24- Mr. S. Tebay's Demonstration of the Rule of Descartes. 



oxide, 3 equivalents of ammonia, 2 equivalents of potash, and 

 1 equivalent of protoxide of iron. 



r 6 eq. carbon. 6 eq. carbonic oxide. 



1 eq. ferrocyanide potassium = \ a " "S?"' 



9* eq. water, 



At a subsequent period, when the evolution of carbonic 

 oxide ceases and the temperature rises very high, the iron be- 

 comes peroxidized at the expense of a portion of the acid, 

 sulphurous acid is emitted, and the iron-alum gradually 

 formed, the excess of alkaline sulphates remaining in solution. 



In conclusion, it may be worth while calling the attention 

 of those whom it may concern to the foregoing experiments, 

 as furnishing an extremely easy and ceconomical method of 

 preparing carbonic oxide for purposes of research or demon- 

 stration. A single half-ounce of the yellow salt treated with 

 some oil of vitriol in a common Florence flask fitted with a 

 perforated cork and conducting tube, gives more than 300 

 cubic inches of gas, which has all the marks of the most per- 

 fect purity : it does not in the least affect lime-water, and be- 

 comes entirely converted into carbonic acid by explosion with 

 half its volume of oxygen. The gas given off during the whole 

 of the reaction is equally pure, except quite at the end of the 

 operation, when, as before noticed, a little sulphurous acid 

 appears. 



V. Demonstration of the Rule of Descartes. 

 By Mr. Septimus Tebay of Preston. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 

 f TAKE the liberty of sending you the following simple 

 method which recently occurred to me of demonstrating 

 the rule of Descartes. 



Let x = v be any equation, and X p X 2 , X 3 , &c. the first, 

 second and third, &c. limiting polynomials derived from X. 

 Let the roots of the equations X = 0, Xj = 0, X 2 = 0, &c., 

 written in descending order, be represented by a v ff 2 , a 3 . . ., 

 &j, & 2 , b s . . ., c,, c 2 , c 3 . . ., &c. respectively, these numbers 

 being known to arrange themselves as follows: — 



* Probably G eq. from the oil of vitriol, the acid of which has combined 

 with the ammonia, potash and oxide of iron, and 3 eq. being the water of 

 crystallization of the salt. 



