88 GRAVITATION. 



example, let A be 

 the attracting body, 

 and b another body 

 which it attracts; ^ 

 now from what was f== 

 stated before, it will 



readily appear, that the force of gravitation exerted by a, 

 between the points c and d, is the same with that between 

 b and e. But at d, the body is under the influence of 

 only half this force, for all that part which is between c 

 and e does not act upon the body, whereas at be it feels 

 the whole. It would appear therefore from this diagram, 

 that if we double the distance of any attracted body, we 

 diminish the amount of force which acts upon it by one 

 half. This however is not strictly true, for the preced. 

 ing diagram represents only a part of the increase of 

 space, in receding from a 

 point. In the adjoining fig- 

 ure, where c represents the 

 centre, and oc, od, &,c, lines 

 diverging from it, and 6 and 

 a corresponding spaces at dif- 

 ferent distances, it will be seen that b is more than twice 

 as large as a, for it doubles in length, and also in breadth; 

 it is consequently four times as large. If b were three 

 times as far from o, as a is, it would accordingly be nine 

 times as large. Consequently the force of gravitation, in 

 order to be equal at every distance, must be diffused, as 

 it were, in proportion to the square of the distance ; and 

 as the power over any particular body will be inversely 

 as the diffusion of the force at the distance of the body, 

 it follows that this power will be inversely as the square 

 of the distance. This result, it is necessary for the reader 

 fully to understand, and to fix in his memory. It is 

 considered a fundamental law. Expressed in general 

 terms it is as follows : 



The force of gravitation exerted by one body upon 

 another, is inversely as the square of the distance of the 

 bodies* 



* This is usually stated at once as the fundamental law of gravi- 

 tation, and iiot deduced, as we have done, from the simpler state- 



