12 ATTRACTION. 



at the earth's surface, whence it decreases both upwards 

 and downwards, but not in a like ratio ; it decreases up- 

 wards in proportion to the square of the distance from 

 the centre of the earth, while it decreases downwards in a 

 direct ratio of the distance from the earth's centre. Thus 

 a body at the distance of one semidiameter of the earth 

 above its surface, or at a double distance from the earth's 

 centre, will be acted on by a force of only one quarter 

 of what it would at the surface ; while a body at half 

 the distance of the earth's semidiameter from its centre 

 will be acted on by a force of one half of what it would 

 on the surface.* 



General or Universal gravitation is that which relates 

 to the attraction of the sun, moon, and planets, and 

 other heavenly bodies, and by which they are preserved 

 in their orbits. According to the Newtonian theory, 

 the action of the sun upon the earth produces its centri- 

 petal force, and prevents it from flying off in a tangent 

 to its orbit ; while at the same time the earth produces 

 a similar action on the sun. The earth also acts in a 

 like manner towards the moon, and retains her in her 

 orbit, while itself gravitates towards the moon. Thus 

 all the secondaries gravitate towards their primaries, 

 and the primaries towards their secondaries, and this 

 in a degree proportioned to their mass combined with 

 the squares of their distances. This action and reaction 

 of the heavenly bodies have been found, by observations 

 on the double stars, to extend to the most remote re- 

 gions of the heavens. 



* It has been found by experiment that the quantity of descent of 

 a falling body, is in proportion to the square of the time ; thus a body 

 will fall 16 feet during one second, 64 feet during two seconds, 144 

 feet during three seconds, and so on in proportion. The quantity of 

 descent during each second increases according to the ratio of the odd 

 numbers 1, 3, 5, 7, &c. ; thus it will be 16 feet during the 1st second, 

 4S feet during the 2d second, 80 feet during the 3d second, and 112 

 feet during the 4th second. A body will take the same time in travel- 

 ling over a curve as it would in making a perpendicular descent ; thus 

 a ball propelled from a cannon planted on an eminence, will strike 

 the ground, if level, at the same moment it would have done if drop- 

 ped from the cannon's mouth. 



