IMPERIAL STANDARD TROY POUND WEIGHT. 
485 
the air at that moment), and that V , or the height of the barometer when the body 
is weighed in water, must be employed. We thus obtain 
If the brass, of which the weights are made, has a specific gravity = c5, different from 
that assumed (= 8), a must be first multiplied by 8, and afterwards divided by <$. 
This comes to the same as applying to the numbers of Table I. the correction c ; 
c being = log 8 — log h, or c — O' 903 09 — log c>. 
R 3 <7 
30. We come now to —— . If the linear expansion of the weighed body for one 
degree of Fahrenheit’s scale be denoted by e, we have R 3 = [1 -{- ( t — 32°) e] 3 . 
For q we have already the equation (10), in which, by making 
^ = L 230o4-3y .['+(£ — 0-0020833] 
we have q = b (3 : (3 is evidently the specific gravity of atmospheric air at the tempe- 
rature t , and under the pressure of one English inch of mercury, the mercury being 
reduced to its density at the temperature of the melting ice. We thus obtain 
R 3 $- 
A 
~ b 1 3 . L 1 + ~ 3go ) e l'\ 
Table II. contains the logarithms of (3 . Its argument is the temperature of the air 
in Fahrenheit degrees at the moment of the weighing. 
Tables III. IV. V. contain the logarithms of [l -{-(£ — 32°) e] 3 for brass, copper, 
and platina. They suppose 
For brass e — 0'000010436 
For copper e = 0'000009541 
For platina e = O'OOQOOSOOO and 0'000005050 
Table I. — For Brass weights the specific gravity of which = 8. 
t. 
log a. 
t. 
log a. 
t. 
log CC. 
t. 
log a. 
t. 
log a. 
t . 
log «. 
0 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
4-73416 
4-73327 !® 
4-73238 ll 
4-73149 
■4-73061 ll 
4-72972 
472884 88 
4-72796 88 
4-72709 87 
4-72621 
O 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
4-72621 
4-72534 87 
4-72447 87 
4-72360 87 
4-72273 87 
4-72186 87 
4-72100 
4-72 01 3 87 
4-71927 H 
4-71841 
O 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
4-71841 
4'7i756 
4-71670 
4-9585 85 
4-7 14 99 88 
4-71414 88 
4-71329 
4-71245 *Z 
4-71160 85 
4-71076 
O 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 
471076 
4-70991 l 5 . 
4-70907 It 
4-70824 83 
4-70740 8 t 
4-70656 ” 
4-70573 83 
470490 83 
4-70407 83 
4-70324 
O 
68 
69 
70 
71 
72 
73 
74 
75 
76 
77 
4-70324 
4-70241 83 
4 ' 70139 83 
4-70076 83 
4-69994 
4-69912 it 
4-69830 8 ~ 
4-69748 83 
4-69667 it 
4-69585 
O 
77 
78 
79 
80 
81 
82 
83 
84 
85 
86 
4-69585 C1 
4-69504 ®J 
4-69423 81 
4-69342 8l 
4-69261 8 
4-69180 81 
4-69100 8 , 
4-69019 it 
4-68939 8( ( 
4-68859 80 
Log a is taken with the temperature of the air in Fahrenheit degrees at the mo- 
ment of the weighing. If the brass weights are of any other specific gravity = ci, a 
correction c must be applied to the numbers of the table : or c = 0'90309 — log l. 
