Ex. 5. Required the content of a triangular prifm, whose length is 18 inches, and one of the fides 25 inches, and perpendicular 16 inches, in ale, wine gallons.

Anf. 13 ale gallons and 15 wine gallons.

Ex. 6. A cylinder, whose diameter is 72 inches and depth 48; it is required to find its content in ale and wine gallons. Anf. 693 ale gallons and 846 wine gallons.

Ex. 7. How many ale, wine gallons, and malt bushels will a cylinder contain, whose diameter is 564 inches, and height 96 inches?

Anf. 854 ale gallons, 1042 wine gallons, and 112 malt

bufhels.

Ex. 8. A parallelopipedon is 40 inches long, 20 broad, and 15 inches deep; required its content in ale, wine gallons, and malt bufhels.

Anf. 43 ale gallons, 52 wine gallons, and 6 malt bufhels.

PROBLEM V.

To find the content of any pyramid, or af the cone, in ale, wine gallons, and malt bufbels.

RULE.

Compute the folidity of the cone or pyramid, in cubic inch. es, by Problem VI. of folids, then divide this folidity by the di visors, or multiply by the multipliers, and the refult will give the gallons or bushels required.

EXAMPLE I.

How many ale, wine gallons, and malt bushels will a coni

cal

cal veffel contain, whose base diameter is 40 inches, and ältitude 60 inches?

Anf. 89.136 ale gallons, 108.843 wine gallons, and 11.68 malt bufhels.

Ex. 2. How many ale, wine gallons, will a veffel, in the form of a pentagonal pyramid, contain, the fide of whose base is 90 inches, and perpendicular depth 140 inches?

Anf. 2306.1 ale gallons and 2815.2 wine gallons.

Ex. 3. Required the content of a fquare pyramid, whofe fide is 40 inches, and height 60 inches, in ale, wine gallons, and malt bufhels ?

Anf. 113.47 ale gallons, 138.52 wine gallons, and 14.88 malt bufhels?

PROBLEM VI.

To find the content of the fruftum of a cone, or any pyramid, in ale, wine gallons, and malt busbels.

RULE I.

For the cone.-Add the fquare of the two diameters to their product, multiply the fum by .7854, and again by the height; then divide or multiply as in Table I. for gallons of bufhels, as required.

RULE II.

For the pyramid.-Add into one fum the area of both ends, and the mean proportional between them; multiply the fum by the height, and the product is the content in cubic inches; which divided or multiplied by the divifors or multipliers in Table I. gives the content in ale, wine gallons, &c.

EXAMPLE

EXAMPLE I.

A veffel, whose bafes are rectangles, the greater bafe 100 inches by 70 inches, the leffer bafe 80 by 56 inches, and depth 42; required the content in ale, wine gallons, and malt Bushels.

Anf. 847.9 ale gallons, 1035.1 wine gallons, and 111.2 malt bufhels.

Ex. 2. Required the content of the lower fruftum of a cone, the greater base diameter being 38 inches, the less 203, and depth 21, in ale gallons. Anf. 51 ale gallons.

Ex. 3. A fruftum of a cone, whofe diameters are 56.5 inches and 19 inches, and the height 62 inches, required the content in ale, wine gallons, and malt bushels.

Anf. 266.3 ale gallons, 325.1 wine gallons, and 34.92 malt bufhels.

PROBLEM VII.

The divifors for ale, wine, and malt for a cylinder being given, to find a divifor for any of the following folids; namely, the globe, Spheroid, parabolic conoid, hyperbolic conoid, parabolic spindle, and

cone.

RULE".

Find what part each is of the circumfcribing cylinder; then

fay,

Aş

The globe is of the circumfcribing cylinder-the fpheroid the parabolic conoid the hyperbolic conoid

8

the parabolic fpindle and the cone 1.

T

As the numerator

Is to the denominator,

So is the ale, wine, and malt divifors of a cylinder,
To the like divifors for the figures required.

EXAMPLE I.

Required ale, wine, and malt divifors for the cone, thofe of the cylinders being 359.05 for ale, 294.12 for wine, and 2737-47 for malt.

As 13: 359.05: 1077.15 ale divifors
1:3: 294.12: 882.36 wine divifors.
1:3:2737-47: 8212.41

And fo on for the rest.

EXAMPLE II.

malt divifors.

A cone, whofe diameter is 40 inches, and altitude 60, required its content in ale, wine gallons, and malt bufhels.

I all infft no farther on thefe examples at large, becaufe what is here fhewn of the cone is fufficient to inform the meaneft capacity how to proceed with the other folids mentioned in the problem; but fhall only offer a few practical exercifes.

EXAMPLE. I.

How many ale, wine gallons, and malt bufhels will a veffel,

in the form of a spheroid, contain, whose fixed axis is 100, and revolving 60 inches?

Anf. 668.4 ale gallons, 816.4 wine gallons, and 87.6 malt bufhels.

Ex. 2. Required the content of the parabolic conoid in ale and wine gallons, the height being 30, and diameter of its base

20.

Anf. 16.7 ale gallons, and 20.4 wine gallons.

Ex. 3. Required the content of the hyperbolic conoid, the bafe being 100 inches, and altitude 60 inches.

Anf. 696.2 ale gallons, and 850 wine gallons.

Ex. 4. Required the content of a parabolic spindle whofe length is 60 inches, and greatest diameter is 64, in ale and wine gallons.

Anf. 103.02 ale gallons, and 125.7 wine gallons.

INCHING Tuns and Coolers.

THE practical method of gauging any fixed tun of copper, and of making a table to fhew what it will hold at every inch deep.

First, You must know that moft (if not all) brewers tuns are fo fixed as to lean a little, for conveniency of cleaning their drink, which is ufually called the drip, or full of the tun. Now, the drip, or fall, is the hoof of fuch a folid as the tun is fuppofed to reprefent. The beft and readieft way is to measure into