PROCEEDINGS OF SECTION H. 



56^ 



To set out a circular curve with a givtn length of Lemniscate 

 transition curve at each end between two pieces of straight. 



Let 01 aud O'l (Fig. 2) be the two pieces of straight iutersecting 

 at /, the included angle being i. CO is the circular curve of radius 

 R.' OCand O'C the lemniscate curves at each end. 



At the outset we must fix the lengths of the chords OC and O'C. 

 If we have already fixed upon a suitable value for a, as indicated 

 in the preceding paragraph, OC is deternained by the equation 



OCzz -—-. Otherwise we may fix the length of OC arbitrarily and 

 then compute the proper value of a^ from the same equation. 



Denoting the angle IOC by a, this is determined bv the equation 



■ o OC 

 sin 2a z=. — . 



6R 



get 



By projecting at right angles to the bisector of the angle 010' we 

 01 sin ~ = Ecos (^ + 3a) + OC sin fj + « V 



Since i, a, OC and R are known this equation determines the 

 length 01 and consequently fixes the point 0. 



