INTRODUCTION TO MECHANICS. vi 



space of time. It may be objected, that since attraction is proportioned to 

 the quantity of matter which a body contains, the earth must necessarily 

 attract a heavy body more strongly, and consequently bring it to the 

 ground more rapidly than a light one. In answer to this, it must be 

 observed that bodies have no natural tendency to fall any more than to 

 rise, or to move laterally, and that they will not fall unless impelled by 

 some force ; and this force must be proportioned to the quantity of matter 

 it has to move. A body consisting of 1000 particles of matter, forjnstance, 

 requires ten times the force of attraction to bring it to the ground, in the 

 same space of time, that a body consisting of only 100 particles does. If 

 you draw towards you two bodies, the one of 100, the other of lOOOlbs. 

 weight, will you not be obliged to exert ten times as much strength 

 to draw the heavier one to you in the same time that would be re- 

 quired for the lighter one ? Therefore if the earth draw a body of 1000 Ibs. 

 weight to it in the same space of time that it draws a body of 100 Ibs., 

 it follows that it does actually, as we have stated it to do, attract the 

 heavier body ten times more than the lighter one. So that the more 

 matter there is in a body, the more forcibly it will gravitate ; the more 

 force there is, the more there is for the force to do. The consequence of 

 this should be, that all bodies, whether light or heavy, being at an equal 

 distance from the earth, should fall to it in the same time, or, in other 

 words, that their velocities should be equal. But experience seems to 

 contradict this, for we see bodies falling quickly or slowly in proportion 

 as they are heavy or light. We must inquire, therefore, what is the cause 

 which interferes with the regular action of gravity on bodies, and makes 

 them fall with such various degrees of velocity. This cause is the resist- 

 ance of the air through which bodies fall. They must force their way 

 through this medium ; and heavy bodies overcome this obstacle more 

 easily than lighter ones, for the resistance which the air opposes to the fall 

 of bodies is proportioned to their bulk, not to their weight ; the air, being 

 inert, cannot do more to support the weight of a cannon ball than that 

 of a ball of leather of the same size ; now as the cannon ball contains 

 perhaps 100 times more matter than the leather ball, it would require 100 

 times more resistance to impede its fall equally. The larger the surface 

 of a body the more air it covers and the greater is the resistance it meets 

 with from it. A sheet of paper expanded descends gently to the ground. 

 If rolled up in a ball it offers but a small surface to the uir, encounters but 

 little resistance, and falls with much greater velocity. The heaviest bodies 

 may be made to float awhile in the air by extending their surface so as to 

 counterbalance their weight ; gold is one of the most dense bodies we 

 know ; but when beaten into a very thin leaf it offers so great an extent of 

 surface in proportion to its weight that its fall is still more slow than that 

 of a sheet of paper. When bodies have but little bulk in proportion to their 

 weight, the resistance of the air has but a very trifling effect 5 and stones 

 of different sizes let fall from the top of a house will reach the ground 

 very nearly at the same time. 



The air itself is also subjected to the law of gravity, the lower stratum is 

 actually in contact with the earth, and the superior strata are supported by 

 it, just as water at the bottom of a basin supports that which is at the 

 surface. But the air is an elastic fluid, the peculiar property of which is, 

 to resume, after compression, its original dimensions; and the air of the 

 atmosphere must be considered as constantly in a state of compression, 

 from the attraction of the earth ; it has therefore a constant tendency to 

 expand itself, and this is called the spring or elasticity of the air. This 



