168 
Proceedings of the Royal Irish Academy. 
Dividing now (1) by (3), and putting 
I=KC, G = K'C, 
we have 
o-KUK',J-^^., (4) 
again dividing (2) by C we have 
„. ^, 1004. 
Adding these equations, we have the amount of the cane sugar given by 
the equation 
and substituting this value in (4), 
These equations, combined with that obtained by means of Barres- 
wil's solution, are, as was shown by Dr. Apjohn for Soleil's instrument, 
sufficient for the solution of the question — when the coefficients K, K' 
have been previously determined. 
It may be well to mention some precautions which are necessary 
for the success of this experiment : — 
1. It has been shown that the amount of cane sugar can be found 
by the optical method alone, without the aid of the copper solution. 
The truth of this conclusion, however, depends on the identity of the 
temperature in the first and second experiments. If the temperature 
be not the same, / will have different values in (1) and (2), and it will 
be no longer possible to determine the amount of the cane sugar by 
the optical method alone. I^ow, it may often happen that the deter- 
mination of the cane sugar is the only point of practical importance in 
the investigation. It is therefore desirable that the experiments (1) 
and (2) should be made at precisely the same temperature. 
2. It is known that the rotatory power of a solution of grape 
sugar, when freshly made, is greater than that of a solution which has 
been allowed to stand for some time. This power, however, may be 
reduced to its minimum value by heating the solution to 180° Pahr., 
and then allowing it to cool. It is therefore necessary to heat to the 
same temperature the given syrup containing the mixture of the three 
sugars, in order to reduce to a fixed value the rotatory power of the 
grape sugar which it contains. 
