dicular height of the tub 29.976 inches; re- 
quired its content ? Ans. 81410.3 cubic inches. 
! To Gautre a Cas:c. — Casks are distinguished 
into the following four varieties : 
1. Such as resemble the middle frustum of a 
spheroid. 
2. Such as resemble the middle frustum of a 
parabolic spindle. 
3. Such dS being cut through in the middle, 
the two parts are parabolic conoids. 
! 4. Such as being cut through in the middle, 
Ithe parts are the lower frustums lof two equal 
j<Ones. 
Measure the head and bung diameters, and the 
length of the cask in inches ; and then, 
1. If the staves are very much curved, the 
(cask is supposed to be the middle zone, or frus- 
: turn of a spheroid ; and its content may be 
! -found by this rule : 
To twice the square of the bung diameter, 
j add the square of the head diameter ; multiply 
the sum by the length of the cask, and divide 
| the product by 3.8197, the quotient is the con- 
I tent in cubic inches. 
E \am . Suppose there is a spheroidal cask, its 
bung diameter — • 31 .5 inches, head diameter = 
| 24.5 inches, and the length of cask — 42 inches; 
1 required its content in English ale gallons ? 
Ans. 100.78. 
2. If the staves of a cask are less. curved than 
; was supposed in the last article, the cask is taken 
| for the middle frustum, or zone, of a parabolic 
j spindle; and its content is computed by this rule : 
To twice the square of the bung diameter, add 
! the square of the head diameter, and from the 
j sum subtract four-tenths of the square of the 
difference of the diameters ; divide the remainder 
by 3.8197, and multiply the quotient by the 
| length of the cask ; the product is its content in 
cubic inches. 
Exam. Let the bung diameter = 34 inches, 
j -the head diameter — 30, and the length of the 
I cask 40 inches ; what is its content in English 
I ale gallons ? Ans. 119.039. 
3. When the staves of a cask are very little 
- curved, the cask is supposed to consist of the 
1 two lower frustums of two equal parabolic co- 
noids. their greatest bases joined together in the 
middle of the cask ; the content of such a vessel 
may be found by this rule ; 
To the square of the bung diameter, add the 
square of the head diameter ; multiply the sutn 
by .3927, and the product by the length of the 
| cask ; the last product is the content in cubic 
j inches. 
Exam. Let the hung diameter of such a cask 
— 32 inches, the head diameter — 29, and the 
length of the cask ==. 42 inches; required its 
content in cubic inches and ale gallons ? 
Ans. 30760.191 cubic inches, or 109.07 ale 
gallons. 
4. If the staves of a cask are straight between 
the bung aria the ends of the cask, the vessel is 
supposed to consist of the two lower frustums of 
| equal cones ; and its content is found by this rule : 
T6 the sum of the squares of the head and 
| bung diameters add their product ; multiply the 
J sum by the length of the cask, and divide the 
product by 3.8197 ; the quotient is the content 
I in cubic inches. 
Exam. Required the content of a cask in ale 
| gallons, its bung diameter being 32 inches, its 
] he?xl diameter 24 inches, and the length 40 
I inches ? Ans. 87.93. 
By these rules, the content of any cask may 
be found, it being known to which of the four 
I varieties the cask belongs ; but in common prac- 
I fice, a mean diameter, whereby the cask is re- 
duced to a cylinder in either variety, is found 
J thus : 
VOL. I. 
GAUGING. 
5. Multiply the difference between the bung 
and head diameters by .7 for the spheroid, by 
.65 for the spindle, by .6 for the conoids, and 
by .55 for the cones ; add the product to the 
head diameter ; the sum is a mean diameter ; or 
the diameter of the base of a Cylinder equal to 
the cask, their lengths being the same. The mean 
diameter being squared and multiplied by .7854, 
and the product bv the length of the cask, gives 
the content in cubic inches, which may be re- 
duced to gallons by the table. 
Ex-. Suppose the bung diameter is 30 inches, 
the head diameter 20 inches, and the length of 
the cask 40 inches ; required its content in ale 
gallons according to each variety ? 
Difference of Bung and Head Diameters 
is 10 Inches. Jk D 
10 X -7 = 7. and 20 -j- 7. = 27. for the 
spheroid 
10 x -63 = 6.5 and 20 -f 6.5 *6.5 for the 
spindle 
10 X -6 = 6. and 20 -f 6. = 26. for the 
conoids k 
10 X <55 = 5.5 and 20 -f 5.5 = 25.5 for the 
cones. 
For the Content in Ale Gallons. 
27. X 27. x -7854 X 40 X .003546 = 81.21 
spheroid 
26.5 X 26.5 X .7854 X 40 X .003546 = 78.23 
spindle 
26. X 26. X -7854 X 40 X .003546 = 75.3 
conoids 
25.5 X 25.5 .X .7854 X 40 X .003546 = 72.43 
cones. 
Mr. Ward, who had much practice in gau- 
ging, [says, he never gauged a cask that contained 
so much as the first variety makes it ; and there- 
fore, recommends the 2d and 3d varieties as the 
best general rules for gauging casks. 
The following rule is given by Dr. Hutton, 
which is not only general for all casks that are 
commonly met with, but easily to be worked, 
and accurate in its application. 
General Rule. Add into one sum, 
39 times the square of the bung diameter, 
25 times the square of the head diameter, and 
26 times the product of those diameters ; 
multiply the sum by the length of the cask, and 
the product by the number .00034 ; then this 
last product divided by 9 will give the wine gal- 
lons, and divided by 1 1 will give the ale gallons. 
a. l 
Or, 39B 2 4- 25H 2 26BH X ttt ,s t!ie con ' 
1 1 114 
tent in inches ; which being divided by 231 for 
wine gallons, or by 282 for ale gallons, will he 
the content. 
For Ex. If the length of a cask he 40 inches, 
the hung diameter 32, and the head diameter 24, 
Here - 32 2 X 39 = 39936 
and - 24 2 X 25 = 14400 
and 32 X 24 x 26 = 19968 
the sum - 74304 
multiplied by - 40 
and divid. by 114)2972160 
gives - 26071 cubic inches ; 
this, divided by 231 gives 112 wine gallons, 
or divided by 282 gives 92 ale gallons. 
But gauging, as now practised, is chiefly 
done by means of instruments called gau- 
ging rods or rulers, which do the business at 
once, and answer the question without so 
much calculation, which is no inconsiderable 
addition both to the ease and dispatch of the 
work, though it is not so much to be depend- 
ed on. 
The method of gauging which is mostly 
used, is by the four-feet gauging-rod and 
5 M 
825 
Everard’s sliding-rule ; the description and 
uses of both are as follows: 
The four-feet gauging-rod (Plate Miscel. 
tig. 101) is usually made of box, and consists 
of four rules, each a foot long, and about 
three-eighths of an inch square, joined toge- 
ther by three brass joints; by which means 
the rod is rendered four feet long when the 
four rules are opened,, and but one fool when 
all are folded together. On the first face oi 
this rod, marked 4, are placed two diagonal 
lines, one for beer and the other for wine; 
by means of which the content of any com- 
mon vessel in beer or wine gallons, may be 
readily found, by putting the biased end oi 
the gauging-rod into the bung-hole ot the 
cask, with the diagonal lines upwards, and 
thrusting this brased end to the meeting of the 
head and staves ; then with chalk make a 
mark at the middle of the bung-hole of the 
vessel, and also on the diagonal lines ot the 
rod, right against or over one another, when 
the brased end is thrust home to the head 
and staves ; then (urn the gauging-rod to the 
oilier end of the vessel, and thrust the brased 
end home to the end as before. lastly, see 
if the mark made on the gauging-rod, come 
even with the mark made on the bung-hole, 
when the rod was thrust to the other end , 
which if it be, the mark made on the diago- 
nal lines will, on the same lines, shew the 
whole content of the cask in beer or wine 
gallons. If the mark made on the bung-hole be 
not right sfgainst, that made on the rod, when 
you put it the other way, then right against 
the mark made on the bung-hole, make an- 
other on the diagonal lines; and the division 
on the diagonal line, between the two chalks, 
will shew the whole content of the vessel in 
beer or wine gallons. 
Thus, if the diagonal line nf a vessel be 
28 4-10 inches, its content in beer- gallons 
will be nearly 51, and in wine-gallons 62. 
If a vessel be open as a half-barrel, tun, 
or copper, and the measure from the middle 
on one side to the head and staves be 38 
inches, the diagonal line gives 122 beer-gal- 
lons ; half of w hich, viz. til, is the content 
of the half-tub. 
If you have a large vessel, as a tun or 
copper, and the diagonal line taken by a 
long rule be 70 inches, then every inch at 
the beginning-end of the diagonal line call 
10 inches; thus 10 inches become 100 in- 
ches, and every tenth of a gallon call 100 
gallons, and every whole gallon call 1 000 
gallons. 
, Example.’ At 44.8 inches on the diagonal 
beer-line is 200 gallons; so that 4 inches 
48 parts, now called 44 inches eight-tenths, 
is just two-tenths of a gallon, now called 
200 gallons ; so also, if the diagonal line 
be 76 inches and seven-tenths, a close cask 
of such diagonal will hold 1000 beer-gal- 
lons ; but an open cask but halt so much, 
viz. 500 beer-gallons. 
On the second face, 5, are a line of inches 
and the gauge-line, which is a line express- 
ing the areas of circles (whose diameters 
are the correspondent inches) in ale-gallons; 
at the beginning is written ale-area. Thus, 
to find the content of any Cylindrical vessel 
in ale-gallons, seek the diameter of the vessel 
in inches, and just against it, on the gauge- 
line, is the quantity of ale-gallons contained 
