A new Solution of two Fluxions proposed hy Simpson. 383 

 Before the blow-pipe the spiculae of this substance are 

 separated from each other, becoming white, opake, and tri- 

 able, without any mark of fusion. The flame by passing 

 over it acquires a slicht tinge of green. 



The nodules above mentioned are not untrequently de- 

 composed throughout; having lost their internal lustre and 

 hardness, and acquired a dull grey or brownish colour. 

 Thev sometimes, when in this state, ccmtain numerous 

 small spontry cavities; and in some instances have been 

 found reduced altogether to the state of clay, apparently 

 from the effects of decomposition. ,.,,;, t>. 



It would appear that the fluoric acid, of which Mr. Davy 

 has ascertained the presence in the Waveihte from Devon- 

 shire, exists also in that from Cork ; for glass is corroded, 

 by heating upon it, in a drop of sulphuric acid, a tragment 

 of the mineral from either of those places. 



LVII. A new Solut'wn of two Fluxions proposed hj 

 Simpson. By James Andrew, LL.D. 



To Mr. Tilloch. 



Sir, In Simpson's Fluxions, pages 100 and 101, of 2d 

 edition, there are two fluxions proposed, whose fluents are 



to be found, viz. 1st, ^ ^ ^' ^ ^ ; and 2dly, a -Jz j" x 



z "'""'», and these fluents are determined in the places 

 referred to by means of rules investigated in pages 95 and 

 98 of the same work. The fluent in the former example 



beincr ^' + 3/"] - X 2^^ - ■■ig\ and in the latter case, - 



n-ys^' X (30a»+ 24/z" + l6/"z"") 



lOSwa' z'" 

 As I never much relished the rules in question, as they 

 have a tendency to confound beginners, and are neither 

 useful nor necessary in .he place where they have been 

 introduced, I trust the two following new solutions will 

 not prove unacceptable to some of the readers ot your valu- 

 able Magazine, as being more practicable m general, and 

 iTiore easily understood than the methods and rules re- 

 ferred to. I am, sir, your most obedient servant, 



Addiuombe Place, 20dM»y 1812. JaMES AnDBEW, LL.D. 



Bb4 1- ^'^'^"^ 



