$66 On the Rejijlance experienced ly 



wheel be OG = a, fo that cos. GOR = 2—*--, Let this 



a 



angle GOR be for the fore-wheels = p, for the hind- wheels 

 Ka <r y and for the two- wheeled carriages 3£ t. The increafe 

 of refinance anting from this obftacle in the cafe of the fore- 

 wheels will be = (!-P+/) cos. a tang, p; in that ol the 

 hind-wheels - ({P-j-^) cos. a tang, v; and of the two- 

 wheeled carriages (P -f- n) cos. a tang. /x. But of the firft 

 two, as one only acts at a time, the whole refinance on each 

 kind of way where fuch ob ft a cleg occur will be much eafier 

 overcome by the four-wheeled than by the two-wheeled 

 carriages. 



Fifth Division. 



General Conjidcrations and Refults* 



Seel ion 39. 



I have already mown, in regard to all the three claries of 

 roads in general, the conditions under which the one kind of 

 carriage is to be preferred to the other. But as the multi- 

 tude of elements which occur in all thefe formulae render a 

 general view of them difficult, it may not be fnperfluous to 

 collect here a few of the principal refults as deduced from a 

 clofer comparifon of the general conditions. 



Seclion 40. 



On roads of the firft clafs, when the axles and wheels are 

 in the common ratio, the difference between R and R' can 

 never be very considerable. But as the wheels of the two- 

 wheeled carriages are generally made as high or higher than 

 the hind-wheels of the four-wheeled carriages, we (hall al- 

 ways have R > R' as long as P, e and a are not very great. 

 But if the road be exceedingly lleep, and the load very high 

 and heavy, we (hall have R< R'; consequently the four- 

 wheeled carriages will be preferable. 



Seclion 41. 



In the commencement of this effay, feci ion a. among roads 

 of this clafs, I included thofe with folid broad ruts, to which 

 every thing obferved, in general, in regard to folid and fmooth 

 roads is applicable. But if the folid ruts are narrow and deep, 

 a friction is produced on the fides of the fellies which increafes 

 the refinance ; but I cannot determine accurately this increafe, 

 as we are unacquainted with the laws according to which this 

 friction acts : all that we know of it, and it is furncicnt for 

 our purpofe, is, that the increafe of refiftance thence arifingis 

 for four-wheeled carriages nearly double that for two-wheeled 



carriages ; 



