NOTES. 



393 



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 tiie axis X S less, than if it were a sphere. Therefore, in both 

 cases, the Ibrce deviates from the exact law of gravity. This deviation 

 arises from the protuberant matter at the equator ; and as it diminishes 

 toward 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 center of the sun, or of a satellite from the center 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 PQ, A D, 

 fig. 6, be the orbit or path of the moon or of a planet ; then P A is the 

 major axis, C the center, and CS is equal to CF. 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 <i, 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 cen- 

 ter to the surface of the earth, regarded aa a sphere. It is intermediate 

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

 the equator. 



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

 another. 



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 tunes 60. 



NOTE 18, p. 5. Centrifugal force. The force with which a revolving 

 body tends to fly from the center 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 mT, 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 increases with the 

 angular swing of the body, and with, 

 its distance from the center of mo- 

 tion. As the orbit of the moon does 

 not differ much from a circle, let it 

 be represented by m dg h, fig. 4, 

 the earth being in C. The centri- 

 fugal 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 mT by 

 the action of the centrifugal force 

 atone, or fall through mp by the 

 earth's attraction alone. T n, the 

 deflection from the tangent, is parallel and equal to mp, 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. T w, 



