On extracting the Roots of Equations. 173 



It may be interesting to mention, in reference to the siliceous 

 calculus I have described to you, that the urine of the indi- 

 vidual (who voided the fragments of which silica formed a 

 constituent part) after a repose of nine days had deposited 

 (spontaneously) a xchite sediment with mucus superimposed, and 

 much urea beautifully crystalline. 



At page 332 of Mr. Children's very excellent translation of 

 Berzelius on the blowpipe (and which adds to the high claims 

 Mr, Children, as an accomplished chemist, has on our respect 

 and gratitude) " siliceous calcuU " are described as leaving 

 2)er se " an infusible, sometimes scoriaceous ash, which fuses 

 with a small quantity of soda, slowly and with effervescence, 

 into a more or less transparent glass globule." 



It is respectfully submitted, as a query, whether the follow- 

 ing, page 330, be sufficiently explicit to prevent the obtrusion 

 of error ? — " The slight ammoniacal odour which potassa de- 

 velops with almost all animal substances has nothing to do 

 with this," viz. that evolved in the case of calculi composed of 

 urate of ammonia. I always am, gentlemen. 



Your obliged and obedient servant, 



J. Murray. 



XXIX. Ne'uo Demonstrations of the Method iiivented by 

 BuDAN, and improved by others, of extracting the Roots of 

 Eqications. By Mr. Peter Nicholson*. 



Them-em. 



If Aa:*^'+B^"-'-hCa;*'-' + &c = P/-' + Q/-'+ R/-=^ + &c. 



andAx" +B/-' + C^'''"V&c = P'/ +QV'-' + R'/-' + &c. 

 and if x—e=.voxx = v + e, then will the coefficient of the 

 ni\\ term of the second side of the second equation be equal to 

 the product of the coefficient of the («— l)th term of the se- 

 cond side of the first etjuation, and the given quantity e plus 

 the coefficient of the n\h. term next following. 



That is, P'= P, Q'=: Ve^Q, R'= Qe-\-\i, S'= Rt-H-S &c. 



Demonstration. 

 For by hypothesis. 



Ax 4-l5.r +Cx 4-&c.= Pu +Qy + Rv +&c. 



Multii)ly tlie first side of this ecjiialion by x, and the second 

 side by its ccjiuil v-\-c, and wc have the ecjuation 



* Coiuinuiiicutcd by the Aiitlior. 



Ax 



