24i4 Mr. P. Nicholson on derivative Analysis. 



state, was precipitated by carbonate of soda: 0*0 IV gr. of 

 oxide of manganese was obtained, =0'340^er cent. 



h.) The excess of hydrosulphuret of ammonia being re- 

 moved, the hquid was decomposed by acetate of barytes ; the 

 sulphate of barytes was separated by filtration, and the fluid 

 containing acetic acid being evaporated, and heated, and the 

 residuum boiled in water, 0*21 7 gr. of carbonate of soda were 

 obtained, containing 0"13057 of soda, =2*611 percent. It 

 must be observed, however, that in dissolving this carbonate of 

 soda in water, some traces of magnesia remained undissolved, 

 which had previously been dissolved in the alkaline solution. 



i.) The residual matter {h) was dissolved in muriatic acid, 

 the barytes precipitated by sulphuric acid, and separated on a 

 filter; and the liquid in a state of ebullition precipitated by 

 carbonate of soda: 0*271 gr. =5*420 pe7- cent, of pure mag- 

 nesia was obtained, which entirely crystallized with sulphuric 

 acid, into sulphate of magnesia. 



The fluoric and phosphoric acids were sought for, in an 

 assay made for the purpose, but no traces of them were dis- 

 covered. Erlan, therefore, consists of 



Silica 53*160 



Alumina 14*034 



Lime 14*397 



Soda 2*611 



Magnesia 5*420 



Oxide of iron 7*138 



Oxide of manganese 0*639 



Volatile matter 0*606 



98*005 



L. Derivative Analysis ; being a new and 7nore covtprehensive 

 Method of the Transformation of Functions than any hitheito 

 discovered: extending not only to the Extraction of the Roots 

 of Equations, hit also to the Reduction of Qtiantities from 

 the Mtdtiples of Powers or Products to other equivalent Ex- 

 pressions, by which the Summation of any rational Series may 

 be readily effected. By Mr. Peter Nicholson*. 

 5 Claremont-place, Judd-street. 



To the Editors of the Philosophical Magazine and Journal. 

 Part 1 . — Midtiplication. 

 IVTULTIPLICATION is performed in the usual way; but 

 ^^^ instead of the compound coefficients of the entire pro- 

 duct, substitute a letter for the amount or aggregate of each 

 jiuch coefficient; then as many equations as the entire product 

 * Coninuinicated by the Author. 



has 



