1821.] Chemical Compounds by Algebraic Characters. 215 



one atom : hence it will be - for the ratio by weight. In the 

 same way ch- carburetted hydrogen will want two for the carbon 

 and two for the hydrogen = four, making -^-. 



In some chemical investigations, it is found necessary to have 

 recourse to real algebra ; in which case the same means may be 

 employed to represent the atoms and volumes. An instance of 

 this kind occurred to me in reading a very excellent paper by 

 Dr. Henry, upon the gases used for illumination, read before the 

 Royal Society, Feb. 22, 1821. 



After, by his very elegant process, he has separated the ole- 

 iiant gas, by means of chlorine, he states that the proportions of 

 the residual gases have to be estimated from the joint data of 

 the quantity of oxygen required to saturate the gas, the quan- 

 tity of carbonic acid produced, and the specific gravity found by 

 experiment, which was *534, common air, being 1, or unity. In 

 examining this method I found that the datum of the sp. gr. is 

 not necessary to find the proportions of the remaining gases, 

 which are carburetted hydrogen, free hydrogen, and carbonic 

 oxide. The oxygen which 100 volumes of the mixed gas 

 required was 110 volumes, and the carbonic acid produced was 

 70 volumes. 



Now let a: = volumes of carburetted hydrogen in 100 volumes 

 of mixed gas ; y = the hydrogen ; and z = the carbonic oxide. 

 Then x + y + z = 100 the quantity employed. 



Then since x will take 2 x volumes of oxygen, y ±y volume, 

 and % \z volumes, we shall have 2 x + ±y 4- i-z = 100. 

 The carbonic acid produced by x will be equal to x, and that by 

 z equal to z. 



Therefore x + z = 70. 



Hence we get the three following equations : 



x + y + z = 100 



2 x + ±V + v 2 = 110 

 x + z = 70 



By subtracting the third from the first, we get, 



y = 30 



The second, multiplied by 2> gives, 



4 x + y + % = 220. From this subtract the first, 

 x +)/ + z - 100 



This gives 3 x = 120 



Hence x =. 40. And since z + 40 + 30 = 100. 



Therefore z = 30. 



These numbers are the same with Dr. Henry's. 



If the datum of the specific gravity be employed, one of the 



