algebraically it will stand.

Then, if these are added together, as+z added to destroys itself, it will then stand a+b= 2y; which,

divided by 2, gives

23+3

and by restoring a and b, it will stand

y, or

26

2

13, Eliza's age, and Emily's being 13-3 will, of course, be 10.

2

2. A child, to whom the first four rules of arithmetic and the characters are known, may be made to understand this; and I advise no female or young person to pass it as a difficulty. A course of Algebra may be undertaken, after a youth is master of vulgar and decimal fractions.

561. Fluxions are the different velocities whereby any quantities, in a flowing state, increase or decrease, according to the ratio of the velocities.

Quantities and their fluxions are, (as in algebra) represented by letters; known quantities, by the first letters, a, b, c, d, &c.; and the fluents, by the last, as v, x, y, z; and their fluxions, by the same with a point over them, as v, x, y, z.

Obs. As the ratios of velocities, in many cases, are perpetually altering, as in the motion of falling bodies, these fluxions vary every moment, and produce fluxions of fluxions, or second fluxions, thus marked, v, x, y, z;

and the fluxions of these are third fluxions, as, v, x, y, z.

XXV. Optics.

562. This science is founded on the properties of Light, which derives its chief source from the Sun, and is also generated or decomposed by bodies in a state of combustion.

We ascertain the utility of light, by the intro

duction of a candle or ray of sun-shine into a
dark room. This, in an instant, renders every
thing visible, by the emission of innumerable
rays, or particles proceeding from the candle or
ray, to the objects, and from them to the eye,
producing therein a figure of the objects; and a
corresponding sensation in the brain.
Fairest of beings! first created Light!

Prime cause of beauty! for, from thee, alone,
The sparkling gem,—the vegetable race,—

The nobler worlds that live and breathe, their charms, The lovely hues peculiar to each tribe,— From thy unfading source of splendour, draw! In thy pure rays, with transport, I survey This firmament, and those her rolling worlds;Their magnitudes and motions. MALLET. Obs. Two hypotheses have been invented to account for the principal operations of light. In the first, it is supposed, that the universe contains a highly rare elastic substance, which when put into a state of undulation, produces those effects on our organs of sight, which constitute the sensations of vision, and the other phenomena occasioned by solar and terrestrial rays. In the second, it is conceived, that particles are emitted, or sent off, from luminous or heat-making bodies with great velocity, and that they produce their effects by communicating their motions to substances, or by entering into them, and changing their composition. The first of these suppositions, was adopted by Hook, Huygens, and Euler; the second, by Newton,-and the philosophers of the Newtonian School. Most of the phenomena may be accounted for, by either hypotheses; but the Newtonian doctrine applies more happily, to some of the facts discovered, respecting the modifications of light by double refraction and reflection.

563. By observing the regular eclipses of Jupiter's moons in different parts of the earth's orbit, it is found, that rays, or vibrations of light, travel

X

twelve millions of miles in a minute; yet they do not affect the eye in passing into it; and they could never be found to produce the slightest impression on the most delicate balance.

It requires 12 rays or pulsations of light to fall on the eye in every second, to produce a constant perception of the object, whence the rays or pulsations proceed.

Hence, rays or pulsations of light, in passing from distant bodies to the eye, may be 16,000 miles behind each other, and yet produce con

stant vision.

Obs.-The eclipses of Jupiter's moons are calculated for a mean distance of the earth; but they happen sooner or later, as the earth is nearer, or more distant from Jupiter. The number of rays necessary to produce vision, is ascertained, by turning a piece of burning wood in a circle till the circle is wholly illuminated. The twinkling of the stars, doubtless, arises from paucity of rays.

564. Pulsations of light pass freely through air, water, glass, the coats and humours of the eye, and other transparent mediums. At the back of the eye, is spread a net of nerves, called the optic nerve; to receive their impression, and communicate their effect to the brain.

The rays pass through the pupil, and form, on the optic nerve, a beautiful and perfect picture of the objects before the eye. A camera obscura acts on the principle of the eye: and a common spectacle-glass will shew the same effect, held at a proper distance, from a wall.

565. But though effects of light pass in straight lines through any medium when in it; they are turned out of their course, as they pass obliquely

out of one transparent body into another; and this effect is called refraction..

If a stone be thrown obliquely into water, it will be evident, that when it strikes the water, it will fall to the bottom in a direction more perpendicular than before it came into contact with the water. Such, too, is the effect of refraction on rays of light; which, on passing into water, or any heavier transparent body, are bent downward.

Obs. To verify and understand this principle, put a halfpenny into an empty basin, and stand at such distance that the coin may not be visible; then, let another person pour water into the basin, and the halfpenny will become visible: this arises from the bending of the rays in their passage into air at the surface of the water.

566. Hence, when the rays of light coming from the celestial bodies, arrive at our atmosphere, they are bent downward; and those bodies appear, when in the horizon, higher than they are.

Many rays of light are reflected at the surface of a new transparent medium, in an angle equal to that in which they fall on the surface, and on this principle all mirrors are constructed.

567. Advantage is taken by man of the property of refraction, to construct new mediums of such shape, as that all rays that fall on them may, on coming out of them, converge in one point instead of going straight forward.

The construction of surface which produces this effect is the convex; and all rays of light which fall on a circular surface of glass, &c., are converged on the other side into a series of corresponding points, representing the objects. whence the light proceeded.