GAUGING. 
to a cylinder of equal contents; and this is done by confi- ° 
ing what is called the variety of t uppofe acy- 
linder raga in acafk, and another yey alias about 
it, th will be a cylindrical ie included between the 
ipaicene of the two cylinders, ‘whofe dameteor thicknefs 
the ‘ante between the bung and head diame- 
urvature of _ itaves of the cafk 
eafed fo ast 
a 
» 
=] 
[avy 
or 
a 
2 
a>) 
ct 
a 
oO 
Q 
+o 
fevers) 
nw 
ves O ik : and in 
linder will be equal in eon tent. The dian id a ihe inferi 
ed cylinder is the head diameter of the the thicknefs 
of the cylindrical {pace is equal to the diffe erence between the 
bung and head diameters. The only difficulty, therefore, 
lies in determining what portion of this difference mufi be 
added to the head diameter of the cafk, in order to 
obtain the diameter of the mean inde, or ay pe 
equal content. 7-1ot 
ung ce oa an 7 
= 3 
a: 
cont 
8 
3 
5 
afk, t 
though the "have ea the greatelt degr curvature that 
is ever given to the And as the difference between the 
bung and head Siatctens of cafks is feldom very great, the 
contents of a cafk whofe ftaves are quite ftraight from 
bung to head, or of acafk made up of two equal fruftums 
of two equal cones, will generally be nearly equal to the 
contents of a cylinder, whofe diameter is equal to the fum 
of the head diameter of the cafk, and a little more than 
half the difference between the bung ae head diameters, 
and whofe length i is equal to the length o 
fore, all the varieties of which ane are capable 
ths of the difference be eee ine i 
rs; and the gauger isooityt to take field par art 
of this difference (always between 5-1oths and 7-r1oths) 
as fetes Saori tandexperience inform himto be moft fuit- 
able to the curvature of the caflc ; and this, waded to the 
head dee gives the diameter of the mean cylinder. 
It may not be amifs to note here, that the difference be- 
tween the bung con head diameters red be very ¢g 
yet the cafk hav o bulging at all, 
bend or eee ‘of the half-ttave, nee the bung and 
the head. 
Mathematicians give us abftrufe theorems, for computing 
the contents o {uppofed refemblance be- 
cafk and that of an ellipfis, para- 
ne 
the forms of calks do not cnactly a» walwer any oo eaceal 
figures. The bufinefs of gauging is at belt but guefs-work ; 
but it is fuch a way of guefling, as comes near ~ enough the 
truth for the common purpofes of life. 
Hence we may add fuch decimal multipliers, for the dif- 
ference between bung and head diameters as have been found 
by experience to be the truett, and beit fuited to the feveral 
varieties or curvatures 0 Se 
Fir rft variety, or ftaves | much 
Second variety, or aves not fo much curved, 
bulging, 7 or “695 
-65 or .63 
Third variety, or faves ftill lefs curved, 6 or 156 
Fourth variety, or ftaves almoft ftrai ht, 255 or. 
The following rule will ferve for gauging cafks by the 
ound, and multiply that fquare by the length, 
and divide the product by 359 for beer gallons, and 294 for 
wine, 
The multipliers for a sc which is taken for varieties ; 
f a {pher 
1. Of a {phe -7 ( greateft bulge. 
The middle } 2. Of a par, idle -63 } next lefs. 
fruftum ’) 3. Two -56 } next lefs to that. 
i ne cones 51 f next lefs to that. 
Example ae a cafl be taken as the middle fruftum of a 
ipheroid the bung diameter of which is 32 inches, ae head 
a6, and length 50 inches; what is the content in beer and 
wine ee 32 — 26X .7 = 4.2. Towhich add 26, and 
ve fhall have 30,2 for the mean diameter; and 30.2|'= 912.04, 
ore multiplied by the length so 0 will give 45602; and 
45602 d 4500 
359 
lons. The contents of other ai may be found in the fame 
manner by ufing the proper multipliers. See Everard’s 
SLIDING rule. 
For the ready computation of the contents of veffels, or 
of any folids in the meafures in ufe in Great ritain, we 
fhall here infert the following rules taken from a Treatife of 
Pratical Geometry, publifhed at Edinburgh in 1745, 8vo. 
bee pas: 137. feq. 
nd the content of a cylindric veffel in Englifh 
wine gallons, « the diameter of the bafe and altitude fa ca 
veffel given in inches and decimals of an inch: 
the cere of inches in the cm of the veffel ; ae ae 
fquare by the number of inches in the hei ght, then mul- 
tiply this product by the decimal fraction 0.0034, you 
wil have the contents o SIF 
= 127 beer gallons; an = 155.1 wine gal. 
f the veffel in a and decims a 
ofagallon. For cap let the diameter be = D == 
inches, the height = H = 62.3 inches, vars w “ill the once 
e D ee a i 2.3 X 0.0034 = 
555: -27342 wine gallon 
- Suppofing “the Engli fh ale gallon to contain 282 cubi. 
a inches, the content of a cylindric veffel is computed in 
fuch gallons, Py multiplying the fquare of the diameter of 
ad sie by its height as before, and their produ& by the 
eal aetcs 0.0027851, that is, the folid content in 
gallons wi il be DDH x 0.0027851 
the Scotch pint hase ns 103. 4 cubical een the 
eontent ‘of fuch a veffel in Scotch pints, willbe DDH x 
0.0076. 
4°. Suppofing the Winchefter bufhel to contain 2178 cubic 
inches, the content of a cylindric veffel is computed in thofe 
bufhels, by multiplying the {quare of the diameter of the 
veffel by the see = the product by the decin al fraG@ion 
0.0003606. But the legal Winchefter bufhel containing 
eel 2150.42 folid ee the content of a cylindric vefiel 
mputed in fuch bufhels, by multiplying the fquare cf 
ce cee by the height, and whe product by the de Cle 
Or th eDDH .0.co_36s 
Le 
ae Suppoling the —— wheat firlot to contaia 213 
Scotch pints, or abou cubical inches, the cont -nts ar 
a cylindric veffel in fach Arlots will be DD H x 0.000358. 
