CENTRE OF GRAVITY. 



221 



CENTRE OF GRAVITY. 



BY the earth's attraction, all the particles which compose the mass of a body 

 are solicited by equal forces in parallel directions downward. If these com- 

 ponent panicles were placed in mere juxtaposition, without any mechanical 

 connexion, the force impressed on any one of them could in nowise affect the 

 others, and the mass would in such a case be contemplated as an aggregation 

 of small particles of matter, each urged by an independent force. But the 

 bodies which are the subjects of investigation in mechanical science are not 

 found in this state. Solid bodies are coherent masses, the particles of which 

 are firmly bound together, so that any force which affects one, being modified 

 according to circumstances, will be transmitted through the whole body. Li- 

 quids accommodate themselves to the shape of the surfaces on which they rest, 

 and forces affecting any one part are transmitted to others, in a manner de- 

 pending on the peculiar properties of this class of bodies. 



As all bodies, which are subjects of mechanical inquiry, on the surface of 

 the earth, must be continually influenced by terrestrial gravity, it is desirable 

 to obtain some easy and summary method of estimating the effect of this force. 

 To consider it, as is unavoidable in the first instance, the combined action of. 

 an infinite number of equal and parallel forces soliciting the elementary mole- 

 cules downward, would be attended with manifest inconvenience. An infinite 

 number of forces, and an infinite subdivision of the mass, would form parts of 

 every mechanical problem. 



To overcome this difficulty, and to obtain all the ease and simplicity which 

 can be desired in elementary investigations, it is only necessary to determine 

 some force, whose single effect shall be equivalent to the combined effects of 

 the gravitation of all the molecules of the body. If this can be accomplished, 

 that single force might be introduced into all problems to represent the whole 

 effect of the earth's attraction, and no regard need be had to any particles of 

 the body, except that on which this force acts. 



To discover such a force, if it exist, we shall first inquire what properties 



