On Percylite, a Mineral not hitherto described. 131 



dividing the preceding by 4 ; and in this way we get at once 



355 



-— =3- 1415929203539823008849557522123 

 *^^ 893805309734513274336283185840 



707964601 76991 1 504424778761061 

 946902654867256637168 14159292 



where the decimals recur after the 8 in the 112th place. If 

 the remainder at which we stop, in the operation of determi- 

 ning the leading decimals by common division, be a multiple 

 instead of a submultiple of a preceding remainder, then the 

 continuation of the development would be obtained in a man- 

 ner analogous to that by which the development of — is ob- 

 tained above. And even should the remainder, 5, at which 

 we stop, be neither a multiple nor a submultiple of a preceding 

 remainder, «, yet the development may be carried on upon 

 the same principle; the multiplier, by aid of which each 

 group of decimals is derived from the preceding group, being 



always -. 



Had the arithmetical facilities noticed in this paper occurred 

 to the older mathematicians, who spent so much time in ap- 

 proximating to the ratio of the circumference of a circle to its 

 diameter, much of that time would have been spared. 



London, Jan. 14, I850> 



XVI. On Percylite^ a Mineral not hitherto described. 

 By H. J. Brooke, Esq., F.R.S."^ 



I RECEIVED many years since from Mr. Heuland a very 

 small specimen of an undescribed sky-blue mineral in 

 minute cubes, accompanied by gold, on a matrix of quartz and 

 red oxide of iron, which was said to have come from La Sonora 

 in Mexico. 



In consequence of the quantity of the mineral on the spe- 

 cimen being too small for analysis without destroying the spe- 

 cimen itself, the mineral has remained until this time unex- 

 amined. But it having been pointed out to me by Mr. Lett- 

 som that there was a much larger one in the British Museum, 

 placed among those of gold, from which, without the slightest 

 injury to it, a sufficient portion could be taken for analysis, 

 I applied through Mr. Konig to the Trustees of the British 

 Museum, and obtained their permission to detach the small 

 quantity that has been analysed by Dr. Percy. 



* Communicated by the Author. 

 K2 



