MEN
195
MEN
To this area add the allowances for workmanship and"®ste.
t , ^ tll ere he no flat, add the two adjoining sides and twice' eri gt)i of the ridge, for the length; multiply the sum bythe breadth of the slope, for the area of the space covered ;n a dd the allowances as before.
Mensuration of Timber .iwing rules are from Dr. Hutton’s Mensuration .LEm I.— To jl n d i} le area or superficial feet in a board« rj or plank.
«i -kt —Multiply the length by the mean breadth.
th e tw° 6 —^ r ^ len the board is tapering, add the breadth atbre adth 6n ^ a to a e ^ ler > and take half the sum for the mean
On sliding rule. —Set 12 on b to the breadth in inches
then
against the length in feet on b, is the content on
“ E * and f rac t'onal parts,is f2 i? am P le 1-—What is the value of a plank, whose lengthSqa are 6 inches, and mean breadth 11 inches; at 1 \d. per
By decimals.12.51 1
By duodecimals.
12
H* is i
137.5
11.46
Is. 5d. ans.
1 id. is i
5 in. is
12
6
11
11
5 6
Is
44 d.
0
i
Is.
5d.
<t “ By the sliding rule.
“That • 12b : Ha : : 121b
' at ,s > as 12 on ' '
111a.
is to 11 on A, so is 124- on B to
l Hon A
«c p
2.—Required the content of a board, whoseVswV 8 ^ ^ ^ eet 2 inches, and breadth 1 foot 10 inches.
''JeI' ^ eet > 5 inches, and 8 seconds.
9 : am ple 3.—What is the value of a plank, which is 12■''-A,,' nc ' l(!S long, and 1 foot 3 inches broad, at 2\d. a foot3s. Sjd.
!i d. 4.—Required the value of five oaken planks, at
s sve r „, , ° ot > each of them being 174 f eet l° n g> and theirrea dths as follow, namely, two of 134 inches in thel "g U J of 141 inches in the middle, and the two remain-> 0 > eac h 18 inches at the broader end, and ll£ at t* 16
1 ^■ nswei ’» £l 5s. 8 \d.
!■£*■—To find the solid content of squared\ or four-Ivtjj p sided timber.
t] le '"Multiply the mean breadth by the mean thickness,'A t)i^^ r ° duc f again by the length, and the last product will
* e content.
“ By the sliding rule.
“» c d d 0
n “ That • ngtl1 : 12 or 10 :: quarter girt : solidity.
. Ie q Ua , Is > as the length in feet on c, is to 12 on d when,'th s girt is in inches, or to 10 on d when it is in
0n ° c f f cot; ■
other the tree taper regularly from the one end to
' mean breadth and thickness in the
‘ > so is the quarter girt on d, to the con-
'Sir
<i Join fo^ d ’ rnens ions at the two ends, and then halffiii„i ‘ If tho . e mean dimensions.
<i r '
>n SO f“ t! Piece do not taper regularly, but is unequallyUie'^'oria e P arts . and small in others, take several differentl '0tnh e 4 of ii |em all together, and divide their sum byfhem, for the mean dimensions.
“ 3. The quarter-girt is a geometrical mean proportionalbetween the mean breadth and thickness ; that is, the squareroot of their product. Sometimes unskilful measurers usethe arithmetical mean instead of it, that is, half their sum ;but this is always attended with error, and the more so as thebreadth and depth differ the more from each other.
“Example 1 .— The length of a piece of timber is 18 feet6 inches, the breadth at the greater and less end 1 foot 6inches and 1 foot 3 inches, and the thickness at the greaterand less end 1 foot 3 inches and 1 foot: required the solidcontent.
Decimals.
Duodecimals.
1.5
1
6
1.25
1
3
2 ) 2.75
2)2 9
1.375
mean breadth
1
4
6
1.25
1
3
1.0
1
0
2 ) 2.25
2)2
3
1.125
mean depth
1
1
6
1.375
mean breadth 1
4
6
5625
1
1
6
7875
3375
4
6
1125
6
9
1.546875
1
6
6
9
18.5
length
18
6
7734375
27
10
1
6
12375000
0
9
4
1546875
28.6171875
content
28
7
4
10
“ By the sliding rule.
BABA j
“ As 1 : 13| :: I64 : 223, the mean square.
c d c d j
“ As 1 : 1 : : 223 : 14.9, quarter-girt,
c n d c
“ As 184 : 12 : : 14.9 : 28.6, the content.
“ Example 2.—What is the content of the piece of timber,whose length is 244 feet, and the mean breadth and thicknesseach 1.04 feet?—Answer, 264 f eet -
“ Example 3.—Required the content of a piece of timber,whose length is 20.38 feet, and its ends unequal squares, theside of the greater being 194 inches, and the side of the less9| inches.—Answer, 29.7562 feet.
“ Example 4.—Required the content of a piece of timber,whose length is 27.36 feet; at the greater end the breadtli is1.78, and thickness 1.23 ; and at the less end the breadth is1.04, and thickness 0.91 ?—Answer, 41.278 feet.
“Problem III.— To find the solidity of round or unsquaredtimber.
“Rule 1, or Common Rule. —Multiply the square of thequarter-girt, or of one-fourth of the mean circumference, bythe length, for the content.
“ By the sliding rule .—As the length upon c : 12 or 10 jupon d : : quarter girt, in 12ths or lOths, on d : content 1on C.
“Note 1.—When the tree is tapering, take the meandimensions, as in the former Problems, either by girting it inthe middle for the mean girt, or at the two ends, and takehalf the sum of the two. But when the tree is very irregular