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



fore, A m cannot represent the second impulse of the central 

 force. Then, therefore, the first law of Kepler, if true, is not yet 

 demonstrated to be true. 



Let us now try if any other law, more conformable to the nature 

 of analysis, and the spirit of demonstration, can be substituted in 

 the place of the inverse ratio of the square of the distance, to show 

 the variations of the force with which any two attracting points 

 act on each other, when at any distance asunder. 



When the points are in contact, the spaces which they would 

 uniformly describe in the same time by their total actions on each 

 other, were they free to move, would be inversely as their forces. 

 Let C be the straight line, which any of them may uniformly de- 

 scribe in any given time, by an action equal to that, which the 

 other point would exercise on it when in contact with it; and let 

 x be the distance of this point from the point of contact, which I 

 call the centre of gravity of the two attracting points ; then, 



c 3 



will always represent the force whatever may be x. And no 



(c + x) 2 



other can be the law of universal gravity, if such a principle exists. 



Let a and y correspond to the second attracting point, then we 



shall have for the relation between the forces with which they act 



on each other, c 1" + ?/?" a constant quantity, whatever may be 

 a 3 (c + x)- 



x and y. 



John Walsh. 



Art. X. Description of a Giotto in the Interior of the 

 Colony of the Cape of Good Hope. By Mr. G.Thompson. 



[Communicated by the Rev. F. Fallows.] 

 The Grotto is situated in the Kango, in the district of George, 

 about 350 miles from Cape Town. It was first discovered by a 

 Mr. Botha, a farmer, by accident, when on a hunting party, and a 

 few days afterwards it was entered by him and a party of far- 

 mers ; this occurred in the year 1780. 



The hill, where the grotto is, is between 5 and 600 feet in 



