140 Railway Curves. 



further proceedings, which were merely to set out the two arcs of an 

 S curve of common radius. 



By Formulas I. and II, page 132. 



• . 5, sin. a + sin. 8, x , d , s 



viz. : — sin. 8 = £Yi.) and r= ~ «. ^ (n.) 



2 v ' cos. a + 2 cos. 8 + cos. 8 ^ 1 



N.B. — Cosine a is positive, a being in the fourth quadrant to the 

 right out of DB, but cosine 8 is negative, 8 being, similarly con- 

 sidered, in the third quadrant. 



Calculation. 



For the Radius. 

 Nat. sin. 92° 57 = -9986748 — cos. = -0514645 



„ „ 68° 50 = -9325340 — 



cos. = -3610821 



2) 1-9312088 J" 

 Nat. sin. 8 = -9656044 * 



cos. = -2600130 

 cos. = -2600130 



:• *= 74° 56' 



•8811081 

 •0514645 



by 24-32 = 1-3859636 

 by -8296436 = 1-9188917 



sum == -8296436 





log r = 1-4670719 



For the Chords. 



\-r = 29-314 chains. 



DA = 2 r cos. a J^ AB = 2 r cos. 3 + 8 



2 2 



log r = 1-4670719 1-4670719 



log 2 = 0-3010300 0-3010300 



by cos. 71° 53 = 94926946 by cos. P +6 58° 56|' = 9-0234222 



log DA = 1-2607965 log BA = 0-7915241 



••• DA = 18-23 chains. -.- BA = 6-1876 chains. 



Angle protracted from tangent-radius, 71° 53, and 58° 5 6 J, 

 or their complements, severally deflected from tangents. 



The chords being protracted, duly intersected on the arc of contact 

 the same point, and measured the calculated lengths. 



