11(5 - MENSURATION. 
the circumference is ufed, we mull multiply its fquare 
by ‘0795s X 
Hence, to find the true content of a piece of cylindri¬ 
cal timber, vve ought to multiply the fquare of the quar¬ 
ter-girt by the conllant number t‘ 2732.8, and that pro¬ 
duct by the length ; inltead of which, the conllant multi¬ 
plier is omitted, and confequently the folidily is returned 
about parts lels than it is. But, as the utmoll accu¬ 
racy is not neceffary in thole cales, the following Rule 
might be ufed, which is as fimple as can be defired, viz. 
Multiply the fquare oft of the mean girt by double the length 
for the content, which is not far from the truth. 
Of MEASURING LAND. 
The inllruments moft commonly employed in jnea- 
furing land are the chain, the plane table, and the crofs. 
A ilatute acre of land being 160 fquare poles, the chain 
is made 4 poles or 66 feet in length, that 10 fquare chains 
(or 100,000 fquare links) may be equal to an acre. Hence 
each link is j-qz inches in length. 
The plane table is ufed for drawing a plan of a field, 
and taking liic'h angles as are neceffary to calculate its 
area. It is of a rectangular form, and is furrounded with 
a moveable frame, by means of which a lheet of paper 
may be fixed to its furface. It is furnilhed with an index 
by which a line may be drawn on the paper in the direc¬ 
tion of any objeCl in the field, and with feales of equal 
parts, by which fuch lines may be made proportional to 
the diftances of the objects from the plane table when 
meafured by the chain; and its frame is divided into de¬ 
grees for obferving angles. 
The crofs confills of two pair of fights fet at right angles 
to each other upon a ftaff having a pike at the bottom to 
Hick into the ground. Its ufe is to determine the points 
where a perpendicular drawn from any objeCt to a line 
will meet that line; and this is effected by finding by 
trials a point in the line, fuch that, the crofs being fixed 
over it fo that one pair of the fights may be in the direc¬ 
tion of the line, the objeCt from which the perpendicular 
is to be drawn may be leen through the other pair; then 
the point thus found will be the bottom of the perpendi¬ 
cular, as i3 evident. 
A theodolite may alfo be applied with great advantage 
to land-furveying, more efpecially when the ground to 
be meafured is of great extent. 
In addition to thefe, there are other inllruments em¬ 
ployed in furveying, as the perambulator, which is ufed 
for meafuring roads and other great diftances. Levels, 
with telelcopic or other fights, which are ufed to deter¬ 
mine how much one place is higher or lower than ano¬ 
ther. An off-fet ftaff for meafuring the off-fets and other 
fhort diftances. Ten fmall arrows, or rods of iron or 
wood, which are uled to mark the end of every chain 
length. Pickets or Haves with flags to be fet up as marks 
«r objefts of direction ; and laftly, feales, compalfes, &c. 
for protraCting and meafuring the plan upon paper. See 
the article Surveying. 
The obfervations and meafurements are to be regularly 
entered as they are taken, in a book which is called the 
Field-book, and which ferves as a regifter of all that is 
done or occurs in thecourfe of the fuivey. 
To Meafure a Field by the Chain. — Let Am BCD q, 
fig. 21, reprefent a field to be meafured; Let it be refolved 
into the triangles A in B, A B D, B C D, A q D. Let all 
the fides of the large triangles ABD, BCD, and the per¬ 
pendiculars of the fmall ones A m B, A q D, from their 
vertices m, q, be meafured by the chain, and the areas 
calculated by the rules before given ; and their amount 
is the area of the whole. But if, on account of the cur¬ 
vature of its fides, the field cannot be wholly refolved into 
triangles, then, either a ftraight line maybe drawn over 
the curve fides, fothat the parts cutoff from the field, and 
thofe added to it, may be nearly equal; or, without 
going beyond the bounds of the field, the curvilineal 
Ipaces may be meafured by the rule given at p. 112. 
4 
To Meafure a Field with the Plane Table .— Let the plane 
table be fixed at F, fig. 22, about the middle of the field 
ABODE; and its diftances FA, FB, FC, &c. from the 
feveral corners of the field meafured by the chain. Let 
the index be directed from any point aflumed on the 
paper to the points A, B, C, D, &c. fucceflively, and the 
lines Fa, Fb, Fc, drawn in thefe directions. Let the 
angles contained by thefe lines be obferved, and the lines 
'themfelves made proportional to the diftances meafured. 
Then, their extremities being joined, there will be formed 
a figure a b cd e, fimilar to that of the field; and the area 
Qt’the field may be found by calculating the areas of the 
feveral triangles of which it confifts. 
To plan a Field from a given bafe Line. —Let two ftations 
A, B, fig. 23, be taken within the field, but not in the 
fame ftraight line with any of its corners ; and let their 
diftance be meafured. Then, the plane table being fixed 
at A, and the point a aflumed on its furface direClly above 
A, let its index be directed to B, and the ftraight line a b 
drawn along,the fide of it to reprefent A B. Alfo, let the 
index be directed from a to an objeCt at the corner C, 
and an indefinite ftraight line drawn in that direction; 
and fo of every other corner fucceflively. Next, let the 
plane table be fet at B, fo that b may be direCtlyover B, 
and b a in the fame direction with BA; and let a ftraight 
line be drawn from b in the direction BC. The interlec¬ 
tion of this line with the former, it is evident, will de¬ 
termine the point C, and the triangle a be on the paper 
will be fimilar to A B C in the field. In this manner all 
the other points are to be determined; and, thefe being 
joined, there will be an exaCt reprefentation of the field. 
If the angles at both ftations were oblerved, as the 
diftance between them is given, the area of the field 
might be calculated from thefe data ; but the operation 
is too tedious for praCHce. It is ufual therefore to mea¬ 
fure fuch lines in the figure that has been conftruCted as. 
will render the calculation eafy. 
Of GAUGING. 
As the forms of calks are merely hypothetical, it may 
reafonably be expeCted that fome degree of uncertainty 
will attend the application of the rules to aClual meafure - 
ment. The following rule, however, given by Dr. Hut¬ 
ton in his excellent Treatife on Menfuration, will apply 
equally to any calk whatever. And, as the ingenious 
author obferves that its truth has been proved by feveral 
calks which have been actually filled with a true gallon- 
meafure after their contents were computed by it, we 
prefume that it is more to be depended upon in praClice 
than the others. 
Rule. Add into one fum 39 times the fquare of the 
bung-diameter, 25 times the fquare of the head-diameter, 
and 26 times the produCl of the diameters; multiply the 
fum by the length, and the produCl by ‘00034; then the 
laft produCl divided by 9 wall give the wine-gallons, and 
divided by x 1 will give the ale-gallons. 
In inveftigating this Rule, the ingenious author af- 
fumes as an hypothefis, that one-third of a calk at each 
end is nearly the fruftum of a cone, and that the middle 
part may be taken as the middle fruftum of a parabolic 
fpindle. This being fuppofed, let AB and CD, fig. 24, 
be the two right-lined parts, and B C the parabolic part} 
produce A B and D C to meet in E, and draw lines as in 
the figure. Let L denote the length of the calk, B 
the bung-diameter, and H the head-diameter. Then, 
fince AB has the fame direClion as EB at A, ABE will 
be a tangent to a parabola B F; and therefore FI=*-EI. 
But BI=^AK, and hence, by fimilar triangles, EI=^EK; 
confequently FI=|EI=iEK=^FK= 1 i g (B—H) ; fothat 
the common diameter BL=FG—2FI=B—i(B—H)— 
(4B4-H), which call C. Now, by the rules tor parabolic 
fpindlesand conic fruftums, we obtain (putting n for 7 854) 
8 B 2 -H-BC~ 1 - 3 C 2 Lrt 3 ^B 2 + 44 BH+ 3 H 2 
- . - 1 ■ --— . - x ——-XLti tor the 
15 3 25X4S 
parabolic 
