two and four-wheeled Carriages, 259 



fame order, 26, 39, and 45 inches ; fo that m - !, n — V , 

 and //, = -,\ : alio, let P 1000 Iih., /> 74 lib., // 106 lib., 

 and 7T 130 lib.; and let the coefficient oF the .fri&ion be x 

 = ty In the laft place, as TG zz TF n 3 inches, we (hall 

 have for the wheels in the above order TO = 16, 11 and LL 



TF 

 inches, and becaufe fin. TOF = ^ ; the angle TOF, that U 



to fay, <p — io° 48'* \ = 7" 40'; « = 6° 45 . From thefe 



elements we obtain, 



4 (w + n) \ P = 23*148 



(;- P H- />) tang. <p = 109-496 



p (*P + />)tang.+ = 81-575 



R = 214-219 

 /i^P = 18-518 



(P + tt) tang.» = 133744 



R' = 152 262 

 For a horfe, then, whofe ftrength M — 400 lib. and velo- 

 city G = 13 feet on fuch a road, we have g = 3-484 feet, 

 and g' 4' 97 9 feet in a fecond. 



It might be conjectured that four-wheeled carriages, the 

 fore-wheels being fo fmall, would experience a refinance 

 confiderably greater than the two-wheeled. Were m fab 11 

 = — , and/) = p' = 106, we mould have R = 181*669, 

 and g 33 4*238. 



Example II. 

 Sedion 23. 

 Let the road be deep and compofed of ftones, the angle of 

 elevation being a ~ 14 , and let the pavement be of fuch a 

 nature, that the diftance between the points of contact G, 

 G'= 3 inches, confequently the angle <p — 5 45 ; xj, 4' 6', 

 and a zr 3° 49 . Let the burden be P — 1800 lib., the mean 

 diameter of the axle-trees of the foje-wheels — 3 inches, of 

 the hind- wheels 3^ inches, that of the two- wheeled car- 

 riages 3! inches* let the diameter of the wheels in the fame 

 order be 30, 42, and 45 inches • fo that m \ . n _ { , and 

 fju =z r \. The weight of the wheels we flia.ll fuppofe to be 

 p = 80 lib. p ' = 1 10 lib., and t 1 20 lib. In the laft place, 

 let A = 1, and t - ; T . Hence we obtain 



£ (m + n) * P cos. a = 33*96° 



(P + p + p ) fin a =-= 481*425 



(' P 4- p) cos. a tang. <p =r 95*750 

 ( ' P + p ) cos. a tang. -4> = __7°/247 

 R = 681*382 



ftxP 



