We give a copy of the figures upon one of these cards as an illustration. (See Case 5, pages 218, 219):

With the use of a book containing the angles required, the angle is read, and the book generally has to be placed away in the pocket, so as to leave both hands free for setting the instrument; but with the use of a special card temporarily fixed upon the theodolite, the angles to be set out are constantly under the Surveyor's inspection.

Messrs. Cutler & Edge's tables are intelligible even to a workman who may not understand the formula upon which they are based. The book is clearly printed and of a convenient size to carry about as a pocket book.

When the theodolite is not divided to the same fractional parts of a degree given in the printed list of tangential angles, these angles may be set out to the nearest subdivision upon the vernier to the amount furnished by the tables. If, as is usual in railway work, the radius of the curve is expressed in chains of Gunter's links, the same chain must be employed for the measurement of the chord, otherwise any other unit measurement can be employed

CAN BE ATTACHED

HERE

IN THE ANNEXED
TABLE, THE UNIT

CARD
SPECIAL

ASUREMENTS

SETTING OUT CURVES

WITH THE USE OF A THEODOLITE

NOTE- THE THEODOLITE IS SET UP OVER THE POINT
MARKED A.AT THE JUNCTION OF THE CURVE WITH THE
STRAIGHT LINE,AND THE VERNIER UPON THE HORI-
ZONTAL PLATE CLAMPED TO 360: OR ZERO-THE
CROSS HAIRS IN THE TELESCOPE ARE THEN DIRECTED
TOWARDS ANY PEC UPON THE TANGENT LINE, THE
LOWER LIMB OF THE INSTRUMENT IS CLAMPED WITH

THE CROSS HAIRS ACCURATELY SET ON THE TANCENT

CONCULCLINE, THE VERNIER PLATE UNCLAMPED, AND THE

TANGENTIAL ANGLES SET OUT AS REQUIRED.

TANCENTIAL ANCLES FOR CHAIN CHORDS

CA

RADS OF

CURVE TANGENTIAL
CHAINS ANCLE

RADS OF
TANCENTIAL
CURVE
RADSOF
CURVE TANGENTIAL
CHAINS ANCLE CHAINS ANCLE
DEC MIN
1-25.9

-RA

DEC MIN

50

34.4

8

3-34-8 25

1- 8.7

60

- 28.7

OF LE NC TH FOR A
RADIUS, IS OF THE
SAME DE NOMINATION
AS THE UNIT OF
LENGTH EMPLOYED
FOR THE CHORD: SO
THAT THE SAME
CHAIN, MUST BE
USED IN ANY SIN CLE
CURVE, FOR THE MEASUREMENT OF THE CHORD, AS IS.
ASSUMED FOR THE RADIUS-IN RAILWAY WORK, CUNTER'S
CHAIN IS MOST CENERALLY EMPLOYED-CURVES OF
OVER TWO MILES(160 CHAINS RADIUS CAN BE SET OUT
ACCURATELY BY TWO CHAIN-CHORDS, & ACCOMPLISHED
BY MEASURING THE CHOODS WITH A COUPLE OF CHAINS
TIED TOGETHER, AND TAKING AS THE UNIT ANCLE DOUBLE
TIK VALUE OF THE TANGENTIAL ANCLE FOR A SINGLE CHAIN CHORD.
NOTE BEARELEY'S TABLES OF CURVES, A SET PRINTED
ON CARDS, ARE MOST CONVENIENT FOR USE IN THE FIELD, AS THE
SPECIAL CARD CIVIC THE TANGENTIAL ANCLES FOR THE REQUIRED
RADIUS, CAN BE PLACED ON THE THEODOLITE, THUS LEAVING BOTH
HANDS FREE FOR SETTING THE INSTRUMENTA FOR SIGNALLING.
THEY ARE PUBLISHED BY CROSBY LOCKWOOD & CO, LONDON.
KENNEDY & HACKWOOD'S TABLES A SMALL BOOK PUBLISHED
BY E&FN. SPON, LONDON ALSO CONTAIN THE TANGENTIAL
ANCLES REQUIRED FOR SETTING OUT CURVES OF FIVE
CHANS TO THREE MILES RADIUS WITH CERTAINTY
AND EXPEDITION ——

CURVES OF LESS THAN 15 CHAINS RADIUS SHOULD BE
SET OUT IN HALF CHAIN-CHORDS-THE UNIT ANCLE FOR
HALF CHAIN-CHORDS IS HALF THE ANCLE FOR/CHAIN CHORDS

THE TANCENTIAL ANCLE FOR A CHORD CONSISTING OF ANY NUMBER OF LINK
MULTIPLYING THE TANGENTIAL ANCLE GIVEN FOR A CHORD ONE CHAM IN L
HUNDRED LINKS, CONTAINED IN THE LENGTH OF CHORD REQUIRED.

OLE

Land Surveying and Levelling pp. 218, 219.

HOTE-TO RETURN TO A TANCENT LINE AT THE END OF A CURVE, SET UP
CHE THEODOLITE OVER THE POINT OF JUNCTION OF THE STRAIGHT LINE
OH WITH THE CURVE DCB. LET THE CROSS HAIRS CUT SOME DISTANT BACK
EC IN THE CURVE WHICH CAN BE SEEN, AND LET THE VERNIER PLATE BE
LAMPED AT THE CALCULATED TANGENTIAL ANCLE FOR THE LENGTH OF
RC TAKEN-THEN CLAMP THE LOWER LIMB OF THE INSTRUMENT.
EVERSE OR TRANSIT THE TELESCOPE-TRAVERSE AND RECLAMP
THE VERNIER PLATE TO ZERO-THEN SET OUT A STRAIGHT
INE DHIN THE DIRECTION SO OBTAINED

5

CURE I
E'S SYSTEM-

C! ANCLE = CHORD x 1719 MINS

PEC

ANCENT LINE

RAD

POLE

D

PEC

PEC

NEW TANCENT LINE

POLE

NOTE TO CONTINUE ACURVE

POLE

FROM AN INTERMEDIATE PEC D-SET
UP THE THEODOLITE OVER THE PEC FROM WHICH
THE CURVE IS TO BE CONTINUED, PROCEED AS
DESCRIBED ABOVE FOR FINDING THE DIRECTION
OF THE TANGENT LINE AT THIS PEC, THEN CLAMP
THE VERNIER PLATE AT THE REQUIRED TANGENTIAL
ANCLEEDH, MARK OUT THE POINT EAT A DISTANCE
FROM DEQUAL TO THE LENGTH OF CHORD TAKEN
AND CONTINUE AS MANY MULTIPLES AS REQUIRED.
NOTE-IN SETTING OUT A CURVE TO THE LEFT OF A
TANCENT LINE, AS SHOWN IN FICURE I,THE TANCEMTIAL
ANCLES CIVEN IN THE TABLE, AND THEIR MULTIPLES, MUST
BE SEVERALLY SUBTRACTED FROM 360°,TO OBTAIN THE
ANCLES TO BE READ UPON THE VERNIER PLATE.

AY BE OBTAINED FROM THE PRINTED TABLES, EY
H, BY THE FRACTIONAL EQUIVALENT OF ONE

.F

FICURE I-THE LENGTH OF A CURVE IS GENERALLY
ARRIVED AT, IN PRACTICE, BY MEASUREMENT WITH A
CHAIN ROUND THE POINTS A-B-C-D-E-SET OUT
IN THE FIELD THE LENGTH MAY BE CHECKED IF
DESIRED BY THE FOLLOWING CALCULATION

LENGTH=RX2 X3-1416x/FA)=000582xR
XIND OF MINE IN TANC! ANCLE

with the use of these tables, provided the same denomination is taken for the chord as is assumed for the radius. The tangential angle in minutes for 100 ft. chords when the radius is expressed in chains of 66 ft.

The tables of multiples give the tangential angle in minutes and decimals for units of radius up to 9, and are intended to facilitate the determination of the tangential angle for fractional chords (page 217). Thus if a curve of 20 chains radius commence at ... miles, ... furlongs, and 37 links from the starting point, the tangential angle for the fraction 63 links will be ascertained thus :

The length of chord of 63 links is then set out at an angle of 54 minutes with the tangential line, after which the unit angle for chain chords is added to this value at each setting out of points one chain apart. Again, if a curve is to terminate at 63 links beyond a full chain measurement, this value is to be added to the tangential angle taken for the last whole chord of the curve. To return to a straight line, as at D in fig. 1 (pages 218, 219), the theodolite is set up over this point, and any previous point along the curve C, B, or A is selected, the distance of which measured by chords is known. The instrument is clamped to the tangential angle for this distance, and the telescope is directed to this point and the lower plate clamped. The vernier is then unclamped and set back to 360°, when the telescope will be found to be in the direction of the tangent line D K, and when traversed vertically to be in the direction of D H. If, as in fig. 1, the vernier for a radius of 20 units has been successively set to 358° 34' -357° 8', 355° 42' for pegging out respectively the points B, C, D, when the tangent line is to the right hand of the curve, we must remember that the tangent line D K being to the left of the curve when the instrument is set up at D, the point A must be viewed with the vernier

clamped to 4° 17' or the point B with the vernier clamped to 2° 52', and then the direction of a line joining the 360° or zero point with the centre of the instrument will give the direction D K. (Pages 218, 219.)

The poles shown in the direction of the chord lines A B, A C, A D (Case 5) are not generally necessary. The usual method is for one man to hold one end of the chain at the last point determined, taking care, if the curve be flat, to place his body upon the outside of the curve, so as not to impede the line of sight when the theodolite is set for fixing the next point in the curve. The other assistant pulls out the chain or the tape to the given length, and holds up a peg or lath, which he keeps vertical at the correct distance, moving it about as directed by the surveyor, to the right or left hand, until it accurately appears in the required direction. Should any obstacle render it necessary to remove and reset up the theodolite over a new point in the curve, the direction of a new tangent line must be found by the method shown in fig. 1 (Case 5), and the same process of setting out by means of tangential angles re-commenced. The use of the tangential angles, which are calculated from the formula proved by Case 1, enables the curve to be set out to the right-hand side of the tangent line, when the theodolite is placed over the beginning of the curve, as the primary scale of divisions upon the horizontal circle of the instrument is numbered to read in the direction of the hands of a watch; hence when the curve is to be set out to the left-hand side of a tangent line, the column upon the card containing the differences of the tangential angles must be adopted. Thus with a radius of 20 chains, if 1° 25′ 57′′ be the tangential angle for a chord of one chain in length, and an angle of 2° 51′ 54′′ be the tangential angle for the intersection of a second chord of one chain's length round the arc, when the curve is to be set out to the right-hand side of the tangent line; then the tangential angles to be employed for setting out two points at the same distances for a curve to the left-hand side of the tangent line will be 358° 34′ 3′′ and 357° 8′ 6′′ respectively.

Fig. 2 (pages 222, 223) illustrates a method of setting out