I08 JOURNAL OF THE 



We shall assume with Mr. Howard, no matter what the 

 leng-th of chord c is, that, 



a (in minutes) := 6 N" (7). 



This assumption is warranted by the previous equation, 

 as a varies as N^; hence equating these two values of a^ 

 we deduce, 



^ -0017453 

 a = = .... (8). 



1800 c- c- 



On substituting- this value of a in (6), we have, 



36000 - 20 .V 20 N<; 20 N 



D° = . . 5 = = = (9). 



- 1800 c^ r c^ c 



This is a fundamental equation of the transition curve 

 and gives the degree of curvature at any point of the 

 curve. Where it "connects'' with the circular curve, of 

 course D° must be the same for both curves. 



s 



By multiplying both sides of eq. (9) by we have, 



200 



D° s D° N^ 20 N N^ N 



200 200 c 200 10 



6 N' N^ 



But a in degrees from (7) =rr := — ; hence, a (in de- 



60 10 



grees) is given by the formula, 



a (in degrees) = = .... (10). 



200 200 



In figure i at O, the center of the circular curve DLM, 

 having at L the same tangent and degree of curvature as 

 the transition curve or spiral SEL, drop a perpendicular 

 OC upon the tangent SY, cutting the spiral at E and the 

 circular curve produced at D, and draw the chords SL and 



