two and four-wheeled Carriages, 1 19 



in the direction FA is for the former = {. w x P cos. a, and 

 for the latter =|tzaP cos. a.Hence the whole firft part of 

 the refinance arifing from the friction of the axle-tree will be 

 = I (m •+• n) xP cos. a. 



Seclion 8. 



The fecond part of the refiftance arifes from the power of 

 gravity acting in the direction OCt. If the weight of the 

 two fore-wheels be />, and that of the hind-wheels />', the 

 power in the direction OQ. is for the fore-wheels {- P 4- p 9 

 and for the hind-wheels Jf»P -h ft \ but, in the direction OP, 

 directly oppofite to the power OV, it is for the former (J P 

 4- p) fin. a, and for the latter ^ P + ft) fin. a. Confe- 

 <juently, the fecond part of the refiftanee = (P + p + ft) 

 fin. a. 



Seclion 9. 



The power OV — M ( 1 c)> therefore, on roads of 



this clafs, and in regard to four-wheeled carriages, has to 

 overcome a refiftance which is compounded of Doth thefe 

 parts, fection 7 and fection 8 ; 



R *a 4 (m + n) xP cos. a + (P + p + ft) fin. a. 



II. Two wheeled Carriages, 

 Seclion 10. 

 In regard to thefe carriages OE (fig. 3.) = M«OF, and if 

 the weight of the two wheels be =7, it will be found in the 

 fame manner as before, fection 7. and fection 8. that the re- 

 fiftance from the friction of the axle-tree is = fx x P cos. a, and 

 that from the power of gravity zz (P + ^r) fin. a. 



Sc&ion 11. 



But in this cafe, a third part is to be taken into confidera- 

 tion. When we aflume the centre of gravity of the load P 

 in the point S of the line FO continued, and draw through S 

 the vertical line SH, as a weight P preftes on the fupporting 

 lever IH in the point H, the horfe at I muft employ a power 

 IK, which fhall counteract that power SH = P. This power 



IK = ^^. Now if OH = OS tang, a = *.OI, the 



power, according to the direction IK, will be = tP; and 

 hence there arifes in the direction JL a power eP fin. a. 



Seclion 12. 



Conjequently, the power OV = M (1 — -Ip V on roads 



