W.G. divisor 231) 600 (2·59 wine gallons.

A. G. divisor 282) 600 (2·12 ale gallons.

M. B. divisor 2150) 600 (0.27 malt bushels.

BY THE SLIDING RULE.

on A. (231)

G. P. 282 to 1 against 600 are 2.12 A. G.

2150]

PROBLEM VII.

0.27 M. B.

To determine the Content, for an Inch in Depth, of a Quadrilateral having two Parallel unequal Sides.

RULE.

By the Pen.

Multiply half the sum of the parallel sides by the perpendicular distance between them, and divide the product by the number of cubic inches in the proposed integer.

By the Sliding Rule.

Set the gage-point, for the proposed integer, on A, to half the sum of the parallel sides on B, and against the perpendicular distance of the sides on A, will be the content on B.

EXAMPLE.

Let ABCD be a quadrilateral wherein two unequal sides are parallel, namely, AB and CD, the former being 121 inches, the latter 143 inches; and let EF, the perpendicular distance of the parallel sides, be 80 inches: the content, for one inch in depth, is required in wine gallons, ale gallons, and malt bushels.

W.G. divisor 231) 10560 (45.71 wine gallons.

A. G. divisor 282) 10560 (37-44 ale gallons

M. B. divisor 2150) 10560 (4.91 malt bushels.

K

on B. (45.71 W.G.

4.91 M. B. J

G. P. 282 to 80 against 132 are 37-44 A. G. 2150

Since the lines A and B are perfectly alike, and may be used for one another indiscriminately, as it may best suit particular numbers, we have here set the gage-points on A to the perpendicular distance on B, and taken the half sum of the parallel sides on A, because by this mode of operation it is not necessary to shift the slide, which, in the case before us, it otherwise would be.

PROBLEM VIII.

To determine the Content of any Right-lined Multilateral plane Figure, taken an Inch in Depth.

RULE.

By the Pen.

Divide the given plane figure into triangles by diagonal lines, and find the area of the several triangles. Then divide the sum of the areas by the number of cubic inches in the proposed integer, and the quotient will be the content.

By the Sliding Rule.

Find the number of cubic inches in the given figure by the pen, and set the gage-point for the proposed

integer, on A, to 1 on B; then look opposite to the number of cubic inches in the area, on A, and you will have the content on B.

EXAMPLE.

Let ACDEFGHB be a multilateral plane figure, whereof the area is required for an inch deep, in winegallons, ale-gallons, and malt-bushels.

Draw the diagonals AD, AE, BE, BF, and BG, dividing the given figure into triangles. Then demit the perpendiculars Cl, Em, Eo, Fn, Fk, Hi; and take the lengths of the lines required in the calculation, which let be the following:

SOLUTION BY THE PEN.

66.7 half of AB.

60.7 perpendicular Eo.

4669

40020

Product 4048-69 area of AEB.

46.1 half of AD.

45.8+13·4 = 59.2 sum of Cl and Em.

922

4149

2305

Product 2729-12 area of ACDE.

13.2 half of Fn.

105 base BE.

660

1320

Product 1386·0 area of EFB.

43.1 half of BG.

29.1+10= 39·1 sum of Hi and Fk.

431 3879

1293

Product 1685-21 area of BFGH.

Having now found the several areas constituting