396 NOTES. 



ber is that number twice multiplied by itself. For example, the squares 

 of the numbers 2, 3, 4, &c. are 4, 9, 16, &c., but their cubes are 8, 27, 64, 

 &c. Then the squares of the numbers representing the periodic times of 

 two planets are to one another as the cubes of the numbers representing 

 their mean distances from the sun. So that throe of these quantities 

 being known, the other may be found by the rule of three. The mean 

 distances are measured in miles or terrestrial radii, and the periodic times 

 are estimated in years, days, and parts of a day. Kepler's laws extend to 

 the satellites. 



NOTE 27, p. 5. Mass. The quantity of matter in a given bulk. It is 

 proportional to the density and volume or bulk conjointly. 



NOTE 28, p. 5. Gravitation proportional to mass. But for the resist- 

 ance of the air, all bodies would fall to the ground in equal times. In 

 fact a hundred equal particles of matter at equal distances from the sur- 

 face of the earth would fall to the ground in parallel straight lines with 

 equal rapidity, and no change whatever would take place in the circum- 

 stances of their descent, if 99 of them were united in one solid mass; for 

 the solid mass and the single particle would touch the ground at the 

 same instant, were it not for the resistance of the air. 



NOTE 29, p. 5. Primary signifies, in astronomy, the planet about which 

 a satellite revolves. The earth is primary to the moon. 



NOTE 30, p. 6. Rotation. Motion round an axis, real or imaginary. 



NOTE 31, p. 7. Compression of a spheroid. The flattening at the poles. 

 It is equal to the difference between the greatest and least diameters, 

 divided by the greatest ; these quantities being expressed in some stand- 

 ard measure, as miles. 



NOTE 32, p. 7. Satellites. Small bodies revolving about some of the 

 plane'ts. The moon is a satellite to the earth. 



NOTE 33, p. 7. Nutation. A nodding motion in the earth's axis while 

 in rotation, similar to that observed in the spinning of a top. It is pro- 

 duced by the attraction of the sun and moon on the protuberant matter 

 at the terrestrial equator. 



NOTE 34, p. l.Jlxis of Rotation. The line, real or imaginary, about 

 which a body revolves. The axis of the earth's rotation is that diameter, 

 or imaginary line, passing through the center and both poles. Fig. 1 being 

 the earth, N S is the axis of rotation. 



NOTE 35, p. 7. Nutation of lunar orbit. The action of the bulging 

 matter at the earth's equator on the moon occasions a variation in the 

 inclination of the lunar orbit to the plane of the ecliptic. Suppose the 

 plane Np n, fig. 13, to be the orbit of the moon, and N m n the plane of the 

 ecliptic, the earth's action on the moon causes the angle pNwi to become 

 less or greater than its mean state. The nutation in the lunar orbit is the 

 reaction of the nutation in the earth's axis. 



NOTE 3G, p. 7 . Translated. Carried forward in space. 



NOTE 37, p. 8. Force proportional to velocity. Since a force is meas- 

 ured by its effect, the motions of the bodies of the solar system among 

 themselves would be the same whether the system be at rest or not. The 

 real motion of a person walking the deck of a ship at sea is compounded 

 of his own motion and that of the ship, yet each takes place independently 

 of the other. We walk about as if the earth were at rest, though it has 

 the double motion of rotation on its axis and revolution round the sun. 



NOTE 38, p. 8. Tangent, A straight line which touches a curved 

 line in one point without cutting it. In fig. 4, m T is tangent to the curve 

 in the point m. In a circle the tangent is at right angles to the radius C m. 



NOTE 39, p. 8. Motion in an elliptical orbit. A planet m, fig. 6, moves 

 round the sun at S in an ellipse P D A Q, in consequence of two forces 



