MECHANICS. 



bodies which determine their mutual 

 attractions. Their distances from each 

 other affect this force. It is found that 

 the force of attraction decreases as the 

 distance is increased, but in a still 

 greater proportion. Thus, for example, 

 a body placed upon the surface of the 

 earth, at the distance of 4000 miles from 

 its centre, is attracted with a certain 

 force towards that centre. At double 

 that distance, or at 4000 above the sur- 

 face, it would be only attracted with the 

 fourth part of that force, and it would, 

 in fact, lose three-fourths of its weight. 



We shall not, however, pursue this 

 investigation further, since it more pro- 

 perly belongs to another department of 

 the science. The motions to which we 

 shall have to call the attention of the 

 student, all take place upon the surface 

 of the earth, or so near it that the 

 change in the intensity of the force of 

 gravity arising from the difference of 

 distance is altogether insignificant. We 

 shall, therefore, consider gravity as an 

 uniform force, that is, as an attraction 

 which affects the same body in the same 

 degree, whatever its position may be, 

 and which affects equal bodies equally. 



(24.) The earth being globular, or 

 nearly so, it follows, that the lines in 

 which its attraction acts converge to- 

 wards its centre, and that at different 

 Earts of the earth the lines in which 

 tiling bodies descend are not parallel, 

 but are such as, if continued, w r ould in- 

 tersect at the centre. In considering, 

 however, the action of gravity on bodies, 

 at places not far distant on the surface 

 of the earth ; we may assume, without 

 sensible error, that the directions in 

 which it acts are parallel, and that they 

 are all perpendicular to the same hori- 

 zontal plane. A distance so great as one 

 mile will only produce a deviation from 

 paraDelism amounting to less than one 

 minute, or the sixtieth part of a degree. 



(25.) If a body be put in motion by 

 an impulse, the consequence would be, 

 that it w r ould continually move in the 

 direction of that impulse, with the same 

 uniform velocity with which it com- 

 menced its motion, provided that it were 

 free from resistances, such as those of 

 friction, air, &c. The force of gravity, 

 or any other attraction, differs essentially 

 from an impulse. An impulse acts in- 

 stantaneously, and produces all its effect 

 at once, and time does not change that 

 effect. On the other hand, attraction, 

 such as gravity, requires time to pro- 

 duce any effect at all, and the effect 



produced increases exactly in the same 

 ratio as the time of producing it. When 

 a body, suspended at any height above 

 the surface of the earth, is first disen- 

 gaged, it commences to move with an 

 infinitely small velocity, but, by the con- 

 tinual action of the attraction of the 

 earth, that velocity is increased, and is 

 constantly increasing during the descent 

 of the body. This peculiar species of 

 motion is therefore called accelerated 

 motion, and the force which produces 

 it is called an accelerating force. 



(26.) To explain the uniformity of 

 the attraction of the earth upon a falling 

 body, let us suppose that, at the] end of 

 the first second of the fall, the body has 

 received a certain velocity. At the end 

 of the first two seconds it will be found 

 to have received twice that velocity ; at 

 the end of the first three seconds, three 

 times that velocity, and so on, the velo- 

 city continually increasing, and in the 

 same ratio, as the time from the com- 

 mencement of the descent increases. 



There will, therefore, be no difficulty 

 in calculating arithmetically the velo- 

 city which a falling body will acquire in 

 any time from the commencement of its 

 fall. Let g express the velocity which 

 it would acquire in one second, and let 

 T be the number of seconds from the 

 commencement of its fall, and V be the 

 velocity acquired. From what we have 

 stated, it must be evident that V is as 

 many times g as there are seconds in T. 

 Hence, expressing this algebraically, 

 we haveV=g-T. 



(27.) We have stated that the earth's 

 attraction acts on all bodies in propor- 

 tion to their quantities of matter; in 

 fact, it would seem that it impressed a 

 separate force upon each particle of a 

 body, and equal forces on all the parti- 

 cles. Thus, if it impress a certain force 

 on a solid body, that force is made up 

 of the forces which it impresses on all 

 its several parts, so that if the solid body 

 be broken into small pieces, each piece 

 will be attracted as strongly by gravity 

 as it was when united in one solid mass 

 with the other pieces. From this a 

 very remarkable, and, apparently, false 

 consequence follows : viz. that all bo- 

 dies whatever, large and small, heavy 

 and light, must descend with the same 

 speed. We know, however, that under 

 ordinary circumstances, a feather and a 

 piece of gold will not fall with the same 

 speed ; and we know further, that some 

 bodies, an inflated balloon for example, 

 will, instead of falling, actually rise. 



