GAUGING... 
Acd if the beer firlot conta 1 Scotch pints, contents © 
P 
of = a pues in beer firlots will be D D Hx 0.000245. 
a to be obferved, that when the fection of re 
veffel is not a circle, but an ee the product of t 
eteateft diameter by the leaft i oe fubitituted in ie 
oe for the fquare of the jn 
7° mpute the content oa a veffel, which may be 
confidered as ie fruitum of a cone in any of thofe mene, 
et A reprefent the number of inches in the diameter of tl 
greater bafe, B the number of inches in the diameter of de 
aa bafe. Compute the fquare of A, the produ&t of A 
fquare o Take the third part of the 
and fubftitute it in = preceding rules for 
€ the diameter, and proc in all refpects as 
Thus for exan as the pave in wine ellen will 
4H x 0.0034. Or thus : To the 
{quare of half the fum "of «A. and B add one-third of the 
fquare of half their eulcrenc} and fubftitute this fum in 
the preceding rules for the fquare of the diameter of the 
and the 
is os all thefe, 
the fquare of 
before. 
bafe of the veffel. For the {quare of E A + 1 B added to 
2 of the eas Bye SH fA A +3 ee 
aes: Be =iA A. +3 
3BB+7AA—IAB+ 
+3B B. 
8’. When the veffel is a fruftum of a parabolic conoid, 
meafure the aed 3 the feGtion at the middle of the 
height of the fruft and the content will be the fame as 
of a cylinder of this ae. of the fame height with the 
veflel. 
That r ae t the eee of the middle fe@ion, 
and H the height of the pera you are to fubftitute 
the ae the diameter of the cylindric 
ae 
<< in the firft fix r 
°, When the on. is a fruftum of a fpheroid, if the 
ie are equal, the content is readily found by the rule given 
from Oughtred. Ino ~ er ee tet the axis of the folid be 
to the conjugate axis, ; let D be the diameter of 
10 af im “rafton ,H he height or length 
of the frauftum, and fubftitute in the firft fix rules D D— 
for the fquare of the diameter of the veffel. 
- 
°, When the veffel is a hyperbolic oe let the axis 
of ie folid be to the conjugate axis as 2 to r, D the diame- 
ter of the fe€tion at the middle of the ies H, the height 
or length, compute D D + foe and fubftitute this fum 
for the fquare of the diameter of the cylindric veffel in the 
firft fix rules 
2°. In general, it is ufual to meafure any round veffel, 
ae ora a it into feveral fruftums, and a the diame. 
jon at the middle of each fruftum ; thence to 
veffel. 
disy Rhea fucceflively the numbers which exprefs the cir- 
cular areas that correfpond to thofe mean diameters, each as 
often as there are inches in the altitude of the fruftum to 
which it belongs, beginning with uppermoft.; and in 
a ted a little too high, if the 
this manner Fe den a table o isi veffel, _ by which it 
re aero y appe h 
When the veflel is a portion of a eone cr 
1yperbolic conoid, the content by this method is found lefs 
than the truth; but 
e difference or error is on 
parts of te fame, or eee veflels, when the altitude of 
the fruftum is given. when the altitudes are ae 
the error is in the eee: ratio of the altitude. If exact 
fimilar to the veflel, of an slide equal to the height of the 
fruftum, In a {phere 3d of a cylinder, of a diameter 
and height aa to the froifum, In the fpheroid and hy- 
per rbolic conoid, it is the fame as i 
the right-angled triangle contained by 
the figure revolving about that fi ide which is ae 
the fraftum. Th a treatife of fluxions. 
y Mr. Maclaurin, ae ae nae are extended to 
fruftums that are bounded by planes oblique to the axis in all 
the folids, that are generated by any conic fection revolving 
about either axis. Vide p. 25. an 
In the ufual method of ae a ‘a table for a veflel, by 
fubduéting from the whole content the number that exprefles 
— uppermott area, as often as there are inches in the up- 
motit fruftum, and afterwards the numbers for the other 
areas {ucceffively, it is obvious that the contents affigned by: 
table, when a few of the uppermoft inches are dry, are 
veflel ftands on its leffer bafe, 
but too low when it itands on its greater bafe; becaufe, when 
one inch is dry, for example, it ig not the area ba - Zs mid. 
dle of the uppermoft fruition, but rather the 
middle.of the uppermoft inch, that ought to be “fubduéed 
rom the total content, in enler to find the content in this 
cafe. 
o 
rt 
om 
auging, as now practifed, is chiefly done by means 
of card aa ae called gauging ods, or _ which do the 
bufineis at once, and anfwer the queition without fo much 
calculation; which is no inconiderabl addition, both to 
the eafe and difpatch of the w This inftrumental way 
of gauging, thenelore. we fhall oe chiefly infift upon 
Dr. Hutton in his  Menfuration” has given oe for 
computing the contents of the various fruftums of folids, 
which bear refemblance to the feveral varieties or forms of 
different cafks. Rules adapted to thefe forms will be found 
under the denominations of the feveral folids to which they 
be ee in this Cyclopedia ; ae they occur in moft books, 
y written on the fubj 
neral rule, extra 
cited treatife, (p. es .) which may be eafily applied to the 
cafes that occur. 
General Rule. 
Add into one fum 39 ee the fquare of the bung diameter, 
25 times the fquare of the head diameter, 
and 
26 times the product of thofe diameters. 
Multiply the fum by the length of the cafk, and the predu@ 
by the number .00034.; then this laft product divided by 9 
will 
