ELISHA MITCHELL SCIENTIFIC SOCIETY. II 3 



Stations of a transition curve. For greater values of N, 

 (19) should not be used at all and the angles a must all be 

 computed by the strict method. 



The angle made by any chord connecting anv two sta- 

 tions of the curve with the Y axis, will be desig-nated bv / 

 with two subscripts, giving the station numbers through 

 which the chord is drawn; thus 2\,^ indicates the angle 

 made by the chord joining stas. 3 and 9 with the Y axis. 

 Its value is readily found from the equation, 



x^— X3 40.7803 



tan 2._^ = = , 



Yg— Y3 598.208 



to be, 2\_^ = 3°54'oo''. Similarly we find the inclinations 

 of the chords, to the Y axis, connecting a?iy two stations. 



In the general table given at the end of this paper the 

 values of X, Y, a, a and / are inserted corresponding to 

 the stations given at the tops of the vertical columns. 



[Note. — The general table does not give the quantities 

 X, Y, and Q as closely as the preceding table, and the 

 values of a and ?' in it are only expressed to the nearest 

 minute.] 



The angles given below the horizontal row a, are the 

 values of i for the chords joining the stations in the verti- 

 cal columns to which they refer. Thus line (2) column (4) 

 angle 0^56' = /^^ or the inclination of chord (2) (4) to 

 SK. 



The angle a^ = 2^30' is that which the transition curve 

 at sta. (5) makes with SK. Also the angle between chord 

 (5) (8) and tangent at sta. (5) = 4°i8' — 2^30' = 1^48' 

 and the angle between chords (5) (8) and (2) (5) = 4° 18' 

 — i°i8' = 3°oo'. 



Similarly we can find any angle needed in running the 

 curve. 



The quantity Z of the table = D°j- = 20 N-, whence 



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