370 On Wheel Carriages, 



And in the fame manner we find for two- wheeled carriages^ 

 p, __ p, (P -f tt cos. a cos. x 7 fin. w, fee. (cu — x 7 ) 

 cos x 7 + f' A fin. x 



If therefore x — o and *' - o, we obtain for R and R' the 

 values found in the fecond divifion, fe£tion 19 andfe&ion 20, 



Example. 



SeSliofi 50. 



Let every thing he as in the cafe calculated fe&ion 23 ; 

 alfo let IW es 42 inches, for R let 01 — 9 feet, and for R' 

 let 01 = 12 feet : hence k — 14 29', and k' - *£ 47'. Now 

 as OH = 2 tang. 21 47 / = 0799268 feet, therefore t = 

 C06660. Hence we obtain, 



R _ ( ' m + n) A P cos, a + (P + p + pi) fm. cl _ 6$ 



cos. x •+• m A fin. x ~ O ? 



(y P+/>) cos. a cos. x fin. p, fee, (<p— x) _ 



cos. x + wAfina "** * 



( f P + /> 7 ) cos, a tang. ^ __ ^ 



cos. x + /n A fin. x ' ^" 



R= 697-243 

 ■ aXPcos.a + (P+sP-f it) fin. a <» . 



cos. jc'+jxX nn. x< " 



(P + ft) cos. ct cos. x ; fin. w, fee. (w — x) 



= 124*021 



cos. x 7 + ft A fin. yd 



R' s= 650281 

 In the example fe&ion 23 we had R — R 7 = 45'357, but 

 here R — R 7 = 46*962; confequently in this cafe the dif- 

 ferences are nearly equal. 



III. Roads of the third Clafs. 



After what has been faid, fection 49, it is needlefs to repeat 

 #ep by ftep the procefs for roads of this clafs. It may be 

 cafily feen that here, 



(^ P + p) cos. a fin. (3 cos. x fin. £ 



in, _ cos. x + mA fin. x 



R + 



fee. (£ — x') -f- (I P + p 1 ) cos. a fin. /3 tang, yi 



cos. x -f- m A fin. x 

 (P-f r) cos. a fin. |8 cos. x' fin. S, fee. (3-— x 7 ) 



R' = R'-i- 



cos. x 7 + p A hn. x' 



So that when x = o, and *! — c, we obtain for R and R y the 

 fame values as thofe found fe&ion 26 and fe&ion 27. 



Example, 



