«6o On the Rejijlance experienced ly 



/ux P cos. a = 29*109 



(P + e P + it) fin. a = 483-634 

 (P + 5r) cos. a tang, w = 1 24*282 



R' = 636-025 

 Three horfes, therefore, whofe ftrength is M ~ 1200 lib. 

 and their velocity on this kind of road G — 10 feet, could 

 draw the burden P = 1800 lib. on a four-wheeled carriage 

 at the rate of ,§" — 2*47 feet per fecond, and on a two-wheeled 

 carriage about g'zz 2*7 2 feet. 



SeBion 24. 



On a horizontal road of the above nature we (hall have 

 for the fame carriages and load R rr 206*08 and R' _- 158*09. 

 For a horfe therefore whofe itrength M — 400 lib., and velo- 

 city on this horizontal road G •= 15 feet, we (hall have g z= 

 4-23 and/ = 5*58 feet. 



Third Division. 



Of the Rejijiance on foft and even Roads, 

 SeBion 25. 



Tf the furface of the road be compofed of foft fand, (late, 

 earth, clay, dirt, &c. the wheels will fink into it, and the 

 depth to which they fink will be greater the fofter and more 

 fluid the matter is of which the road confifts. 



Now as the increafe of refiftance depends on the depth to 

 ■which the wheels fink, and as this depth depends on the 

 nature of the matter, that is to fay, its hydroftatic power, 

 which can be determined only by experiment, I fhall afTume 

 that a prifmatic body the thicknefs of which is dd fquare 

 inches and its weight 9 lib. finks merely by its gravity c 

 inches deep in the fluid matter, or difplaces ddc cubic inches 

 of it before it comes into equilibrium : this matter, then, in 

 regard to hydroftatic power produces the fame effect as would 

 be produced by an aqueous fluid a cubic foot of which weighs 



A load Q^, PI. II. fig. 5. will prefs down both wheels 



on the axis O till they have difplaced — - ~ cubic inches of 



the fluid matter. If FR be the depth to which the wheels 

 iink, and n' the circumference of a circle whofe diameter 

 = 1, the fuperficial content of the funken fegment GFG'R 



= GO 1 ( * - ''^? R — i "n. GOG')., And if the fellies 



be 



