M. Arago on Double Stark. > . 16 



simple result from the aggregate of the action of so many miU 

 lions of particles so differently placed. The problem is, in truth, 

 insoluble, when the attracting body is of an irregular form. 

 But when, on the contrary, this form is spherical, the calcula- 

 tion becomes of a remarkable simpUcity. For Newton has 

 proved, that the material particles^ when uniformly distributed in 

 the shape of a sphei-e, act^ on the whole, upon a point exterior to 

 them, as if they laere all united in its centre. 



Thus, then, so far as we have to do with bodies which are 

 accurately spherical, or nearly so, we shall have no need to oc- 

 cupy ourselves with the distances, whether great, lesser, or least, 

 of the different attracting particles, to the point attracted. All 

 will then turn out accurately, as if the sum-total of these par- 

 ticles were actually at the centre of the sphere ; there will only be, 

 in virtue of an abstraction which the theorem of Newton legi- 

 timately involves, a single distance to consider, viz. that from this 

 centre to the point that is attracted. 



There is yet another point, which, before proceeding to the 

 question of celestial physics, which is the proper object of this 

 chapter, it is necessary for us to examine, viz. How the attrac- 

 tive force of the earth exerts.itself, not so much on a body in re- 

 pose, as on a body in motion. 



Let us supppse that a ciinnon, placed at a certain height, has 

 been pointed, in a direction perfectly horizontal. The bullet 

 would fly from the piece horizontally. But every one knows, 

 that it would very soon leave this direction, — that it would gra- 

 dually descend, — that, at length, it would fall to the earth. Nor 

 is it doubled by any one, that this gradual descent of the bullet 

 is the effect of the attractive power of the earth. It is not, how- 

 ever^ so generally known, whether this attractive power is modi- 

 fi^d^jlji^its effects by the rapidity of the course of the bullet. A 

 very simple experiment will teach us. 



Let us suppose that, in fr9^1 of the cannon, there is a perpen, 

 dicular wall; and. that the distance of this wall shall be such, 

 that the bullet occupies exactly a second in flying to strike it. 

 Let us also mark the exact .point to which the axis of the can- 

 non is directed — the point which the bullet would strike, if ,it 

 moved ia a straight line — if, during its course, the earth didnpt 

 attract it. The vertical distance between the point thus marked. 



