M. Arago on Double Stars. IS 



to weigh the planets. And were we here to reveal all our mind, 

 it would be seen, although we have really to discuss all the 

 fundamental principles of the theory of attraction, that we less 

 fear not being understood, than to hear it remarked by those 

 who shall have the patience to follow the demonstration to its 

 close, " Why ? is that all !'' 



A body left to itself falls to the earth ; but an inert body, that 

 is to say, one having no will of its own, cannot move, cannot 

 fall, or rise, or stir in any direction, unless some power forces 

 it. All the elements of this power emanate from the material 

 particles which compose our globe. Their whole effect, their 

 result, is what is called attraction — gravitation — weight. 



The total force which solicits any individually attracted par- 

 ticle, being the sum of the actions of each material particle of 

 the attracting body, it will be, so far as its intensity is concern- 

 ed, proportional to the number of their ultimate particles. Thus 

 suppose that the earth, without any change of its dimensions, 

 were to become one hundredth part more compact, — that it were 

 to come to include a hundredth part more matter in the same 

 volume, its attractive force over the bodies placed on its surface 

 would become one hundredth part greater than it was before. 



There is now, then, no difficulty in comprehending the ex- 

 pression so often used — that the attraction is proportional to tJw 

 mas^ ! 



Inquire we now, how a variation in the mass, or, which is the 

 same thing, in the attractive power of our globe, will manifest 

 itself.'' We answer — by a correspondent variation in the velo- 

 city of falling bodies. This velocity (which daring exceedingly 

 short periods may be considered as uniform) ought in effect to 

 be proportional to the power which produces it; in other words 

 — the power is as the mass. The velocity, then, will also be 

 proportional to the mass. Under present circumstances, a heavy 

 body, at Paris, passes, in the first second of its fall, through 

 (4j^j5) 4*9 metres. But if the mass of the earth were to be aug- 

 mented one hundredth part, the space gone over in this first se-- 

 cond would be increased by a hundredth part : instead of 4.9 

 metres, we should find it measured 4*9 and .049 ; which toge- 

 ther make 4*949. Is there now, then, any difficulty in perceiv- 



