M. Arago on Double Stars. 17 



(in place of the radius we had almost said the perpendicular wall 

 CT, as in the case of the bullet), it is in M that the two meet. 

 But the moon could not quit the direction AT, according to which 

 it was moving, unless some power had turned it aside from this 

 first course. 



But it is to be remarked, that this power is the energy of the 

 attraction of the earth placed at C ; — that this power, in acting 

 upon our satellite during the time it required to transport itself 

 from the radius CA to the radius CMT, has attracted it, — ^has 

 made it to fall the length of TM,— the distance, so to express 

 it, from the fixed point T to the point M, which is really struck 

 by the projectile moon. 



To demonstrate the proposition, is to make the following ob- 

 servations and calculations. By the help of a direct experiment, 

 we determine the angle which the radius CA, directed from the 

 earth to the moon at a certain epoch, forms with the radius CM 

 carried towards the same luminary, a second of time afterwards. 

 The radius CA, that is the distance from the moon to the earth, is 

 known in leagues and yards. Hence it ought to be, or rather 

 it in fact is, easy to calculate for the angle ACM, the measure of 

 the angular displacement of the moon in the interval of a second, 

 how much the point T, the extremity of the tangent, is distant 

 from the point M, situated upon the small arc of the circle AM, 

 that is to say, by what fraction of a yard the moon has fallen 

 towards the earth in a second of time. 



The space through which a body falls in a second, when it is 

 left to itself at the surface of the earth, when, in other terms, it 

 is 1600 leagues from the centre, is 4.9 metres. That we may 

 obtain the distance it would fall, if it were removed from this 

 same centre, even to the distance of the moon, we reduce the 

 preceding number in the ratio of the squares of the distances. 



The result of this very simple calculation is found to be, with 

 an astonishing degree of accuracy, the numerical value of the 

 distance MT, such as it has been deduced from the velocity of 

 the moon, and the dimensions of her orbit. Thus it is nothing 

 but the power whose effects we daily observe at the surface of 

 the earth, — the power to which the falling of a body is owing, 

 that maintains our satellite in the curve which it describes 

 around our globe. This power alone, compared with its inten- 



VOL. XVII. NO. XXXIII. JULY 18B4. B 



