10 PHILOSOPHICAL TRANSACTIONS. [ANNO 1781. 



namely, 1.401. And since 11 gr. of this spirit of nitre contain 3.55 gr. of acid 

 and 7.45 of water, its loss of weight should be — — = 7-855; and. subtracting 

 the loss of the aqueous part from this, the remainder 0.405 is the loss of the 

 3.55 gr. acid, and consequently the true specific gravity of the pure and mere 

 nitrous acid is — -— = 8.7654. This being settled, the mathematical specific 

 gravity, and true increase of density of the above mixtures, will be found. Thus 

 the mathematical specific gravity of 1 2 gr. of that spirit of nitre, whose specific 

 gravity by observation was 1.389, must be 1.355, supposing it to contain 3.55 



3 55 

 sr. acid and 8.45 of water; for the loss of 3.55 gr. acid is -'—^ = o.405, and 

 o ° 8./03 



the loss of water 8.45; the sum of these losses is 8.855. Then — ~—= 1.355, 

 and consequently the accrued density is 1.389 — 1-355 = .034. In the same 

 manner it will be found, that the mathematical specific gravity of 13.08 gr. of 

 that spirit of nitre whose specific gravity by observation was 1.362, must be 

 1.315, and consequently its accrued density .047- 



But the whole still rests on the supposition that each of these portions of spirit 

 of nitre contain 3.55 gr. of acid. To verify this supposition, I could think of 

 no better method than that of examining the mathematical specific gravities of 

 the first mixture I had made of spirit of nitre and water in large quantities; for 

 if the mathematical specific gravities of these agreed exactly with those of the 

 quantities I had supposed in smaller portions of each, I could not but conclude, 

 that the supposition of such proportions of acid and water, as I had determined 

 in each, was just; and that this was the case will appear by the following calcu- 

 lations. 1st. When to 1963.25 gr. of spirit of nitre, whose specific gravity was 

 1.419, were added 179-5 gr. of water, the quantity of acid on the above suppo- 

 sition should be 634.53 gr.; for 11 : 3.55 :: 1 963.25 : 634.53; the quantity of 

 water in those 1 963. 25 gr. of spirit of nitre should then be 1328.72, and after 

 adding 179-5 gr. of water, the whole quantity of acid and water should be 



2142-75 ; the loss of acid was ' =71 .24, and the sum of the losses 1580.46: 



8.7054 



then the mathematical specific gravity should be tt^tt = 1.355, which is ex- 

 actly the same as that which was found in 12 gr. of this spirit of nitre, on the 

 supposition that they contained 3.55 gr. of acid. 



Again: when to 1984.5 gr. of this mixture I added 1 78.75 gr. of water, the 

 whole quantity of diluted spirit of nitre was 21 63.25 gr. and the quantity of acid 

 in 1984.5 gr. was 587.081 gr. for 12:3.55 :: 1984.5 : 587.081 ; the loss of this 

 quantity of acid is 66.96 gr. and the sum of the losses of acid and water is 

 1643.129 gr.; and consequently the mathematical specific gravity should be 



2i63.75 _ _ j which is the same as that determined in 13.08 gr. of the same 



1643.125 ° 



mixture. 



