( 400 ) 



No. LVIIL 



Extract from a paper on the Meteoric Stones, written by F. R. Hass- 

 ler Esq. Mathematical Professor in the Military School at West 

 Point, 



Read June 17th, 1808. 



THE first thing to be considered on the supposition that 

 these bodies are projected from the moon, is, whether the pow- 

 er exerted by any lunar volcano can be sufficient to throw a 

 heavy body beyond the sphere of its predominant attraction, 

 and of course enter that of the earth. This may be made a 

 subject of calculation on the following principles. 



Heavenly bodies exercise an attractive power in the direct 

 ratio of their masses, and inverse ratio of ihe squares of their dis- 

 tances. Let A, M, and D, represent the attraction, mass, and 

 distance of the earth; a, m, d, those of the moon; then the 



M m 

 whole force exerted by the two bodies will be A : a :: — : — . 



D* d 2 

 A body placed in circumstances most favourable to the hy- 

 pothesis would of course be between the two bodies, and in a 

 right line with the centers of both ; and in order to be merely 

 suspended in equilibrio between them, the two first terms of 

 this proportion must be equal to each other, and the two last 



M m 

 must also be equal, that is, — = — . 



D 2 d 2 

 Now, taking M to be, in round numbers, equal to 70m, and 

 D+d equal to the distance of the moon from the earth=D, the 



70m m 

 equation transformed becomes — =— , from which d is 



D=df d 2 

 D 



ibund= ; but D=60xfhe radius of the earth, which is, 



1+^70 

 in round numbers, equal to the mean distance of the moon ; 



