Proceedings of the Riryal Society. 381 



" In pure mathematics, though their nature, as a work of 

 intellectual combination, framed by the highest efforts of 

 human intelligence, renders them incapable of receiving aids 

 from the observation of external phaenomena, or the invention of 

 new instruments ; yet, they are, at this moment, abundant in the 

 promise of new applications ; and many of the departments of 

 philosophical inquiry which appeared formerly to have no re- 

 lation to quantity, weight, figure or number, as I shall more 

 particularly mention hereafter, are now brought under the 

 dominion of that sublime science, which is, as it were, the 

 animating principle of all the other sciences. 



" When the boundary of the Solar System was, as it were, 

 enlarged by the discovery of the Georgium Sidus, and the 

 remote parts of space accurately examined by more powerful 

 instruments than had ever before been constructed, there 

 seemed little probability that new planetary bodies should be 

 discovered nearer to our earth than any of those already known; 

 yet this supposition, like most others, in which our limited 

 conceptions are applied to nature, has been found erroneous. 

 The discoveries of Piazzi, and those astronomers who have 

 followed him, by proving the existence of Ceres, Pallas, Vesta, 

 and Juno, bodies smaller than satellites, but, having the mo- 

 tions of primary planets, have opened to us new views of the 

 arrangements of the Solar System. Astronomy is the most 

 antient and the nearest approaching to perfection of the sciences; 

 yet, relating to the immensity of the universe, how unbounded 

 are the objects of inquiry it presents, and amongst them, how 

 many'grand subjects of investigation ; such for instance, as the 

 nature of the systems of the fixed stars, their changes, the 

 relations of cometary bodies to the sun, and the motions of 

 those meteors, which in passing through our atmosphere, 

 throw down showers of stones : for, it cannot be doubted, that 

 these bodies belong to the heavens, and that they are not for- 

 tuitous or atmospheric formations ; and in a system, which is 

 all harmony, they must be governed by fixed laws, and in- 

 tended for definite purposes. 



** The grand question of universal gravitation, and its con- 



