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 CARD ASUREMENTS SETTING OUT CURVES WITH THE USE OF A THEODOLITE NOTE- THE THEODOLITE IS SET UP OVER THE POINT 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 RADS OF -RA DEC MIN 50 34.4 8 3-34-8 25 1- 8.7 60 - 28.7 OF LE NC TH FOR A CURVES OF LESS THAN 15 CHAINS RADIUS SHOULD BE THE TANCENTIAL ANCLE FOR A CHORD CONSISTING OF ANY NUMBER OF LINK OLE Land Surveying and Levelling pp. 218, 219. HOTE-TO RETURN TO A TANCENT LINE AT THE END OF A CURVE, SET UP 5 CURE I 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 AY BE OBTAINED FROM THE PRINTED TABLES, EY .F FICURE I-THE LENGTH OF A CURVE IS GENERALLY LENGTH=RX2 X3-1416x/FA)=000582xR 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 |