460 



NOTES. 



Fig. 4. 



NOTE 15, p. 6. 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. 6. Ratio. The relation which one quantity bears to another. 



NOTE 17, p. 6. 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. 6. 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 centrifugal 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 

 centre of motion. As the orbit of 

 the moon does not differ much from 

 a circle, let it be represented by 

 m d g h, fig. 4, the earth being in C. 

 The centrifugal 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 m T by the action 

 of the centrifugal force alone, or 

 fall through m p by the earth's 

 attraction alone. T n, the deflection from the tangent, is parallel and equal to 

 m p, 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 n, or m p, is the space the moon would fall through in the first second 

 of her descent to the earth, were she not retained in her orbit by her centrifugal 

 force. 



NOTE 19, p. 6. Action and reaction. When motion is communicated by 

 collision or pressure, the action of the body which strikes is returned with 

 equal force by the body which receives the blow. The pressure of a hand on 

 a table is resisted with an equal and contrary force. This necessarily follows 

 from the impenetrability of matter, a property by which no two particles of 

 matter can occupy the same identical portion of space at the same time. When 

 motion is communicated without apparent contact, as in gravitation, attrac- 

 tion, and repulsion, the quantity of motion gained by the one body is exactly 

 equal to that lost by the other, but in a contrary direction ; a circumstance 

 known by experience only. 



NOTE 20, p. 6. Projected. A body is projected when it is thrown : a ball 

 fired from a gun is projected; it is therefore called a projectile. But the word 



