Railway Curves. 139 



The little tables of sines and cosecants might be written on a card 

 for the waistcoat pocket. 



Curving of Practice on Durdham Down. 



Example for Setting Out. 



Fig. Y. 



The tangents of an imaginary railway being marked ont, the dis- 

 tance BD measured 24*32 chains, a was found to be 68° 50', and 

 ft 92° 57', measured by the theodolite. An $ curve being required, 

 it was proposed to find, first, the arc of contact, or "locus" of the 

 various points of possible contact for the two arcs. 



Then r v arc of contact = _ cosec. fl f ; 



2 



or . 

 sm. 



4 d* 12-16 



—5- sin. 12° 3£' 

 92° 57' log. 12-16 = 1-0849336 



68° 50' log. sin. 12-3| = 9-3199538 



2)24° V log. r v = 1-7649798 



v = 58-218 r" 



12° 3A' 



It was next assumed that c = 1 chain 

 2 r" 116-436 



cosec. = 



The nearest cosecant to 116-436 on our card was the cosecant of 

 30', whose sine (as found on the card) is -0087265. 



We adopt 30' as 0, and, using the reverse equation, 

 say c = 2 r v sin. 30' = 116-436 x -0087265 =1-016 



The arc of contact was then set out by radiating the angle 30' 

 from the point D, deflected from the prolongation of tangent to the 

 extent of sub-chord T016 chain, and the first point was thus fixed ; 

 and then the same angular quantity 30' was subtended by the like 

 distance from this first point, and the ground being clear, the whole 

 arc was set out without removing the theodolite from D. 



The arc of contact was set out for practice merely, although it 

 served the purpose of verifying the formulae and as a check on our * 



* Having no table of log. cosecants, the value of r s in terms of 

 sine was preferred. 



