two and four -wheeled Carriages, 369. 



If we therefore put for this clafs of roads V~ M f 1 — j? r 



— R, the required refinance for four-wheeled carriages will be, 

 p _ 1 (« + ") * P cos - a 4- (P •/>-*- />') fin, a. 

 cor. x 4 m A tin. k 



If we make for two- wheeled carriages the angle MOI = 

 *' and V = M (1 &-)* = R', we (hall find in the 



fame manner, 



u, XP cos. a + (P + sP + tf) fin. « 



_l^ * — • 1 t in 1 .. 



cos. k 1 "X- a A fin. >c ; 



OH 



Where it is however to be remarked, that though t — -*st- 



we have here OH = OS tang, {a 4- «')• If * = o, and *' 

 *= o, then will R = R (fection 9), and R' = R' (fe&ion 12). 



Example. 

 Seel ion 48. 

 Let every thing be as in the example fection 18, and, be- 

 fides, let IW = 42 inches. For R let 01 = io Feet, and for 

 R let 01 = 12 feet, fo that * =13° 30' and V ■= 7 1 1' ; 

 confequently OH = 2 tang. 13 ii / z= 0*46848, and e = 

 C03904. Hence we (hall have R — 1 99*557 and R' == 

 189-943. In fection 18 we had R — R' — 9*510, and here 

 R — R' as 9'6i4. Therefore the difference is nearly equal. 



II. Roads of the fecond Clafs, 

 Section 49. 

 On roads of this kind in the fore-wheels of four-wheeled 

 carriages the momentum of the part K of the moving power, 

 " which is employed in order to raife it above the obflacle G, 

 isK.GU == OR.GR; that is, K.GO cos. (p — ») = (|P + />) 

 cos. a. GO fin. p. Hence the power K a6ling in the direc- 

 tion OH = (J P 4- p) cos. a fin. <p, fee. (<p — h) ; confe- 

 quently that in the direction OP = OH cos. a == ( , P 4 p) 

 cos. a, cos. k, fin. 0, fee. (<p — *)• The fum of all the powers 

 acting in the direction of OP therefore is, 



{; (?n +n)xP cos. a + (P 4- p 4 p') fin. a ^ 



— m\\ T fin. x. -4 (jP+/>) cos. a, cos. «, fin. <p S^cos.x 

 fee. (p — *) + ({ P 4- />') cos. a tang. 4. J 



Hence we obtain V = M (1 ~). 2 ; or, 



f n (7 P 4 p) cos. a cos. >t fin. <p, fee. (<p — x) 



\K + 1 ■? 



ft _ J cos. k + w A tin. x 



V + (f P + / ; ) cos « tang, ft 



V COS. /i 4 * ^ f ln * 



Vol. XIII. No. ,52, A a And 



