J. Walsh, Esq., on Physical Astronomy. 271 



senting the same magnitude, or the same relation, whatever change 

 takes place in one side, must take place also in the other. If this 

 is not the case, it is a proof that no equality exists. The force 

 of gravity, if such a force exists, is said to vary inversely as the 

 square of the distance from the attracting body. Let F be this 

 force, at any distance R, and /any other force of the same attract- 

 ing body, at any other distance r, then, 



E. — 



7 - R 5 



If we make R nothing, then the force F is infinitely greater than 

 the force/, whatever may be r, which is absurd. Then, therefore, 

 no equality can in every case exist, between the two sides of this 

 equation. Therefore, the law of universal gravity, or rather what 

 is said to be this law, is not the true law. 



It appears to me that the first law of Kepler, if this law is true, 

 is not yet demonstrated to be true. 



Let any body be at rest at B, 

 and let it be acted on at the 

 same instant by two forces, re- 

 presented by, and in the direction 

 of, the straight lines B C, B D ; by 

 the joiut effect of these forces, 

 it will move with a uniform mo- 

 tion along the diagonal B A. 

 Now, at the instant it is arrived 

 at A, let the central force S act 

 again on it, and cause it to 

 move along the line A z. It 

 is required to determine, how 

 shall this second central force 

 be represented. This is always 



done by taking Ah = A B, and drawing k n parallel to A m, and 

 nm to h A ; then, Am is said to represent this force ; now, if this 

 is true, then no force whatever acting in the direction A S, on the 

 body when at A, could cause it to move along this line A S, which 

 is absurd, as the body was not at rest, when at A. Then, there- 



