562 On the Refijlance experienced by 



fame manner as in the preceding; fc&ion, that the increafc of 

 refinance on roads of this clats is = (P 4- n) cos. a fin. £ 

 tang. §i and the whole refiftance for two-wheeled carriages 

 will be, 



R'= ^uxPcos. a + (P + eP + w) fin. a? 

 + (P + w) cos. a, fin. tt, tang. 9. 3 



III. Obfervations on thefe Formula: R and R\ 

 Seclion 28. 



Thefe exprefiions for R and R' as above found contain, as 

 we fhall foon fee, a complete folution of the problem, as 

 they anfwer for all the three clafles of roads. 



lit, For folid and even roads where | = o, n = o, 9 = o, 

 and j3 = 90 , they give for R and R' the fame values as thofe 

 found for refiftance in the firft divifion. 



ad, For folid and uneven roads where £ = 0, w =r 4., 9 

 = w, and jS = 90 , we have the fame values for R and R / as 

 thofe found in the fecond divifion. 



3d, For roads with ftanding water on a folid bottom 

 (which, however, muft not reach to the fpokes, becaufe in 

 this cafe the refiftance muft be determined in another man- 

 ner), where /3 — o, we fhall have R and R' as in the firft di- 

 vifion. In this cafe, no perceptible increafe of refiftance 

 arifes: on the other hand, on fuch roads G and consequently 

 V is lefs than on roads of the firft clafs. 



4th, When one of the angles |, n 9 or 9, is a right angle ; that 

 is, when P is fo great that the wheels fink up to the axle in 

 the foft furface, the refiftance becomes infinitely great, except 

 in that cafe only where the fluid is very thin, and = o; in 

 which cafe inftead of an infinitely great refiftance we fhall 

 have only an indefinite increafe — 0.00 , which cannot be 

 determined from the grounds mentioned in the third observa- 

 tion. 



In the laft place, it is to be obferved in regard to thefe ex- 

 preflions, 



5th, That when the foft tender furface has a folid bottom, 

 and is not fo deep that the wheels can penetrate into it ac- 

 cording to the laws of hydroftatics, the angle GOR muft not 

 be determined according to the abfolute finking, but according 

 to the depth of the folid bottom. 



6th, That for lefs fluid matters, fuch as moid fand, moid 

 earth, ftitTclay, dirt, &c. in the expreflion for the refiftance 

 of four-wheeled carriages, R the laft member for the hind- 

 wheels (a-P + />) cos. a, fin. /3, tang, y, vanifties, becaufe 

 thefe wheels run in the ruts formed by the fore-wheels. 



IV. Com- 



