18 M. Arago on Double Stars. 



sity at the surface of the earth, shews itself there diminished in 

 the proportion of the squares of the distances ; and we repeat it, 

 without our being required to take into consideration the state 

 of motion of the moon. 



With these preliminary ideas, we may now address ourselves 

 to the question of the determination of the masses of the celestial 

 bodies. 



Suppose that we set about finding how much more of a mass 

 the sun is,— how much more matter it includes — than our globe. 

 We shall take the space 4.9 metres, which a body falls at the 

 surface of the earth in the interval of a second ; we shall reduce 

 it in the proportion of the squares of the distances, so as to know 

 what would be (always by the action of the earth) the fall of this 

 same body, if its distance should become equal to that of the 

 sun. The result of this simple calculation will be proportional 

 to that of the mass of the earth. A luminary which, at the 

 same distance, would induce, towards its own centre, a fall 

 double, triple, or a hundred-fold — would evidently be a mass 

 double, triple, or a hundred-fold that of the earth. The ques- 

 tion is thus brought to this, How much does the sun, in the in- 

 terval of a second, cause to fall, towards its centre, a body 

 which is removed from it as far as our globe ? Moreover, this 

 last question, which, at its announcement, might appear un- 

 answerable, since we are not able to transport ourselves to the 

 surface of the sun, there to make experiments on the falling of 

 heavy bodies, finds its solution direct and immediate in the cir- 

 cumstances of the annual motion of the earth. 



In virtue of this motion, our globe describes round the sun, 

 in 365J days, an almost circular curve, the radius of which 

 is 39,000,000 of leagues. Let[us divide the 360° comprehended 

 in this circle, by the number of seconds contained in 365^ days. 

 The quotient will be the very small fraction of a degree,' which 

 the earth goes round in its orbit in a second of time. Let us 

 now look back to the figure on page 16. Let us suppose the 

 sun in C ; the earth in A; let us consider the angle ACM equal 

 to the angular displacement which the earth undergoes in a se- 

 cond ; the radius of the orbit C A of the length of 39,000,000 of 

 leagues, and we can then easily calculate in fractions of a league 

 or in yards, the distance TM, which the sun, by his attractive 

 power, causes the earth to fall in a second. We have recently de- 



