RULE. 
on the line is C 6, the mean proportional 
sought. This done, find the content of a 
circle, whose diameter is 6 feet ; this, when 
found, by the last article, will be equal to 
the content of the ellipsis sought. 
“ Use of Coggeshal’s Rule in measuring 
timber.-'’ 1“. 'To measure timber the usual 
way. Take the lengtli in feet, half feet, 
and, if required, quarters j then measure 
half way back again; then girt the tree 
with a small cord or line ; double this line 
twice very evenly, and measure this fourth 
part of the girt or perimeter in inches, 
halves, and quarters. The dimensions thus 
taken, the timber is to be measured as if 
square, and the fourth of the girt taken for 
the side of the square, thus ; set 12 on the 
girt line D, to the length in feet on the line 
C ; then against the side of the square, on 
the girt-line D, taken in inches, yon have, 
on the line C, the content of the tree in 
feet. For an instance : suppose the girt of 
a tree, in the middle, be 60 inches, and the 
length 30 feet, to find the content, set 12 
on the girt-line D, and 30 feet on the line 
C ; then against 15, one fourth of 60, on 
the girt-line D, is 46.8 feet, tlie content on 
the line C. If the length should be 9 
inches, and the quarter of the girt 35 
inches ; here, as the length is beneath a 
foot, measure it on the line of foot-mea- 
sure, and see what decimal part of a foot it 
makes, which you will find .75. Set 12, 
therefore, on the girt-line, to 75 on the first 
radius of the line C, and against 35 on the 
girt-line is 64 feet on C, for the content. 
2“. To measure round timber the true way. 
The former method, though that generally 
in use is not quite just. To measure tim- 
ber accurately, instead of the point 12 on 
the girt-line, use another, viz. 10.635 ; at 
which there should be placed a centre-pin. 
This 10,635 is the side of a square equal to 
a circle, whose diameter is 12 inches. For 
an instance : suppose the length 15 feet, 
and 1 of the girt 42 inches, set the point 
10.635 to 15, the length ; then against 42 
on the girt-line is 233 feet for the content 
sought ; whereas by the common way, there 
arises only 184 feet. In effect, the common 
measure is only to the true measure, as 1 1 
to 14. 3°. To measure a cube. Suppose 
the sides to be 6 feet each ; set 12 on the 
girt-line D, to 6 on C ; then against 72 
inches (the inches 6 feet) on the girt-line, is 
216 feet on C, which is the content re- 
quired. 4“. To measure unequally-squared 
timber; that is, where the breadth and 
depth are not equal. Measure the length 
of the piece, and the depth (at the end) in 
inches ; then find a mean proportional be- 
tween the breadth and depth of the piece. 
This mean proportional is the side of a 
square, equal to the end of the piece ; which 
found, the piece may be measured as square 
timber. For an instance : let the length of 
the piece of timber be 13 feet, the breadth 
23 inches, and the depth 13 inches ; set 23 
on the girt line D, to 23 on C; then gainst 
13 on C is 17.35 on the girt-line D, for the 
mean proportional. Again, setting 12 on 
the girt-line D, to 13 feet, the length of the 
line C ; against 17.35 on the girt-line is 27 
feet, the content. 5". To measure taper 
timber. The length being measured in feet, 
note one-thii'd of it ; which is found thus : 
set 3 on the line A, to the length on the 
line B ; then against l on A is the third 
part on B : then, if the solid be round, mea- 
sure the diameter at each end in inches, 
and subtract the less diameter from the 
greater ; add half the difference to the less 
diameter ; the sum is the diameter in the 
middle of the piece. Then set 13.54 on 
the girt to the length of the line, C, and 
apinst the diameter in the middle on the 
girt-line is a fourth number on the line C. 
Again, set 13.54 on the girt-line to the 
third part of the length on the line C ; then 
against half the difference on the girt-line is 
another fourth number on the line C ; these 
two fourth numbers, added together, give 
the content. For an instance : let the 
length be 27 feet (one third whereof is 9) 
the greater diameter 22 inches, and the 
lesser 18 ; the sum of the two will be 40, 
their difference 4, and half the difference 
2, which, added to the less diameter, gives 
20 inches for the diameter in the middle of 
the piece. Now set 13.54 on the girt-line 
to 27 on the line C, and against 20 on D is 
58.9 feet. Apin, set 13.44 of the girt-line 
to 9 on the line C ; and against 2 on the 
girt-line (represented by 20) is .196 parts; 
therefore, by adding 58.9 feel to .196 feet, 
the sum is 59.096 feet, the content. 
If the timber be square, and have the 
same dimensions ; that is, the length 27 
feet, the side of the greater end 22 inches, 
and that of the lesser 18 inches ; to find the 
content, set 12 on the girt-line to 27, the 
length on the line C, and against 20 inches, 
the side of the mean square on the girt-line 
is 75.4 feet. Again, set 12 on the girt-line 
to 9 feet, one third of the length, on the 
line C, and against 2 inches, half the dif- 
ference of the sides of the squares of the 
ends on the girt-line, is .25 parts of a foot; 
