a 
376 BIOT ON THE EMPLOYMENT OF POLARIZED LIGHT ~ 
system in which the relation of the total amount of water to the 
tartaric acid is given and expressed by n, adding for this pur- 
pose, if necessary, a known weight of water. It is required, 
moreover, to assign the composition in weight of this new sy- 
stem, that is to say the proportions ¢ of tartaric acid, e of water, 
B of boracic acid which it contains in each unit of weight. 
Let any weight T be taken of the tartaric solution A’, B of 
the boracic solution A", E of additional water, giving for weight 
of the total system T+ B+ E. If T and B are decomposed 
into their respective constituent principles, and E be added, we 
shall have the constituent elements of the mixed system, as re- 
presented in the following table: 
Weight employed of each Absolute Absolute 
partial system. weight of acid. | weight of water. 
Tartaric solution T ... eA ¢T 
Boracic solution B ... . 5 eB 
Additional water E ...|] —seeeee 
Then the composition of the mixed system T+B-+E will be as 
follows : 
Proportion of tartaric acid in each unit of weight of the solution : 
 T 
€ as Bs 
Proportion of boracic acid in each unit of weight of the solution : 
Bee e’B 
~~ T+B4+E 
Proportion of water in each unit of weight of the solution: 
_@T+eUB+E. 
ia ese: SE 
which gives generally, 
e+Bt+e=1. 
Therefore, in order that e should be equal to m«, as is required, 
it will be necessary to lay down the equation of condition 
éT+eB+E=n8#T, 
whence we derive 
E = (née — e) T — e'B, 
in which we have always 
fF+eé=i. 
It is necessary that E should be positive, or at most null ; for 
