them by .009615, the refult will be 138.14 Scots pints, the content of the veffel.

And, if you divide 14367.375 by 282, or multiply them by .c03546, the result will be the content of the veffel in English ale gallons, viz. 59.946.

In the fame manner, the content of any veffel may be found; but thofe who practise gauging proceed thus:

In any veffel equally wide from top to bottom, they compute the area of its base in square inches; and, by dividing or multiplying these by fome of the numbers in the tables, get what they call the area in gallons, (that is, the number of gallons which the veffel contains when the liquid is only one inch deep), which multiplied by the depth of the liquid, gives the quantity contained in the veffel.

EXAM. 2. Suppofe a trough, or ciftern, in form of a right angled parallelopiped, its bafe 27 inches long, and 16 inches wide, and the height of the veffel 324 inches, but the depth of liquor only 20 inches; required its content in English ale gallons?

Anf. 31.594.

27×16.5×.003546=1.579743 the area of the bafe in gallons, which multiplied by 20, produces 31.594, ale gallons,

3. Suppofe a cylindric veffel hath the diameter of its base 20 inches, and its height 30 inches; required the content in wine gallons?

Anf. 40.8.

20X20X.7854X30X.004329=40.8. Suppofe a tube having circular bases, the diameter

of the mouth is 60 inches, and the diameter of the bottom is 36 inches, and the perpendicular depth from top to bottom is 30 inches; required its content in Scots pints and English ale gallons?

This veffel is to be confidered as the fruftum of a cone; and, on this fuppofition, its content will be 55417.8 cubic inches; which, by reduction, is 532.8 Scots pints, or 196.5 English ale gallons.

The calculation is tedious by common arithmetic, but may be easily performed by logarithms; thus,

To twice the logarithm of the diameter of one base add the logarithm of .7854, the fum is the logarithm of the area of that base. Do the fame for the area of the other base, and find the numbers anfwering to each. Then add the logarithms of the areas of the two bases, and take half of the fum, and find the number answering thereto.

Add the areas of the two bafes, and the last found number, and multiply the fum by one third part of the depth, the product is the content in cubic inches.

Operation

The content of any veffel of this form may be found with lefs trouble by this rule.

To the product of the diameters of the two bases, add one third part of the fquare of their difference; the fum is the fquare of a mean diameter; which be ing multiplied by .7854, and the product by the depth of the veffel, gives the content in cubic inches.

EXAM. Let the diameter of the greater base be 60, and of the leffer bafe 57.6, and the perpendicular height of the tube 29.976 inches; required its content?

Anf. 81410.3 cubic inches.

The content of a veffel of this form may be found without measuring the diameter of the bottom, or least bafe; thus, Measure the diameter of its mouth, or up

per base, AB, the diagonal BC, and the length of the ftave AC (Fig. B. plate 4.) Then, in the triangle ABC, the three fides are known; and, having drawn the perpendicular CE, we have,

As AB: BC+CA :: BC-CA: BE-EA, which is equal to CD; and hence AE and EC may be found. And, when AB, CD, and CE are known, the content of the veffel may be found by the last rule.

EXAM. Let the diameter AB-40, the diagonal BC 42, and the length of the stave AC-20 inches; required the content of the veffel?

Anf. 21371.58 cubic inches.

By the above rule, BE-EA, or CD=34.1 inches, and AE=2.95 inches; AC-AE'LC2=391•2975; hence EC 19.7812 inches; and the reft of the operation is the fame as in the laft example.

When veffels are not equally wide from top to bottom, gaugers confider them as fruftums of fome regu. lar folid, and compute their contents at every inch of their depth, which contents they enter in a table, and, when they come to furvey, they have only to take the depth; and, by comparing the wet inches with the table, have the content by inspection.

2. To Gauge a CASK.

Casks are distinguished into the following four va rieties.

1. Such as refemble the middle fruftum of a sphe roid.

2. Such as refemble the middle fruftum of a parabolic spindle.

3. Such as being cut through in the middle, the two parts are parabolic conoids.

4. Such as being cut through in the middle, the parts are the lower fruftums of two equal cones.

Measure the head and bung diameters, and the length of the cask in inches; and then,

1. If the ftaves are very much curved, the cask is supposed to be the middle zone, or fruftum of a sphe roid; and its content may be found by this rule.

To twice the fquare of the bung diameter, add the fquare of the head diameter; multiply the fum by the length of the cafk, and divide the product by 3.8197, the quotient is the content in cubic inches.

EXAM. Suppofe there is a spheroidal cafk, its bung diameter 31.5 inches, head diameter 24.5 inches, and the length of cafk 42 inches; required its content in English ale gallons?

Anf. 100.78.

2. If the ftaves of a caík are lefs curved than was fuppofed in the laft article, the cafk is taken for the middle fruftum, or zone, of a parabolic fpindle; and its content is computed by this rule.

To twice the fquare of the bung diameter, add the fquare of the head diameter, and from the sum subtract four tenths of the fquare of the difference of the diameters; divide the remainder by 3.8197, and multiply the quotient by the length of the cafk; the product is its content in cubic inches.