The globes are to each other as the cubes of their radii. Their radii are the hypothenuse of rightangled triangles, of which the line of least resistance, and the semi-diameter of the excavation, are the other two sides. Therefore, to find the charge to produce any required diameter of the excavation, the following will be the rule, the radius being found as above:

As the cube of the radius of the globe of compression in the following table, (having the same line of least resistance as the required globe,)

Is to the cube of the radius of the required globe;

So is the charge corresponding in the following table,

To the charge required.

Table for the Charges of Mines, according to Valliere.

Line
of least
Resistance.		Charge
for the
Mine.		Line
of least
Resistance.		Charge
for the
Mine.
Feet.lbs.oz.Feet.lbs.oz.
 1  0 221 868 3
 2  01222 998 4
 3  2 823114010
 4  6—241296—
 5 1111251558 9
 6 20 426164712
 7 32 2271815 4
 8 48—282053—
 9 68 5292286 7
10 9312302530 4
1112412312792 4
12162—323072—
1320515333369 1
14257 434368012
15316 4354019 8
16384—364374—
17460 937474811
1854612385144 4
19643—395561 2
20750—406000—

This table is calculated upon a supposition that the excavation of the mine is a paraboloid, having a base double the line of resistance; and that 10 lbs. 10 oz. of powder is sufficient for raising one cubic fathom of earth. By the rule above given may be found the charge for any mine, that shall only shake the ground, without making any excavation, by making the line of least resistance of the required globe only equal to the radius of the globe of compression.

The charges thus found by means of this table, being only for one nature of soil; viz., light earth and sand, (that for which the table is calculated) must be augmented according to the following table of Vauban’s, by one, four, five, seven, or nine elevenths of the charge found.

Table of the quantity of powder required to raise a cubic fathom, according to the soil.