Railway Curves. 137 



The " Setting Out " of Arcs on the Ground. 



The following remarks are themselves rather " lengthy," but if 

 they tend to shorten and simplify the process they refer to, they will 

 perhaps be read with patience. 



If the tangent points and the length and position of the chords 

 have been determined by any of the preceding or other methods, 

 then the setting out of the simple arcs of circles can be proceeded 

 with by either of the well-known methods most adapted to the case. 



It will here only be attempted to explain a simplification of the 

 method by the theodolite, first observing that if there be two tan- 

 gents given on the ground to be united by an arc of a circle, and if 

 no previous fixing exactly of the points of contact has been 

 attempted, the best plan is to take one point — the most convenient 

 — as fixed, on one of the tangents, the point on the other to be 

 afterwards fixed, in subordination to this, and in the following order 

 (supposing that the point of intersection of the tangents is distant 

 or inaccessible). Set up the theodolite at an assumed approximate 

 point on the opposite tangent to that on which the point of contact 

 has been fixed as aforesaid, and direct the instrument along the pro- 

 longation of the tangent on which it stands, the index of the vernier 

 being first clamped at 360° of the limb ; clamp the lower plate, and 

 bisect the pole or arrow that indicates the direction of the tangent 

 with the vertical web or wire (of the diaphragm, fixed in the interior 

 focus of the telescope, and which is common to the eye-piece and 

 object end). Then unclamp the upper plate, and turn the telescope 

 upon the point fixed upon as aforesaid in the opposite tangent, and 

 read off the angle. Now remove the instrument to aforesaid fixed 

 point, and by the same process read the |_ of divergence of the Line 

 of collimation joining this and your previous station from or out of 

 the prolongation of this tangent ; take half the sum of these two 

 angles, which at once deflect from your tangent, as the true direction 

 of the chord, whereby you fix the opposite point of contact. Measure 

 the chord. 



Note. — It is better, as far as the convenience of reading off, in the 

 further process of setting out, is concerned, if we " fix " the first 

 point on the left hand tangent, so that the instrument is first set up 

 on the right hand tangent, and being removed to the left hand tan- 

 gent, there remains, to the end, perhaps, of the setting out of the 

 curve. 



In whatever way the points are fixed, when that is done, and the 

 length and direction of the chords is ascertained, either by calcula- 

 tion or measurement, then 



Let us next consider (Fig. X) that the |_ of deflection of the chord 

 A,B from the produced tangent is the |_ 9 of the alternate segment, 



T 



