1. What is the solidity of a segment of a prolate spheroid, the axis of which is 9, and revolving diameter 6, and height 4?

15

9X3=27; 4X2=8; 27-8=19×16=304.5236 =159.1744; 9×9-81 and 6×6=36.

As 81 is to 36 so is 159.1744 to 70.7447, the solidity.

SECTION XV.

Middle Frustum of a Spheroid.

To find the solidity of the Middle Frustum of a Spheroid.

To twice the square of the middle diameter, add the square of the diameter of the base; this sum multiplied by the perpendicular distance between the bases, and the product by .2618 gives the solidity.

This rule may be useful in gauging. form is called a cask of the first variety.

A cask of this

1. What is the solidity of the middle frustam of a spheroid, the middle diaineter 40, the ends 24, and length 50 inches?

50

40X40=1600×2=3200; 24×24-576; 3200+576 =3776X50=188800×.2617-40931.84 cubic inches. This divided by 231 will give gallons=177.19 gallons.

SECTION XVI.

Parabolic Spindle.

A Parabolic Spindle is an oblong solid, the extrem£ties of which are vertices.

To find the solidity of a Parabolic Spindle.

Multiply the square of the conjugate diameter by the transverse, and the product by .41888 for the solidity.

1. What is the solidity of a parabolic spindle, the two diameters of which are 40 and 16?

Middle Frustum of a Parabolic Spindle.

To find the solidity of the Middle Frustum of a Parabolic Spindle.

To twice the square of the middle diameter, add the square of the diameter of the base; from this sum subtract four tenths of the square of the difference of the two diame

ters; multiply the remainder by the length, and the product by .2168 for the solidity.

A frustum of a parabolic spindle is the form of a cask of the second variety.

1. What is the solidity of the middle frustum of a parabolic spindle, the middle diameter of which is 14, the diameters of the bases 9, and the length 26?

26

GB

14X14-196; 9X9-81; 196+81-277; difference of the two diameters

14-9-5X5-25;

of 25 is

10; 277—10—267; 267×26=6942.2168=1505.0256,

the solidity.

SECTION XVIII.

Parabolic Conoid.

A Parabolic Conoid is a solid formed by the revolution of a parabola about its abscissa.

To find the solidity of a Parabolic Conoid:

Multiply the height by the square of the diameter of the base, the product multiplied by .3927 gives the solidity.

1. What is the solidity of a parabolic conoid, the height being 16 inches, and diameter of the base 15?

Frustum of a Parabolic Conoid.

To find the solidity of a Frustum of a Parabolic Conoid. Multiply the sum of the squares of the two bases by the height, and the product by .3927 gives the solidity.