NOTES. 463 



of the numbers representing their mean distances from the sun. So that, three 

 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. 7. Mass. The quantity of matter in a given bulk. It is pro- 

 portional to the density and volume or bulk conjointly. 



NOTE 28, p. 7. Gravitation proportional to mass. But for the resistance 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 surface of the earth would 

 fall to the ground in parallel straight lines with equal rapidity, and no change 

 whatever would take place in the circumstances 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. 7. Primary signifies, in astronomy, the planet about which a 

 satellite revolves. The earth is primary to the moon. 



NOTE 30, p. 8. Rotation. Motion found an axis, real or imaginary. 



NOTE 31, p. 8. 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 standard measure, as 

 miles. 



NOTE 32, p. 8. Satellites. Small bodies revolving about some of the planets. 

 The moon is a satellite to the earth. 



NOTE 33, p. 9. Nutation. A nodding motion in the earth's axis while in 

 rotation, similar to that observed in the spinning of a top. It is produced by 

 the attraction of the sun and moon on the protuberant matter at the terrestrial 

 equator. 



NOTE 34, p. 9. Axis of rotation. The line, real, or imaginary, about which 

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

 nary line, passing through the centre and both poles. Fig. 1 being the earth, 

 N S is the axis of rotation. 



NOTE 35, p. 9. 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 N p 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 pN m 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 36, p. 9. Translated. Carried forward in space. 



NOTE 37, p. 9. Force proportional to velocity. Since a force is measured 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 



