On the Mensuration of Timber. , 215 



equal, br the tree a cylinder/ as fig. 4j a source of uncer* 

 fcainty and error hereby arises, besides the other source of 

 error in taking l-4th of the circumference to be the side of 

 the square equal to the circle*: these causes operate diffe- 

 rently in different trees, so as to cause the real content of a 

 foot of timber round measure to vary, as before stated, from 

 about 2200 to about 2500 cubic inches, always exceeding 

 the truth by more than one-fourth part of the whole. ■ 



In case the tree does not taper regularly as above de- 

 scribed, but owing to knots or branches tapers irregularly in 

 different parts, as in fig. 5, having at the points B and D' 

 what are called stops or knots, occasioning the tree to lessen 

 suddenly at these places; in such case the tree is measured 

 at three lengths ; first taking the length AB and girt at C, 

 then the length BD and girt at E, and lastly the length DF 

 and girt at G ; and calculating the three pieces separately 

 by the above method, the three contents are added together 

 for the content or measure of the whole tree*. 



The third, br foot square measure, occurs in measuring 

 timber which has been hewn or sided in part, as in fig. 6 ; 

 the transverse section of such a tree being in fact an eight- 

 eided figure, contained under four straight lines and four 

 Curved ones, part of the circumference of the tree; and 

 trees are never so much hewn or sided as to take out the 

 Corners entirely^ for then they would be called die-square, 

 as in the first case. The method of measuring here is to 

 take the length AB, and thereby to determine the middle 

 point C, and, instead of girting it there, its depth DE is 

 taken with a pair of calliper compasses, which are after- . 

 wards applied to a carpenter's rule to get the inches therein i 

 in like manner its breadth FG is taken ; and if these differ, 

 they are added together and the half of their sum taken as 



* In the above tree, if the larger piece is in length AB 17 feet and 

 its girt at C 24 inches, the middle piece in length BD 17 feet and its girt 

 at h. be 15 inches, and the smaller piece in length DF 17 feet and its girt 

 at G be 6 inches, then the whole length, or three times 17, being 51 feet, 

 dhd the girt at its middle 15 inches, (being also in this case the third of 



the sum of the three girts, or - — ~ — ~Y> therefore 1$ multiplied by 



15, this divided by 144, and then multiplied by 51, gives 79^ feet as the 

 content when measured in one piece t but if this tree be measured in 

 three lengths as above directed, then 14 x * 24 4" '44 * 17 =: 68 feet 

 the content of the greater piece, also 15 x 15 -r 144 x 17 = z6j feet 

 the content of the middle piece, an. I 6 x 6 -r >4f x 17 = 4^ feet 

 the content of the smaller piece; the sum of these three or 68 + 26^ + 

 A-k = 9 8 4 feet for the content, when measured as three pieces, exceeding 

 the other by 19-f- feet. 



Qj> , the 



