two and four-wheeled Carriages. 1<%1 



4th, When in regard to the height of the load or of the 

 centre of gravity, 



(/> 4 /' — ir) tanjr. a + 4 * p (^ + « — 2 ,«') 



£ > _ . 



1 J tang a 



5th, When in regard to the fleepnefs of the road, 

 tariff, a i> — r r-« 



b gP + 7T - /> — /' 



IV. Application to fome determinate Cafes. 



A few examples in numbers will illuftrate the ufe of the 

 expreffions found both for R and IV, and alfo the companion 

 of them with the moving power. 



Example I. 



Seclion 17. 



Let us fuppofe that the road goes up a hill at an angle a 

 = io°. Let the mean diameter of the axles of the four- 

 wheeled carriages be 3 ' inches, that of the fore-wheels 28 

 inches, that of the hind- wheels 42 inches; fo that m = -I, 

 and n = -^ T . Let the weight of the fore- wheels be p = 

 80 lib., that of the hind-wheels ff == no lib. Alfo, let 

 the mean diameter of the axles of the two-wheeled carriages 

 be 4y inches, the diameter of the wheels 39 inches; fo that 

 fj. = -i, and the weight of the wheels tt = 110 lib. Let the 

 load of both carriages P = 2400 lib., and the coefficient of 

 the fri&ion * — i-. In the lail place, we fhall fuppofe the 

 height of the centre of gravity OS = 4 feet, and 01 =z 

 12 feet; fo that OH =. 07053, confequently £ = 0*0588. 

 Hence we have, 



4 (m + n) *P cos. a. = 49*240 

 (P + p + p') fm. a. =f 44975° 



R =r 498*990 



(A\V COS. a es ^V^2^ 

 (P + eP + tt) fin. a = 460*352 



R'= 512-875 



In this cafe, then, R < R', about 13*885 lib. 



In regard to the moving power it may be admitted tliat 

 a good draught horfe can draw, for three hours, in the man- 

 ner above defcribed, fe&ion 5, a burthen of 400 lib. ; and. 

 that the fame horfe, unloaded, can travel three hours on the 

 road fuppofed in this example with a velocity of 12 feet per 

 fecond : for two fuch horfes, then, we fhall fuppofe M == 



I 4 • 800 



