NOTES. 459 



mated in degrees, minutes, and se- 

 conds, north and south of the 

 equator, every place in the same 

 parallel having the same latitude. 

 Greenwich is in the parallel of 

 51 28' 4(>". Thus terrestrial latitude 

 is the angular distance between the 

 direction of a plumb-line at any 

 place and the plane of the equator. 

 Lines such as N Q S, N G E S, fig. 3, 

 are called meridians ; all the places 

 in any one of these lines have noon 

 at the same instant. The meridian 

 of Greenwich has been chosen by 

 the British as the origin of terres- 

 trial longitude, which is estimated 

 in degrees, minutes, and seconds, east and west of that line. If N G E S be 

 the meridian of Greenwich, the position of any place, B, is determined, when 

 its latitude, Q C B, and its longitude, E C Q, are known. 



NOTE 12, p. 5. Mean quantities are such as are intermediate between others 

 that are greater and less. The mean of any number of unequal quantities is 

 equal to their sum divided by their number. For instance, the mean between 

 two unequal quantities is equal to half their sum. 



NOTE 13, p. 5. 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 deviation 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 be- 

 tween the equator and the pole. In that latitude the square of the sine is equal 

 to $ of the equatorial radius. 



NOTE 14, p. 6. 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 P A is the major axis, C the centre, and C S 

 is equal 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. 



