126 C. J. MERFIELD. 



asking for solutions of certain problems in connection with 

 tramway location. These problems were not difficult, but 

 sufficiently so, perhaps, to cause annoyance to the practical 

 engineer not accustomed to questions of this nature. 



As the replies to these questions may be useful to others 

 desiring similar information, it was thought advisable to 

 combine them in a short paper for future use. Similar 

 notation will be used here as in previous papers. 1 



Solution of Problems. 

 In tramway location, as practised in New South Wales, 

 it would seem for some reason, not necessary here to 

 explain, that the values of * V and "JR" form the data in 

 the problem for setting out the cubic parabola to connect 

 the straight with the circular curve. With the value of 

 h/R we may find the several quantities usually required to 

 set out the parabola. 



Let us take the equation 



h/R = | sin 2 cf> cos <£ + cos 4> - 1 I 2 



by a simple reduction this may be put into the form 



,3 -i a j i s (a . h 



Cos 3 </> - | cos <£ + f [1 +-gj = 2 



From this equation the angled may be readily determined. 



Putting P = i(l +~\ cos 3 a - - [9-81774186] P 



then Cos <£ = [0*26143938] cos a. 



Example. 

 h ~ 0*025152, R = 2, h/R = 0*012576, p = 1*518864. 



Log const = - 9*81774186 



Log const = 0*26143938 



„.'j8 = 0*18151888 



„ cos a = 9*71327467 



„ cos Sa= - 9*99926074 



„ cos $ = 9*97471405 



3 a = 176 39 28*42 



</> = 19 21 45*2 



a = 58 53 9*47 





1 This Journal, Vols, xxix, xxxi, 



xxxiv. a Vol. xxxi, p. 59. 



