482 
PROFESSOR SCHUMACHER ON THE LATE 
Now as the densities of two bodies are in the direct ratio of their masses, and in 
the inverse ratio of their volumes, we can express the specific gravity of a body as 
the quotient of its mass, divided by the mass of pure water taken at its greatest den- 
sity contained in a volume equal to that which the body occupies at 32° Fahr. : or, 
wliat is the same, as the quotient of its mass, divided by the mass of pure water 
which the body displaces ; the water having the temperature of nearly 39° Fahr., 
and the body that of 32° Fahr. 
If we denote the specific gravity of the body, thus understood, by A, the mass 
of the body by M, and the ratio of one of its dimensions under the tempera- 
ture of the melting ice, and under that of the weighing, by ... 1 : R, the space which 
it occupies at the temperature which it has when it is weighed is = M R 3 , and it dis- 
places a mass of air equal to M R 3 q , where q denotes the specific gravity of the 
air at the moment of the weighing. 
For the weights employed, let c>, m, r denote the same things as A, M, R for the 
body. We have consequently, when the body and the weights put upon the balance 
are in equilibrio, the equation 
M(l-^)= m (l-^) (1) 
whereby M, or the absolute weight of the body, is easily obtained, viz. 
M = m -j- M — — m (21 
AS v ' 
or, as m may in the second number of the equation be generally substituted for M, 
M = in -j- m — m r ^L nearly. (3) 
Should a case occur in which this substitution would affect the last place of decimals, 
we may employ, either the exact equation, derived immediately from (1) 
l — 
r 3 q 
M = 7)1 
1 — 
Wq 
(4) 
T> 3 
or put the value of M, found by the equation (3) as coefficient of _ -^2, into the equa- 
tion (2). 
28. In order to obtain the specific gravity, the body is weighed in air, and also 
when immersed in pure water. In the last case, as in the former, the weights are 
still in air. These two operations give, if we denote by 
