75S 
that of a is subducted, the Z. aAb will be 
found =r 89° 4 O'. 
That if from the observation c, that of b is 
subducted, the Z. bAc will be found — 48° O'. 
That if from the observation d, that of c is 
subducted, the /_ cA</will be found — 129° 50. 
And also, that if the circular complement of. 
the observation d (which is 360° — 329° 50 — 
30° 10 / ) is added to the observation a, the Z. 
dA i will be found — 92° 30. 
The whole together making (as it ought) the 
complete circle 3(10°. 
The content may now be computed by Rule 3 
of triangles. 
A measurer may take the angle at each cor- 
ner of a piece of ground, and measure the sides 
as he goes on, thus : — having set the needle to 
its 350°, and the limb to its 360°, he found by 
observation at © 1, that looking to his picket at 
© 2, the limb cut 304°, from the north towards 
the west, and his needle 124°. — At © 2, having 
directed the theodolite to the back station, his 
observation forward was, on the limb, 45° 30' 
from south to west, and on the needle 45° 30' 
also. At © 3, the limb was at 126° O', from 
south to east, and the needle at 306° O'. — And 
at © 4, the limb and needle both were at 216° O', 
from the north to the eastward. 
Supposing the lines were found to be 1000 
links, 800 links, 1100 links, and 800 links, the 
plan may be made, and the content found by 
the scale. 
In extensive concerns, where all the Helds in 
an estate or manor are to be measured, large 
circuits must be taken with the theodolite, and 
the proceedings carefully noted down in the 
field-book, the pages of which are divided into 
three parts ; the middle column being for in- 
serting the angular observations, and the pro- 
gressive distances from station to station, and 
the points Where it may be necessary to set off 
(with the ten link staff) such short lines as the 
flexures or angles of boundaries may require. 
The sides of the page are employed in noting 
down such off-sets and remarks, on either hand, 
as may be found, necessary and also in making 
sketches of side boundaries, where any devia- 
tions from a straight line occur. Far the more 
readily sketching such side boundaries, it is ne- 
cessary to begin at the bottom of the page, and 
write upwards. 
For an example to exemplify the mode of 
practice with this excellent instrument, we will 
take the estate, fig. 33, and suppose the mea- 
surer to plant his instrument in the road at © 1, 
and having duly adjusted it, by setting the head" 
thereof truly horizontal by the spirit levels and 
adjusting screws ; and setting the index part of 
the limb exactly at 360°, by moving the whole 
head about until the 360 in the compass-box 
comes to the line in the north end of the needle, 
the instrument will thus be completely adjusted: 
here he is to lock all fast by the screw under 
the head between the legs. 
The instrument thus adjusted, the measurer 
sends one of his assistants forward, as far as he 
can conveniently measure a straight line, as at 
© 2. Taking then his angle of observation by 
his telescope, he finds it to be 69° 0' from the 
north towards the east, which he enters in his 
field-book, noting it with N. E. as a memorandum 
on which side of the meridian it lies. He must now 
fix his limb to the other part of the head, by a 
screw for that purpose. His chain-men having 
laid the chain in a direction to the picket at 
© St, he proceeds to measure this line, making 
such off-sets to the right and left as may be ne- 
cessary. At his station he finds, by measuring, 
on the right, with his off-set staff, that he has 
the general line of the road-fence at 30 links, 
and also a corner of 40 links more, and 30 
I) road : on the left of his station he has an off- 
set of 10 links. The chain-men proceeding on 
SURVEYING, 
their line to 300, lie finds 25 oxt the right to be 
the breadth on that- side of the road, where is a 
gate, and on the left 20, which will determine 
the breadth of the road at that spot. At 400 he 
will find 10 on the right, and 20 on the left, to 
be the breadth. At 760 (the end of that line) he 
will find 35 on the right, and 15 on the left, to 
be the breadth ; where also he will find a small 
road branch off to the right. Thus is the first 
station-line finished. 
To this spot (which is his second station) he 
brings his theodolite, and after setting it level, 
unlocks the under screw and turns the whole 
head about, until, through the telescope, he sees 
the back picket or station-staff. Here again, 
locking the head of his theodolite, he must un- 
screw the limb, and turn it about until, through 
the telescope, he has a view of the picket at 
© 3 ; the angle to which he will find to be 
253° 10' from the north to the eastward, which 
he will enter in his field-book. Measuring on 
from © 2 to © 3, he will find, at 130 links, that 
he is come to a turnpike-gate, where the breadths 
on the right and left are 30 and 15. At 200 he 
has an off-set of 15 on the left ; and a .break-off 
at the right of another road, at 25 from his 
line, with two other off-sets, as expressed in the 
field-book. Whereto this road leads, must be 
noted. At 265 he has off-sets of 30 on the left, 
and 20 on the right ; which ends this station 
line. 
Bringing now his instrument to © 3, he is to 
adjust it in the manner we have directed him to 
do at © 2, and turning the limb about towai-ds | 
the picket forward, he will find the angle of j 
bearing to be 57° 45', still from the north to the j 
eastward. At 20 he will find himself opposite 
to a cross hedge on the left, belonging to the 
estate he is surveying. At 293 he ends his line 
of this station ; where the off-sets are 5 and 35, 
as noted in the field-book. 
Coming now to 0 4, and having adjusted his 
theodolite, he finds his next angle == 226° 0' 
N. E. At 20 his off-sets are 20 and 15. At 410 
they are 15 and 30, where, on the left, is a cross 
hedge of a backward direction. At 480 his off- 
sets are 5 and 25, where is another cross hedge. 
At 750 is a break-in of the fence, and the off- 
sets are 30 -(- 15 on the left, and 10 on the right. 
At 1050 the off-sets are 20 on each hand, and 
another cross hedge on the left. At 1 150 are 
off-sets on the right of 20 and 20, where stands 
a house. At 1300 the off-set of 30 on the right 
terminates the house ; and at 5 on the left Is a 
cross hedge of a backward direction : — 1350 
ends this line, where roads diverge to the right 
and left. 
At © 5 the instrument being adjusted, the an- 
gle is 284° 50', nearly W. At 50 the off-set to 
the hedge is 15; at 220 it is also 15, where is a 
cross hedge, which is the same as was noted at 
1050 in the last line. At 320 the off-set is 25. 
At 350 is the end of this station, where the dis- 
tance from the fence is 15. 
At © 6 the hearing is 305° 35' N. \X T . At 1 30 
the oft-set is 30 ; where a cross hedge goes off to 
the point noticed at 750 in the line from © 4 
to 0 5. At 160 the line fs nearly close to the 
fence. 210 ends this line. 
At © 7 the angle forward is 106° 25' N. W. 
The line is 143 long, with an off-set at the end 
of 15. 
At © 8 the bearing is 269° 20' N. W. At 100 
and 300 the off-sets are 15 and 10. 
The bearing at 0 9 is 70° 45' S.W. At 30 
the measurer finds it expedient to cross the 
fence, and to proceed within the bounds of the 
estate. At 90 he has an off-set of 30 to the right, 
where he crosses a hedge. At 880 he crosses 
another hedge, having there an off-set, of 20. 
At 940 he has an off-set of 50. At 990 he 
again crosses the hedge. At 1020 he has an off- 
set of 20 to the left. At 1040 he again crosses 
the hedge. At 1030 he comes to the corner of 
the farm-house; and 1165 ends his liue, where 
is a small curve at the right. 
At © fO the bearing is 204° O' S. W. At 7ft 
is an off-set of 5 on the right At 200 is 15 on 
the left, and a cress hedge. At 6'00 is 25 on the 
left, and 20 -f 15 on the right. 690 ends the 
hne havxng air off-set of 15 on the right, and 
the like on ths left, where is a cross hedfe. 
. 'JTe bearing at © 1 1 is 355° 30' S. E.° At 280 
is an off-set of 30 on the right, and 10 with a 
cross hedge on the left. At 400 is an off-set of 
30, and a cross hedge at the left; and 470 ends 
the line, with off-sets of 10 and 20 on the right 
and left. • ° 
At © 12 the bearing is 155° 0' S. E. At GO is 
a cross hedge. At 219 the off-sets are 10 and 
15 : and at 229 the measurer comes to a close at 
0 1, where he began. 
Having thus taken a circuit of this estate, 
the measurer must proceed to plot off the same 
by some convenient scale in manner following : 
PLOTTING. 
The plotting, or making a draught of an 
estate,, from a field-book or other memoranda 
taken in the field, is thus performed : 
The paper, or vellum, on which the plan is 
to be. drawn, must be smoothly laid down on a 
drawing-board : a line is to be drawn from the 
bottom to the top, to represent the magnetic 
meridian. 
About the middle part of this line a point is 
to be made, on which point the centre of the 
circular protractor is to be laid, the straight edge 
so placed as to coincide with the meridian line : 
round, at the edge of the protractor, draw a 
pencil line. [The protractor is a circular piece 
of brass, having its edge divided into degrees 
&c. answerable to the circumference of the 
theodolite, so that whatever horizontal obser- 
vation is made vyith the latter, it may be laid 
down on paper with the help of this instrument.! 
1 he protractor thus placed, being steadily 
uxed in that position by pins, or by a lead 
weight, look in the field-book for the quantity 
ot the Z. at © 1, which, in the present case, is 
stated to be 69° o' north-easterly. Look for this 
degree, on the circular edge of the protractor, 
and on the paper make a mark, with a fine 
plotting-pin, at that number; mark it i, de- 
noting © 1 . 
Look in the field-book for' the Z. at © o 
which, in this case, := 253° 10', where make a 
marie, as before. 
1 bus do with all the other Z.s, until you come 
to the last station previous to a close on some 
former part of the work. 
Ail the angles being thus pricked off, remove 
the protractor. 
Consider whereabout the beginning of the 
work should be placed, so that the whole may 
come within the compass of the paper laid 
down ; and there make a mark, noting it as © 1 
the beginning of the plot. 
Lay the fore edge of the parallel ruler from 
the central point where the protractor lay, to 
the mark on the pencilled cir :!e denoted © i 
Move the fore edge of the parallel ruler until it 
touches the point determined on for the begin- 
ning of the plot— From thence draw an obscure 
or pencil line (in the direction mentioned i e 
in this case, from the north to the eastward) 
about the length of the whole line of this © — 
760. ’ ~ 
Apply a fearer-edge scale to this obseur* 
line, the 0 division thereof at the beginning • 
and pnek off every progressive number where 
any off-sets have been made; as at 300 400 
and 760. ’ 5 
I . u . n \ the SCJ de across the line (by some cross 
division, and prick off the off-sets on each sida 
o u statoi-ine. At 0, or © 1, the field-hook 
informs us, that on tiie left T.nd, at 10 links i s 
the boundary-line of that side; where is also a 
