ns 
MENSURATIO N. 
Ex. i. Find the contents of fix oak-trees, and the value 
©f the timber contained in each tree, from the following 
dimenfions and values: 
IMumbei 
of 
Trees. 
Bushel; 
of 
Bark. 
S TJ 
-O O 
a* 
Lengths 
in Feet 
Quarter 
Girts in 
Inches. 
Contents 
in Feet. 
Values 
erFoot. 
s d. 
Value of 
each Tret 
!. i. d 
I 
iv 
0 
I 2 
81 
6 
2 
0 
O 12 O 
2 
3 ^ 
0 
16} 
i 4 
17! 
2 6 
239 
3 
32 
1 
2 
39 v 
18 
89 
4 
3 
18 18 3 
4 
15 
T 
4 - 
23 
39 !- 
3 0 
Si 9 3 
5 
O 
15 
9 A 
9 s 
2 3 
1 1 45 
6 
80 
3 
% 
44 
z8± 
248 
6 0 
74 8 0 
Total 
134? 
if 
- 
- 
— 
- - 
103 27^ 
Ex. z. Required the contents of ten trees, and the value 
of the timber in each tree, from the following dimenfions 
and values: 
No. of 
Trees. 
Names of 
the Trees. 
Value 
of the 
Tops. 
1. j. d. 
i Lengths 
1 in Feet. 
Quarter 
Girts in 
Inches. 
Contents 1 
in Feet. 1 
Value 
per 
Foot. 
s. d. 
Value of 
each Tree. 
!• s. d 
I 
Elm 
O 
5 
6 
4 2 i 
12 .V 
44v 
3 
0 
6 
12 
9 
2 
Afh 
O 
5 
O 
381 
nf 
3«1 
3 
0 
5 
9 
6 
3 
Pine 
O 
3 
O 
36 
14s 
5 2 s 
3 
6 
9 
3 
9 
4 
Fir 
O 
I 
6 
28 
IO 
192 
1 
9 
I 
13 
8i 
5 
Beech 
O 
4 
6 
3?! 
164 
75 
2 
6 
9 
7 
6 
6 
Sycamore 
O 
3 
6 
265- 
9t 
i7i 
2 
6 
2 
3 
7 
Poplar 
O 
2 
6 
48 ! 
54! 
3 
0 
8 
4 
3 
8 
Yew 
I 
2 
6 
9s 
3«f 
9 6 u 
4 
9 
22 
18 
4a 
9 
Fir 
O 
2 
O 
3 2 s 
1 3i 
39 i 
2 
O 
3 
19 
O 
IO 
Larch 
O 
2 
6 
3oi 
!5l 
5 l i 
3 
6 
8 
19 
45 
Total 
2 
I 2 
6 
— 
— 1 — 
- 
- 
78 
I I 
1 crhrj 
1 
An erroneous rule has been adopted by perfons con¬ 
cerned in this line of bufinefs, w’hich common praftice 
has fo eftablifhed, that it is rather to be wifhed than ex¬ 
pected it fhould be replaced by fome other, either per¬ 
fectly true, or approaching towards the truth; for, ac¬ 
cording to the prefent rule, a tree frequently contains 
one-fourth more or lefs timber than it is eftimated at, 
which, at the modern price of that article, is a matter of 
fome importance, and merits the attention of the timber- 
grower, as well as the merchant. Government has, in 
fome inftances, come forward to fix a ftandard of meafure, 
as in corn, coals, land, &c. and, as old prejudices can 
never be fo fuccel'sfully combated as by the authority of 
enlightened legiflators, it is to be hoped that we may 
fome day find this, and other topics of a fimilar nature, 
become the fubjeCl of parliamentary inveftigation. Be¬ 
fore we proceed to fiiow the great inaccuracy attending 
the prefent method, it will be proper to date the Rule as 
it is at prefent employed by all perfons concerned in the 
buying or felling of timber. The Rule is this : Multiply 
the fquare of the gtea.n quarter-girt, or quarter-circumfe¬ 
rence, by the lengtu of the tree, for the content; which, when 
the dimenfions are taken in feet, will be alj'o feet; and this 
divided by 50, the number effect in a load, will give the 
number of loads. 
If the piece , of timber is of the fame girt throughout, 
the girt any-where taken is the mean girt. If the tree 
tapers regularly from one end to the other, the girt taken 
in the middle is accounted the mean girt; or take half 
the fum of the girts at the two ends for the fame. But, 
if the tree do not taper regularly, but is unequal, being 
thick in fome places and i'mall in others 5 it is cuftomary 
to take leveral different dimenfions, the fum of which, 
divided by the number of them, is accounted the mean 
girt. When the tree is very irregular, it is bell to divide 
it into feveral lengths, and to find the content of each 
feparateiy. 
That part of a tree, or of the branches, whofe quarter- 
girt is lefs than half a foot, is not accounted timber. It 
is ufual to make a certain allowance in girting a tree for 
the thicknefs of the bark, which is generally one inch 
to every foot in the girt. This practice, however, is un- 
reafonable, and ought to be diicouraged. Elm-timber 
is the only kind in which any allowance is neceffary, 
and even in this, one inch out of the whole girt is quite 
fufficient. 
As an Example in the preceding Rule: Let it be re¬ 
quired to find the content of a tree, the length of which 
is 9 feet 6 inches, and the quarter-girt 3 feet 6 inches. 
By Decimals. 
By Duodecimals. 
3’S 
3 
6 
3‘5 
3 
6 
i7S 
IO 
6 
105 
I 
9 
I 2*25 
I 2 
3 
9’5 
9 
6 
6125 
no 
3 
I 1025 
6 
14 
116-375 Content. 
Feet 116 
hi 
Such is the Rule commonly ufed by perfons concerned 
in buying and felling of timber, on which we intend to 
make a few remarks, in order to point out its inaccu¬ 
racy, which is not fo generally known as it ought to be. 
Suppofe, for inftance, we take a balk 24 feet long, and a 
foot fquare throughout, and, confequently, its folidity 
24- feet. Now, if this piece of timber be flit exadlly in 
two, from end to end, making each piece 6 inches or 
| a foot broad, and 12 inches or a foot thick, it is evi¬ 
dent that the true folidity of each piece will be 12 feet. 
But by the quarter-girt method they would amount to 
much more: for the falfe quarter-girt being equal to half 
the fum of the breadth and thicknefs, in this cafe will be 
9 inches, or § of a foot; the fquare of which is and 
therefore 24=13! feet for the folidity of each part, 
making the two pieces together 27 feet, inftead of 24, 
which is the true content. 
Again, fuppofe this balk to be fo cut, that the breadth 
of the one piece may be only four inches, or •§ of a foot; 
and that of the other 8 inches, or f of a foot. Here the 
true content of the lefs piece will be 8 feet, and that of 
the greater 16 feet. But, proceeding by the other me¬ 
thod, we-have the quarter-girt of the lefs piece J of a 
foot, and of the other piece f of a foot. Whence the con¬ 
tent of the lefs piece will be found X 24=1 of feet, in¬ 
ftead of 8 feet; and the content of the greater piece will 
be i6§ feet, inftead of 16 ; making the fum of the two 277 
feet, inftead of 24 feet. Farther, if the lefs piece be cut 
only two inches broad, and confequently the greater 10 
incites, the true content of the lefs piece would be 4 feet, 
and that of the greater 20 feet. Whereas by the other 
method, the quarter-girt of the lefs piece would be 7 
inches, or of a foot; and T ^x 24=85 feet, inftead of 
4 feet for the content; and, by the fame method, the 
content of the greater piece would be zo-} feet, inftead 
of 20, and their fum 28^ feet, inftead of 24. 
Hence it is obvious, that the greater the proportion 
is between the breadth and the depth, the greater will 
be the error, by ufing the falfe method ; and-the fum of 
the two parts, by the fame method, is greater, as the 
difference of the fame two parts is greater; and, confe¬ 
quently, the lam is leaft when the two parts are equal 
to each other, or when the balk is cut equally.in two; 
and, finally, when the fides of a piece of timber differ not 
above an inch or two from each other, the quarter-girt 
may be ufed without any very fenfible error. To avoid, 
therefore, this inconfiftency in the refult, the following 
method fhould be employed, viz. Multiply the length, 
breadth, and depth, continually together, and the product will 
be the true content in all cafes of this kind. 
With regard to round timber, the error is of a different 
kind. We have feen in p. 112, that the area of a circle 
is found by Squaring the circumference, and multiply¬ 
ing that fquare by '07958} and therefore, if a quarter of 
‘ the 
