NOTES. 435 



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

 planets. 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. 7. Axis 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 centre 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 in- 

 clination 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 p N 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. 7. Translated. Carried forward in space. 



NOTE 37, p. 7. Force proportional to velocity. Since a force is mea- 

 sured 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, one urging it in the direction of the tangent m T, and another 

 pulling it towards the sun in the direction m S. Its velocity, which is 

 greatest at P, decreases throughout the arc to P D A to A, where it is 

 least, and increases continually as it moves along the arc A Q P till it 

 comes" to P again. The whole force producing the elliptical motion varies 

 'inversely as the square of the distance. See note 23. 



NOTE 40, p. 8. Radii vectores. Imaginary lines adjoining the centre 

 of the sun and the centre of a planet or comet, or the centres of a planet 

 and its satellite. In the circle, the radii are all equal ; but in an ellipse, 

 fig. 6, the radius vector S A is greater, and S P less than all the others. 

 The radii vectores S Q, S D, are equal to C A or C P, half the major 

 axis P A, and consequently equal to the mean distance. A planet is at its 

 mean distance from the sun when in the points Q and D. 



NOTE 41, p. 8. Equal areas in equal times. See Kepler's 1st law, 

 in note 26, p. 5. 



NOTE 42, p. 8. Major axis. The line P A, fig. 6 or 10. 



U 2 



