238 
SELECTED ARTICLES. 
gen, we have a second equation containing v and z; ±v-\-iz 
= d, or'f- # + ^==41 ^ Combining this with the equa- 
tion obtained above, z—\\ d — 2 c, and v=S c — 1| d. 
Whence result the following simple rules: 
To obtain the soda from the method of analysis stated 
above, from \\rds of the weight of chloride of silver (B,) 
take twice the weight of the mixed chlorides (A.) 
To obtain the potassa. From three times the weight of 
the mixed chlorides (A,) take ?%rds of the weight of the 
chloride of silver (B.) 
To apply this to the example before discussed, suppose the 
weight of the mixed chlorides to be 24.5 grains, and of the 
chloride of silver 54.75 grains. From rds of 54.75, or 57, 
take thrice 24.5, or 49, the remainder, 8, will be the grains of 
soda in the mixture. 
From three times 24.5, or 73.5, take ffrds of 54.75, or 67.5, 
the remainder, 6 grains, will be the potassa. 
An equally simple method of calculation may be obtained 
without resort to algebra. By the second step of the analysis 
the chlorine in the mixed chlorides, of the metallic bases of 
the alkalies, is obtained, being ^-frds of the weight of the chlo- 
ride; subtracting this from the weight of the mixed chlorides 
obtained by the first step, we have the weight of the metallic 
bases. Taking |ths of the weight of the chlorine, we have 
the oxygen requisite to form the alkalies. Potassa contains 
ith, and soda ith of the weight of oxygen; J-ths of the potassa 
and |ths of the soda, will be equal in weight to five times the 
oxygen, the weight of which has just been obtained. But 
potassa contains f-ths of its weight of potassium, and soda |ths 
of its weight of sodium, and the united weights of these metals 
has also been obtained as above. Taking this latter sum from 
the former, we find that one-half the weight of the soda is 
equal to five times the oxygen less the weight of the metals. 
One sixth of the weight of the potassa is equal to the weigh t 
of the oxygen, less one-fourth the weight of the soda. 
Resuming the example before employed, in which the 
weight of the mixed chlorides is 24.5 grains, and of the chlo- 
