MAGAZINE OF SCIENCE AND ART. 
29 
on the part of wine merchants and wine coopers, to the 
following details in aid of the right construction of 
casks having their contents ranging according to a 
decimal scale of admeasurement; becauso the general 
adoption by the wine trade of casks so constructed 
would greatly promote the convenience and otherwise 
advance the interests of the colonial winist. 
In the annexe*! sectional diagram of a cask, let 
- A he the centre of bung-hole, 
AE, or d, the diagonal, 
CD, or Z, the length, 
AB, or A, the biing-diameter. 
A. 
GE, or h , the head-diameter, 
AF ^(6-j-A)=S i.e. half thosurn of bung and head 
diameters, 
and AF,=J£= half the length. 
Let, moreover, the letter <7 represent the contents of 
a cask in imperial gallons ; then, premising that a cask 
containing 144 imperial gallons has been found to have 
a diagonal of 40 inches, and that the contents of casks 
vary as the cubes of their diagonals, tho following for¬ 
mula?, with die aid of the above symbols, are easily 
deducible, viz.;— 
Log. g= 3 log rf—( 2.647818 )g= log. (Z24-S2)— 
(3.550908) 
Log. J=1'3 log. (7-4-0.882606=4 log. ( Z24-s2)— 
(0.301030) 
Log- Mr | log. (2d+s)4-log. (2 d-a) | 
Log. i=4 j log. (2d-(-l)+log. (2 d-l) J 
"Where it is evident that d being constant, Z and 6* 
may vary, and that d, l. and s being constant, b and h 
may vary. Hence d and Z being constant, the shape of 
the cask will depend on the ratio between the Bung 
and Head Diameters. 
From these formula?, I have calculated the following 
Tabic of Admeasurement for casks of given capacities; 
and of three different shapes—which will be found, by 
the working cooper, of easy application to the construc¬ 
tion of casks suc,h as the preceding observations are in¬ 
tended to recommend, 
HENRY CARMICHAEL. 
Table giving the admeasurement of three descriptions of Cask3, having Capacities from 1 to 1000 Imperial 
Gallons, when the ratio of the length of tho Cask to the Sum of tho Head and Bung Diameters is that of 
three to four; or l: s :: 3: 4, 
I 
Length (Z) 
in inches. 
M <*. 
Head Diameter, in inches (A). 
Bung Diameter (6) in inches. 
Contents in 
Imperial 
Gallons. 
(S') 
’Diagonal (a 
in inches. 
8 _ 
d= S 4 °<7 
When b=d 
*-4 l- 
When 
h:b:: 7:9 
m t v- 
When 
h-b:: 3:4 
h=11 
. When b=d 
When 
h:b:: 7:9 
When 
A : 6. s: 3:4 
b-ih. 
i 
7.6315 
9.1578 
4.578 
5.3420 
5.233 
7.6315 
G.8684 
6.977 
2 
9.615 
11.520 
5.760 
6.730 
G.583 
9.015 
8.654 
3 
1 11.006 
13.207 
6.603 
7-704 
7.547 
11.006 
9.906 
10.062 
4 
12.111 
14.533 
7.200 
8.477 
8.304 
12.111 
10.900 
11.071 
5 
13.049 
15.659 
7.829 
9.134 
8.350 
13.049 
11.745 
11.933 
10 
16-441 
19.723 
9.864 
11.508 
11.273 
16.441 
14.797 
15.031 
15 
18.820 
22.584 
11.292 
13.174 
12.905 
18.820 
16.938 
17-207 
20 
20.715 
24.858 
12.429 
14.500 
14.204 
20.715 
18.644 
18.939 
25 
22.314 
26.776 
13.388 
15.619 
15.301 
22.314 
20.083 
20401 
30 
23,712 
28.454 
14.227 
16.598 
16.259 
23.712 
21.341 
21.679 
40 
26.100 
31.320 
15.660 
18.270 
17.897 
2G.100 
23.490 
23.862 
50 
28.114 
33.736 
16.868 
19.079 
19.278 
28.114 
25.303 
25.704 
60 
29.876 
35.851 
17.925 
20.913 
20.-186 
29.876 
26.889 
27.315 
70 
31.451 
37.741 
18.870 
22.015 
21,566 
31.451 
28.306 
28.755 
80 
32.881 
39.457 
19.728 
23.0)7 
22.547 
32.881 
29.593 
30.062 
90 
34.200 
41.040 
20.520 
23.940 
23.451 
34.200 
30.780 
31.270 
100 
35.422 
42.506 
21.253 
24.795 
24.289 
35.422 
31.880 
32.3,85 
125 
38.157 
45.788 
22.894 
26.710 
20.164 
38.157 
34.342 
34.886 
144 
40.000 
48.000 
24.000 
2S.OOO 
27.428 
40.000 
36.000 
36.571 
150 
40.650 
48.780 
24.390 
28.455 
27.874 
40.650 
36.585 
37.166 
175 
42.686 
51.223 
26.611 
29.880 
29.270 
42.686 
38.418 
39.027 
200 
44.040 
53.508 
26.784 
81.248 
30.611 
44.640 
40.176 
40.813 
250 
48.075 
67.690 
28,845 
33.652 
32.065 
48.075 
43.268 
43.955 
300 
51.087 
61.304 
30.652 
35.701 
35.031 
51.087 
45.979 
46.708 
400 
56.230 
67.476 
33.738 
39.361 
38.558 
56.230 
50.607 
51.410 
600 
60.570 
72.684 
36.342 
•12.399 
41.534 
G0.570 
54.513 
55378 
600 
64,360 
77.232 
38.610 
45.052 
44,133 
64.360 
57.924 
58.843 
700 
67.750 
81.312 
40.606 
47.432 
40.464 
67.700 
£0.984 
61.952 
800 
70.844 
85.013 
42.506 
49.590 
48.578 
70.844 
G3.7CO 
(4.772 
900 
73.680 
88.416 
44.208 
51,576 
50.52-1 
73.680 
66.312 
67.361 
1000 
76.320 
91.584 
45.792 
53.424 
53.334 
76.320 
6S.6S8 
69.778 
