[ 3+2 ] 
quantity lefs than \ of a grain ; yet the differences of 
the preceding numbers, from arithmetical or geome- 
trical progrefiions, are too great to be explained from 
any or all of thefe fources taken together. We 
may obferve that the Ioffes of weight, correfponding 
to equal portions of fait, are, upon the whole, di- 
minifhed; but it will not follow from thence that 
the bulks are not equally augmented. For, ffnce the 
fpecific gravity of every body is properly denoted 
by a fraction, whofe numerator exprefies the abfolute 
weight, and denominator the magnitude of the 
I j , W W-\-X W+2X wA- 2 x o . r • r 
body: let — , — — , , — , &c. be a fenes of 
J m m 4- y w -f- z m -f s 
fractions, whofe feveral numerators exprefs the 
weights of a given quantity of water, as increafed by 
the addition of equal portions of any fait denoted by 
x , and whofe denominators exprefs the bulks of the 
water after the folution of each portion of fait, the 
increments of bulk being denoted by y, z, s ; now 
let us fuppofe that the Ioffes of weight fuftained by 
the fame body, that is, the fpecific gravities, increale 
uniformly, then will the above feries of fractions 
increafe uniformly, 
, tv wA-x , 
let ——a \ — ; — A- bt 
m ’ m-\-y 1 
w -f- 2 x 
m- f-z 
— a 4- 3 by from thefe equations 
inveffigating the proportion between y , z , s, 
which reprefent the augmentations of bulk, it will 
appear that y : z : : a-\- ib : za-\-2b, or in a greater 
ratio than that of i : 2 and that z : s :: 2a-{-6/> : ya 
-\-6b or in a greater ratio than that of 2:3, in 
which ratios they ought refpe&ively to have been, 
had the denominators or the bulks of the fluid in- 
creafed 
