9. Since a cubic foot of water, at the temperature of 40° Fahrenheit, weighs 1000 ounces avoirdupois, or 624 lbs., the nunibers in the preceding tables under the head Spec. Grav. exhibit. very nearly the respective weights in avoirdupois ounces of a cubic foot of the several substances.

We have also given, in another column, the weight in ounces of a cubic inch of each of the several metals: and, with regard to different kinds of wood and stone, the weight in avoirdupois pounds of a cubic foot of each. These, of course, are medium specific gravities and weights; for there are variations, sometimes indeed considerable ones, between the specific gravities of different specimens of the same kind of substance.

These additional columns will evidently facilitate the labour of finding the magnitude of a body from its weight, or the weight of a body from its magnitude. In this respect, too, the following particulars will often be of utility.

10. (1) 430-25 cubic inches of cast iron weigh 1 cwt.

bar iron

(2) 14.835 cubic feet of paving stone weigh a ton

47.762 cubic feet of Riga fir

47.158.

42.066.

36.205

11. Prob. To find the lary or other small tube.

ash, and Dantzic oak

internal diameter of a uniform capil

Let the tube be weighed when empty, and again when filled with mercury, and let w be the difference of those weights in troy grains, and I the length of the tube in inches. Then the diameter required, d=019252

w

Thus, if the difference of weights were 500 grains, and the length of the tube were 20 inches: we should have d=

019252

500

20

019252 × 5='09626 of an inch.*

12. Prob. To find the weight of a leaden pipe.

If I be the length in feet, d the interior diameter, and t the thickness both in inches and parts of an inch, w the weight in hundred weights: then w=1382 lt (d+t).

For a cast iron pipe, the theorem is

w=0876 lt (d+t);

or nearly of the former expression.

11

Ex. Let the internal diameter of a leaden pipe be 4 inches, the thickness of an inch; required the weight of 12 feet in

length.

Here 1382 x 12 × 4 × 44·1382 × 123=1.762 cwts.

13. Prob. To find the weight of the ring or rim of a cast iron fly-wheel.

Supposing this ring or annulus to be similar to a portion of a pipe of large diameter, the expression for the weight will be similar to the above; but it may be advantageous to change the notation. Let then D be the interior diameter of the fly in inches, d half the difference of the exterior and interior diameters, T the thickness from side to side of the fly, and w its weight in hundred weights: then w=0073 T d (D+d).

The same thing may easily be accomplished thus :-Let a cone of box wood, or of brass, be very accurately turned, of about 6 inches in length, and the diameter of its base about a quarter of an inch; and let its curve surface be very accurately marked with a series of parallel rings, about a twentieth of an inch asunder, from its vertex to its base. Insert this cone carefully in the cylinder (so that their axes shall coincide) as in the diagram: then it will be as v Ava: A B: ab; where, as the ratio of v A to va is known by means of the equidistant rings on the surface, and A B is known, at becomes determined.

B

Ex. Let D=100 inches, d=5 inches, or the exterior diameter = 110, and T the thickness = 4 inches.

Then 0073 T d (D+d) =·0073 × 4 × 5 × 1050073 × 2100 15:33 cwt., the required weight of the cylindrical rim.

Note. The reader will observe that this process is much shorter than those usually employed, even with the aid of tables of circles already computed.

See, farther, on kindred subjects, the approximate rules in mensuration, pa. 201, &c.