VOL. LXXI.] PHILOSOPHICAL TRANSACTIONS. 15 



To obtain a synthetical proof of these deductions, I compared them with the 

 specific gravities of the first mixtures I had made: for if these deductions were 

 true, the mathematical specific gravities, and the accrued densities, added to 

 each other, should amount to the same quantity, as the specific gravities by 

 observation; and this I found to happen very nearly: for in the first 

 experiment, where 251 9.7 5 gr. of oil of vitriol, whose specific gravity was 

 1.8 19, were mixed with 180 gr. of water, that oil of vitriol contained 

 by my calculation 1376.171 gr. of acid and 1143.597 gr. of water, 

 besides the 180 gr. of water that were added to it, the loss of the acid was 



■ ° ' ' = 277.22. The whole quantity of oil of vitriol was 2699.75 gr.; then 



the sum of the losses was 1600.8I ; and therefore the mathematical specific 



gravity '" *, = 1.686; to which adding 0.84, the degree of accrued density, 



the specific gravity by observation should be 1 .770, which wants less than 1000th 

 part in 2700 of being just. Again: in the mixture whose specific gravity was 

 1.719, the sum of the losses was 1779.549, and the weight of the whole 

 2878.4; the mathematical specific gravity should be — — '-— - ■== I.617; towhich 



adding O.100, the specific gravity by observation should be J. 7 17, which is 

 nearly the truth. 



By continuing these mixtures till the specific gravities by calculation and 

 observation nearly coincided, I formed the following table. The extra-tabular 

 proportions are to be sought in the manner already shown; the first two series 

 were formed by analogy. 



