14 M. Arago on Double Stars. 



ing, how the velocities will lead to a valuation of the masses ? 

 But let us continue. 



The space through which a body falls, by the earth's at- 

 traction, in the interval of a second, diminishes in proportion 

 as we are elevated above the surface. It is sensibly less at 

 the summit of a high mountain than at the level of the ocean. 

 The power which engenders this velocity, or, we would rather 

 say, the attractive force inherent in the material particles, dimi- 

 nishes then when the distance increases. And the law, accord- 

 ing to which this diminution operates, was desiderated. But 

 Newton has made this grand discovery ; he demonstrated, that, 

 at twice the distance, the attractive power of a body is two mul- 

 tiplied by two, or four times less than before ; that, at thrice the 

 distance, it becomes three multiplied by three, or nine times less 

 than it was ; and that, at ten times the distance, it has only one 

 hundredth part (10 multiplied by 10) of the attractive power. 

 As, then, in arithmetic, we call the square of a number the pro- 

 duct of a number multiplied by itself, we combine all the indi- 

 vidual results in this general formula : The attractive power of 

 a body diminishes in proportion to the square of the distances. 



We shall presently perceive, that the measures of velocities 

 raay lead to the determination of the masses. In the mean 

 while, let us recognise that it is necessary not to forget, how far 

 the experiment regarding velocity has been conducted. 



We shall now retrace our steps for a moment, to remove a dif- 

 ficulty which may occur to the mind of the reader, as to the mode 

 of taking the value of distances, in those cases where the attract- 

 ing bodies are of very large dimensions. 



When any small body, after haVingb^en elevated, we shall 

 say to the height of SO feet, is abahdoned to itself, and so falls, 

 we are convinced that this happens in virtue of the individual 

 action exercised by each of the material particles of which the 

 earth is composed. But these particles are not, one and all, at 

 the same distance from the falling body. The particles ai the 

 surface, to which it vertically corresponds, are, according to our 

 hypothesis, removed only SO feet. In addition to this, there is 

 a distance of 1600 leagues to the central particles^ and nearly 

 twice as much to those situated at the opposite side of the globe. 

 It truly seems next to impossible to draw any thing like a 



