Rail Road Curves. 131 



Art. XIII. — Rail Road Curves; by Thos. Gorton, Civil Engineer. 



To join two straight lines, which, if produced, would intersect each 

 other, by a curve, so that those lines shall be tangents to it. 



Find the difference in the bearing of the two lines, which suppose 

 to be 24°; then, by inspecting the ground, find what curve will suit 

 best, and let it, for example, be one of G°. There will then be five 

 deflections and four stations of curve. These deflections will be 3°, 

 6°, 6°, 6° and 3°, the sum of which is 24°. Then commence the 

 curve at some point in one of the straight lines, and run it round, by 

 making the above deflections at their respective stations, when, if the 

 last deflection coincide with the other straight line, the work will be 

 done : but, which is probable, suppose that it falls to one side of it. 

 Then, at the station where the last deflection was made, turn the in- 

 strument 24°, viz. to the bearing of the first straight line, and look- 

 ing back or forward, as the case may be, see where it cuts the line 

 you wish to run into, which point, if the work has been carefully done, 

 is the place where the curve will join the said line. Measure the 

 distance from the instrument to this point, then go back to where the 

 curve was begun and set off the same distance back or forward as 

 before, in the straight line, from which run the curve round, and the 

 lines will be joined. 



The correctness of this rule will readily be seen. It is simply 

 moving the curve back or forward, keeping the line a tangent to it, 

 until the other end of the curve falls in the other straight line. The 

 rule is also easy in practice, as in every case two lines may be joined 

 in this manner by only two trials, if the curve be carefully run. 



To make a slight change in the direction of a line. 



In running a line for the superstructure of a rail road, it will be 

 found occasionally to vary a little from the grading line. A correc- 

 tion may be made in the following manner, at the curves, by length- 

 ening or shortening them a few feet. Suppose, on coming to the end 

 of a curve, that the line comes out in the centre of the grading, but 

 that, in continuing the straight line to the next curve, it is found to 

 vary 0.44 feet in 100 feet, or one fourth of a degree, and conse- 

 quently, if the line be long, it will full at the other end much to one 

 side of the graded road. Now let the curve just run be one of 4°, 

 tiien the chord of 4° being 100 feet, (the length of a station,) the 



