234 
SELECTED ARTICLES. 
step proposed by Doctor Thomson, the weights of the metals. 
These weights furnish his second equation. 
In the example referred to, we have found by comparing 
paragraphs 1 and 2, the weight of the mixed alkalies to be 14, 
whence calling x and y the unknown number of equivalents 
of the potash and soda respectively, resulted the equation 
14 — 4 y 
6 x + 4 y— 14, and thence x — — - 
From the second paragraph the weight of sulphate of baryta 
obtained is given 43.5 grains; whence using the same equiva- 
lents as Doctor Thomson has employed, the baryta is found 
to be 28.5 grains, of which 25.5 grains is barium and 3 grains 
oxygen. Deducting this oxygen, which belonged to the alka- 
lies, from the weight of the mixed alkalies, we have 11 grains 
for the weight of the metals, and the second equation given by 
Doctor Thomson. 
5 x -{- 3^=11, or x — 1 1 ^ y 
It is plain that these remarks will be true if the nitrate of 
baryta should be substituted for the chloride of barium in ob- 
taining the quantity of sulphuric acid present; for the quan- 
tity of oxygen in the baryta of the precipitated sulphate, will 
always be equal to that in any protoxide, or protoxides, satu- 
rating the same weight of acid. 
The third step in the proposed analysis is therefore super- 
fluous, unless used as a means of verification. 
I propose now to obtain, as Doctor Thomson has done, in the 
sequel of his paper, general equations for calculating the weights 
of the alkalies from the analysis, omitting only a reference to 
the third step, which has been shown to be unnecessary. As 
algebraic notation is repulsive to some who may choose to refer 
to this method of analysis, I will endeavour finally to prove 
the results by arithmetical processes, and to point out a simple 
method of calculation. 
It seems to me more convenient to determine the absolute 
weights of the alkalies from a formula, rather than the number 
of equivalents. 
