Page images
PDF
EPUB

NOTES.

NOTE 1. page 2. Diameter. A straight line passing through the centre, and terminated both ways by the sides or surface of a figure. In fig. 1. q Q, NS, are diameters.

NOTE 2. p. 3. Mathematical and mechanical sciences. Mathematics teach the laws of number and quantity; mechanics treat of the equilibrium and motion of bodies.

NOTE 3. p. 3. Analysis is a series of reasoning conducted by signs or symbols of the quantities whose relations form the subject of enquiry.

NOTE 4. p. 4. Oscillations are movements to and fro, like the swinging of the pendulum of a clock, or waves in water. The tides are oscillations of the sea.

NOTE 5. p. 4. Gravitation. Sensible gravity or weight. It is the force which causes substances to fall to the surface of the earth, and which retains the celestial bodies in their orbits. Its intensity increases as the squares of the distance decrease.

NOTE 6. p. 5. Particles of matter are the indefinitely small or ultimate atoms into which matter is believed to be divisible. Their form is unknown; but though too small to be visible, they must have magnitude.

NOTE 7. p. 5. A hollow sphere. A hollow ball, like a bomb-shell. A sphere is a ball or solid body, such, that all lines drawn from its centre to its surface

are equal. They are called radii, and every line passing through the centre and terminated both ways by the surface is a diameter, which is consequently equal to twice the radius. In fig. 3. Qq or N S is a diameter, and CQ, CN, are radii. A great circle of the sphere has the same centre with the sphere, as the circles Q E qd and QNq S. The circle A B is a lesser circle of the sphere.

NOTE 8. p. 5. Concentric hollow spheres. Shells, or hollow spheres, having the same centre, like the coats of an onion.

NOTE 9. p. 5. Spheroid. A solid body, which sometimes has the shape of an orang-, as in fig. 1.; it is then called an oblate spheroid, because it is

[merged small][merged small][merged small][merged small][ocr errors]

flattened at the poles N and S. Such is the form of the earth and planets.

When, on the contrary, it is drawn out at the poles like an egg, as in fig.2., it is called a prolate spheroid. It is evident, that in both these solids the radii Cq, Ca, CN, &c. are generally unequal; whereas in the sphere they are all equal.

NOTE 10. p. 5. Centre of gravity. A point in every body, which if supported, q the body will remain at rest in whatever position it may be placed. About that point all the parts exactly balance one another.

a

Fig. 2.

N

S

NOTE 11. pp. 6. 8. Poles and equator. Let fig. 1. or 3. represent the earth, C its centre, NC S the axis of rotation, or the imaginary line about which it performs its daily revolution. Then N and S are the north and south poles, and the great circle q E Q, which divides the earth into two equal parts, is the equator. The earth is flattened at the poles, fig 1., the equatorial diameter q Q exceeding the polar diameter N S by about 26 miles. Lesser circles, a AG B, which are parallel to the equator, are circles or parallels of latitude,

[blocks in formation]

which is estimated in degrees, minutes, and seconds, north and south of the equator, every place in the same parallel having the same latitude. Greenwich is in the parallel of 51° 28' 40". Thus terrestrial latitude is the angular distance between the direction of a plumb-line at any place and the plane of the equator. Lines such as NQS, NGES, fig. 3., are called meridians; all the places in any one of these lines have noon at the same instant. The meridian of Greenwich has been chosen by the British as the origin of terrestrial longitude, which is estimated in degrees, minutes, and seconds, east and west of that line. If N GES be the meridian of Greenwich, the position of any place, B, is determined, when its latitude, QC B, and its longitude, E C Q, are known.

NOTE 12. p. 6. A certain mean latitude. The attraction of a sphere on an external body is the same as if its mass were collected into one heavy particle in its centre of gravity, and the intensity of its attraction diminishes as the square of its distance from the external body increases. But the attraction of a spheroid, fig. 1., on an external body at m in the plane of its equator, E Q, is greater, and its attraction on the same body when at m' in the axis N S less, than if it were a sphere. Therefore, in both cases, the force deviates from the exact law of gravity. This deviation arises from the protuberant matter at the equator; and as it diminishes towards the poles, so does the attractive force of the spheroid. But there is one mean latitude, where the attraction of a spheroid is the same as if it were a sphere. It is that latitude the square of whose sine is equal to of the equatorial radius.

NOTE 13. p. 6. Mean distance. The mean distance of a planet from the centre of the sun, or of a satellite from the centre of its planet, is equal to half the major axis of its orbit. For example, let P Q A D, fig. 6., be the orbit or path of the moon or of a planet; then P A is the major axis. When the body is at Q or D, it is at its mean distance from S, for S Q, S D are each equal to C P, half the major axis.

NOTE 14. p. 6. Mean radius of the earth. The distance from the centre to the surface of the earth, regarded as a sphere.

NOTE 15. p. 6. Ratio. The relation which one quantity bears to another.

NOTE 16. p. 6. Square of moon's distance. In order to avoid large numbers, the mean radius of the earth is taken for unity: then the mean distance of the moon is expressed by 60; and the square of that number is 3600, or 60 times 60.

NOTE 17. p. 6. Centrifugal force. The force with which a revolving body tends to fly from the centre of motion: a sling tends to fly from the hand in consequence of the centrifugal force. A tangent is a straight line touching a curved line in one point without cutting it, as m T, fig. 4. The

[blocks in formation]

direction of the centrifugal force is in the tangent to the curved line or path in which the body revolves, and its intensity increases with the angular swing of the body, and with its distance from the centre of motion. As the orbit of the moon does not differ much from a circle, let it be represented by g dm h, fig. 4., the earth being in C. The centrifugal force arising from the velocity of the moon in her orbit balances the attraction of the earth. By their joint action, the moon moves through the arc m n during the time that she would fly off in the

tangent m T by the action of the centrifugal force alone, or fall through mp by the earth's attraction alone. Tn, the deflection; from the tangent, is parallel and equal to m p, the versed sine of the arc m n, supposed to be moved over by the moon in a second, and therefore so very small that it may be regarded as a straight line. Tn, or m p, is the space the moon would fall through in the first second of her descent to the earth, were she not retained in her orbit by her centrifugal force.

NOTE 18. p. 6. Action and reaction. When motion is communicated by collision or pressure, the action of the body which strikes is returned with equal force by the body which receives the blow. The pressure of a hand on a table is resisted with an equal and contrary force. This necessarily follows from the impenetrability of matter; a property by which no two particles of matter can occupy the same identical portion of space at the same time. When motion is cominunicated without apparent contact, as in gravitation, attraction, and repulsion, the quantity of motion gained by the one body is exactly equal to that lost by the other, but in a contrary direc tion; a circumstance known by experience only.

NOTE 19. p. 6. Projected. A body is projected when it is thrown: a ball fired from a gun is projected; it is therefore called a projectile. But the word has also another meaning. A line, surface, or solid body, is said to be projected upon a plane, when parallel straight lines are drawn from every

« PreviousContinue »