NOTES. 



431 



NOTE 13, p. 4. 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 devia- 

 tion 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 a part of the spheroid intermediate 

 between the equator and the pole. In that latitude the square of the sine 

 is equal to ^ of the equatorial radius. 



NOTE 14, p. 4. 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 sum of its greatest and least distances, and, consequently, 

 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 PA is the 

 major axis, C the centre, and C S is eqiial to C F. Now, since the earth 

 or the sun is supposed to be in the point S according as P D A Q is 

 regarded as the orbit of the moon or that of a planet, S A, S P are the 

 greatest and least distances. But half the sum of S A and S P is equal to 

 half of A P, the major axis of the orbit. 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 by the nature of the curve. 



NOTE 15, p. 4. Mean radius of the earth. The distance from the 

 centre to the surface of the earth, regarded as a sphere. It is intermediate 

 between the distances of the centre of the earth from the pole and from 

 the equator. 



NOTE 16, p. 5. Ratio. The relation which one quantity bears to 



another. _. 



Fig. 4. 



NOTE 17, p. 5. 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 18, p. 5. 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 centri- 

 fugal force. A tangent is a straight 

 line touching a curved line in one 

 point without cutting it, as m T, 

 fig. 4. The direction of the centrifugal force is in the tangent to the 

 curved line or path in which the body revolves, and its intensity in- 

 creases with the angular swing of the body, and with its distance from the 



