Il8 On the Refijlance experienced hy 



fufpended weight of M (i — ~\ % pounds. This well known 



formula, however, is only empirical ; but it agrees fo far with 

 experience as to anfwer all the purpofes of practice. 



Secl'ioji 6. 



Now if the refinance which, in regard to four-wheeled 

 carriages we fhall exprefs by R, and for two-wheeled car- 

 riages by R', has been found for both thefe kinds, we fhall 

 have, 



M (i — -£-)* = R; and M (i — -^)* = R'; 



from which we deduce the velocity with which each of thefe 

 kinds of carriages is moved, namely, 



For the four-wheeled g = G (i — V -^r) ; 



For the two-wheeled g' = G (i — «/ -tt-)* 



Having thus eftablifhed the means for eftimating the 

 moving power, I (hall now proceed to determine the refin- 

 ance itfelf in regard to the different kinds of carriages. 



I. DIVISION. 



Of the Refijlance en folid and fmooth Roads. 



1, Four- wheeled Carriages. 



Section 7. 



If the road AB (fig. 2.)> the inclination of which is the 

 angle ABC = a, be perfectly folid and fmooth, the refinance 

 to be overcome by the moving power OV will confift of two 

 parts. The firft arifes from the fricYion of the wheels againft 

 the axle-tree. If the whole burthen retting on the fore and 

 hind axle-trees be zz P, that fupported by each will be ~ P ; 

 confequently, when the vertical lines OQ and OF, proceeq 1 - 

 in«; from O the centre of the axis, the former of which in- 

 tene&s the circumference of the axis in D, and the latter 

 in E, are drawn in the perpendicular direction BA, the pref- 

 fure on the nave of the wheel in D is = ,- P, and in E — 

 \ P cos. a; confequently, the friction, which a6ts in the di- 

 rection EA ss i *P cos. «, where, as is well known, a repre- 

 fents a fraction, the quantity of which depends on the matter 

 of the axle-tree and the nave, and on the fubftance with which 

 they are befmeared. Now for the fore- wheels let OE ts 

 w.OF, and for the hind- wheels OE = //.OF. The refinance 



in 



