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RULE, common way.
Multiply the square of of the circumference by the length, and the product will be the folidity.
Required the folidity of a tree whofe length is 32 feet, and girt 6 inches.
Set the length in feet on the lip to 12 on the girt line, anul over against the side of the square, (which is of the girt) on the girt line, you have the content on the flip.
Now, if we consider the tree a cylinder, its folidity may be found as follows.
The area of a circle, whose circumference is 1, is .0795775; therefore,
By comparing the two methods above, we see that the common way is 13 feet 7 inches ir parts (which is nearly :) less than the true quantity. It is strange that a method so absurd, and so pernicious in its consequences, should ever be practised. The ease with which it is performed is perhaps the only argument which can be alleged for using it.—The following rule will give the content extremely near the truth : It may be performed with equal ease with the false one, and should on that account be universally used.
Multiply the square of of the girt by twice the length, and the product is the content very near the truth *.
Ex. 2. Required the content when the girt is 4 feet 2 incha es, and the length 15 feet.
Anf. 20 feet to inches. Ex. 3. What is the folidity, when the girt is 55 inches, and the length 20 feet 6 inches ? Anf. 34 feet 5 inch. 5 pts.
Ex. 4. Required the folidity of a tree whose girt is 6 feet & inches, and length 16 feet 4 inches.
Anf. 58 feet o inch. 10 pts. 8". Ex. 5. Required the folidity of a tree, the circumference being 30 inches, and the length 6 feet. Anf. 3 feet 3 inches,
Ex. 6. Required the content of a tree whose girt is 35 incha es, and length 17 feet 8 inches,
Anf. 12 feet o inches 3 pts. 4". Ex. 7. The girt is go inches, and the length 19 feet, required the solidity.
Anf. 85 feet 6 inches. Ex. 8. How many solid feet are in a tree whose girt is 95 inches, and length 25 feet? Anf. 125 feet 4 inches 2 pts. 3 A 2
* By this rule these 9 examples are computed.
Ex. 9. How many solid feet are in a tree 5 feet 5 inches girt, and 20 feet long ? Anf. 46 feet 11 inches 4 pts.
Tapering-timber is that which is thicker and broader at the one end than at the other.
When the tree tapers regularly, the dimensions may be taken at the middle for the mean dimensions; or they may be taken at both the ends, and half their sum will be the mean die mensions.
If the tree be very irregular, the dimensions ought to be taken at several equidistant places, and their sum divided : Or the tree may be divided into a certain number of lengths, the content of each part found separately, and their sum will give the content of the whole.
The mean girt of round tapering trees is found in the same manner. When trees have their bark on, it is customary to make an allowance, by deducting so much from the girt as is judged sufficient to reduce it to such girt as it would have without the bark. In tak, the allowance is generally i' or 's of the girt; but in elm, ash, beech, &c. the bark not being sa thick, the deduction ought to be less.
A tapering-tree, whose length is 24 feet, the girt at the greater end being 7 feet, and at the less 1 foot; it is required to find its content according to the true method, also in the common way:
A tree is girt in 6 different places, as follows :- In the first place, 9 feet; in the second, 6 feet 8 inches; in the third, 5 feet; in the fourth, 4 feet 9 inches; in the fifth, 4 feet 2 inches; and in the sixth, 3 feet 5 inches--required its solidity, its length being 12 feet.
3.co Ans. 30 feet 3 inches.