A HISTORY OF SCIENCE 



' Gravity being regarded as the cause of the falling 

 of bodies, a gravitating force is spoken of ; and thus the 

 ideas of property and of force are confounded with each 

 other. Precisely that which is the essential attribute 

 of every force that is, the union of indestructibility 

 with convertibility is wanting in every property: 

 between a property and a force, between gravity and 

 motion, it is therefore impossible to establish the equa- 

 tion required for a rightly conceived causal relation. 

 If gravity be called a force, a cause is supposed which 

 produces effects without itself diminishing, and in- 

 correct conceptions of the causal connections of things 

 are thereby fostered. In order that a body may fall, it 

 is just as necessary that it be lifted up as that it should 

 be heavy or possess gravity. The fall of bodies, 

 therefore, ought not to be ascribed to their gravity 

 alone. The problem of mechanics is to develop the 

 equations which subsist between falling force and 

 motion, motion and falling force, and between dif- 

 ferent motions. Here is a case in point: The mag- 

 nitude of the falling force v is directly proportional 

 (the earth's radius being assumed oo) to the mag- 

 nitude of the mass m, and the height d, to which it is 

 raised that is, v = md. If the height d = /, to 

 which the mass m is raised, is transformed into the 

 final velocity c = I of this mass, we have also v = me; 

 but from the known relations existing between d and c, 

 it results that, for other values of d or of c, the measure 

 of the force v is me* ; accordingly v = md = me*. The 

 law of the conservation of vis viva is thus found to 

 be based on the general law of the indestructibility of 

 causes. 



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