6 Professor Young's Demonstration 



The tribasic salt gives — 

 Dried at 212°. 

 Carbon . . . 21*89 

 Hydrogen . . 3*06 

 Oxygen . . . 23*75 

 Oxide of lead 52*30 



100*00 100*00 



651*1 100*00 



If we consider the xanthorhamnine, as dried in the oil-bath, 

 to be then anhydrous, the bodies analysed become 



Xanthorhamnine, dry = C 23 H 12 ]4 . 



dried at 212° m C^ H 12 14 + Aq. 

 dried in vacuo = C^ H 12 14 + 1 5 Aq. 



1 st lead salt, C 23 H 12 14 + 2. PbO + 3 Aq. 

 2nd lead salt, C^ H 12 14 + 3.PbO + 6 Aq. 



The xanthorhamnine is thus formed by the addition of one 

 equivalent of water and two of oxygen to the chrysorhamnine, 

 as C 23 H n O n + HO + 2 = Cc^ H 12 14 . And if we were" 

 to consider the substance dried in the oil-bath at 320° still to 

 retain an atom of water, it should be simply oxidated chry- 

 sorhamnine, being, when dry, 



III. Demonstration of the Rule of Fourier. By J. R. 

 Young, Esq., Professor qf Mathematics in Belfast College*. 



T^VERY thing relating, to the analysis and solution of nu- 

 -•" merical equations has at length been brought under the 

 dominion of common algebra, with the single exception of the 

 rule which Fourier has proposed for discovering the character 

 of a pair of roots indicated in a given interval. The investi- 

 gation of this rule has hitherto involved the analytical theory 

 of curves, or else the theorem of Lagrange on the limits of 

 Taylor's series. It is desirable that this rule be stripped of 

 its transcendental form, and be reduced to a level with the 

 other general principles that now constitute the doctrine of 

 numerical equations. It is the intention of the following proof 

 to effect this object. 



Let a, b represent the numbers which bound the doubtful 

 interval comprehending the two roots sought. We may con- 

 sider these numbers to be positive, giving rise to the following 

 variations in the three final functions : — 



* Communicated by the Author. 



