380 Mr DAVIES on the Equations of Loci 



dinates, under the aspect which they presented to my mind in 

 the first place. Other methods have since exhibited themselves, 

 and the application of analogous methods to other surfaces be- 

 sides the sphere ; but I cannot enter upon them here, though I 

 have developed them to a considerable extent, and applied them 

 to a variety of purposes. The employment of my method of 

 spherical geometry to physical inquiries has not escaped my at- 

 tention ; and I look forward with great confidence to its furnish- 

 ing its aid to many branches of natural philosophy, so as to com- 

 pletely remodel the mathematical methods of conducting those 

 researches. 



Owing to severe indisposition, which prevented my giving pro- 

 per attention to the proof-sheets when my former paper was 

 transmitted to me from Edinburgh, several errata have occurred, 

 and I here take the opportunity of indicating the corrections. 

 I have also added a few emendations of passages in that paper, 

 supplied certain material omissions, and corrected one faulty 

 process that occurs there. 



I ought also to add, that the present paper was written in its 

 unabridged state more than three months ago ; and that in the 

 preparation of it for the Royal Society, no addition or alteration 

 has been made, except what is merely verbal, the omissions alone 

 excepted. 



BATH, Feb. 24. 1833. 



