"RULE 1, or COMMON RULE.—Multiply the square of the quarter-girt, or of one-fourth of the mean circumference, by the length, for the content.
" By the sliding rule.—As the length upon c : 12 or 10 upon D : : quarter girt, in 12ths or 10ths, on D : content on c.
" Note 1.—When the tree is tapering, take the mean dimensions, as in the former Problems, either by girting it in the middle for the mean girt, or at the two ends, and take half the sum of the two. But when the tree is very irregular divide it into several lengths, and find the content of each part separately.
"2. This rule, which is commonly used, gives the answer about one.fourth less than the true quantity in the tree, or nearly what the quantity would be after the tree is hewed square in the usual way; so that it seems intended to make an allowance for the squaring of the tree. When the true quantity is desired, use the second rule given below.
" Example 1.—A piece of round timber being 0 feet 6 inches long, and its mean quarter-girt 42 inches; what is the content'? Decimals. Duodecimals.
3.5 quarter girt 3 6 3.5 3 6" Example 2.—Required the content of a tree, which is 24 feet long, and mean girt 8 feet.—Answer, 122.88 feet.
" Example 3.—The length of a tree is 141 feet, and mean girt 3.15 feet ; what is the content1—Answer, 11.51 feet.
" Example 4.—The length of a tree is 17 feet, and its mean gii t 6.28 ; what is the content ?—Answer,54.4065 feet.
" Nola 1.—That part of a tree, or of the branches, mhich is less than 2 feet in circumference, or 6 inches quarter-girt, is cut off; not being accounted timber.
"2.—Fifty cubic feet of timber make a load ; and there fore, to reduce feet to loads, divide them by 50." Example.—Ilow many loads of timber are there in 248 feet? 5,0 ) 24,8 Scum.Ium.—In measuring squared timber, unskilful mea surers usually take one-fourth of the circumference, or girt, for the side of a mean square ; which quarter girt thereti)•c multiplied by itself, and the product multiplied by the length, they account the solidity, or content : when the breadth and thickness are nearly equal, this method will give the solidity pretty near the truth ; hut if the breadth and thickness differ considerably, the error will be so great, that it ought by no means to be neglected.
"Thus, suppose we take a balk, 24 feet long, and a foot square throughout ; and consequently its solidity 24 cubic feet : if this balk be slit exactly in two, from end to end. making
each piece 6 inches broad, and 12 inches thick, the true solidity of each will be 12 feet ; but, by the quarter-girt method, they would amount to much more ; for the false quarter girt, being equal to halt' the sum of the breadth and thickness, in this case will be 9 inches, the square of which is 81, which being divided by 144, and the quotient multi plied by 24. the length, we obtain 13; feet for the solidity of each part ; and consequently the two solidities together make 27 feet, instead of 24.
" Again, suppose the balk to he so cut, that the breadth of one piece may be 4 inches, and that of the other S inches. Here the true content of the less piece will be S feet, and that of the greater 16 feet. But, proceeding by the other method, the quarter-girt of the less piece will be S, square, 64, multiplied by 24, and the product divided by 144, gives 101 feet instead of S. And by the same method, the content of the greater piece will be 161- feet, instead of 16. And the sum of both is 271 feet, instead of 24 feet.
"Farther, if the less piece be cut only 2 inches broad, and the greater 10 inches; the true content of the less piece would be 4 feet, and that of the greater 20. But, by the other method, the quarter-girt of the less piece would be 7 inches, whose square, 49, being divided by 6, gives 8-1- feet, instead of 4, for the content. And, by the same method, the content ot' the greater piece would be 201, instead of 20 feet. So that their sum would be 281, instead of 24 feet.
" 1-knee it is evident, that the greater the proportion be tween the breadth and depth, the greater will the error be, by using the false method ; that the sum of the two parts, by the same method, is greater, as the difference of the same two parts is greater, and consequently the sum is least when the two parts are equal to each other, or when the balk is cut equally in two ; and lastly, that when the sides of a balk ditiir not above an inch or two from each other, the quarter girt method may then be used, without inducing an error that will be of any material consequence.