484 
PROFESSOR SCHUMACHER ON THE LATE 
M. Bessel supposes that atmospheric air, at the temperature of melting- ice, and 
under the pressure of 29*922 English inches (= 076 metre) of mercury, has the spe- 
cific gravity of 
13-59606 ] 
10475-6 — 770-488 
where the numerator is the specific gravity of mercury according to Brisson’s expe- 
riments calculated by Hallstrom, and the denominator the ratio of the density of 
air to that of mercury found by MM. Biot and Arago. This gives for q, or for the 
height of the barometer expressed in English inches and reduced to the density of 
mercury at the temperature of melting ice, and for t , the temperature of the air ex- 
pressed in Fahrenheit degrees, 
770-488 ‘29-922* 1 + (t-32°) 0*0020838 — ^ ‘ 23054*39 [1 + (t -32°) 0-0020833] 
Supposing weights of brass whose specific gravity = 8 (the correction for the 
actual specific gravity of the brass weights differing from 8 is easily applied, as will 
immediately be shown), and taking the linear expansion of brass for one degree of 
Fahrenheit’s scale = 0-000010436, we have for this metal 
r 3 = [1 + it — 32°) O'OOOO 10436] 3 
and consequently, 
r 3 ? _ ^ [1 + (7 — 32°) 0-00001 0436 ] 3 J_ 
§ ~ ' 23054-39 [1 + {t ~ 32°) 0-0020833] " 8 
Table I., here following, contains the logarithm of the coefficient of h in this for- 
mula, which coefficient we shall denote by a ; so that a = b a; the argument of 
which is the temperature of the air (the temperature of the weights being supposed 
equal to that of the air), or t in Fahrenheit degrees. If the body is weighed in 
water, it is evident that a! must be taken with the argument t' (= temperature of 
ployed for that purpose, nor even of what metal they are. Indeed, a depends on b and t, and a' on V and t': 
consequently if b' — b, and t' = t, we have also «' = a, and the fraction — — — ( tl 
1 J to (1 — a) — 7ti (1 — a') 
has the common factor in the denominator, and numerator (1 — a), which consequently disappears, and re- 
duces it to 
toR' :1 Q to'R * 1 q 
A = 
m — m' m — to' 
The same result is obtained by the equation (9), in which in this case 
vi to' 
(to — to ') 2 
Q (a — a') = 0 
so that we obtain as before 
^ to R' 3 Q m' R 1 q 
vi — to' to — in' 
If the atmospheric circumstances are nearly the same in both weighings, the precise knowledge of the specific 
gravity of the weights employed has little influence, and always less in proportion as b' is nearer to b, and t' 
nearer to t. 
