3#8 On the Uefifiante experienced hy 



Seclion 45. 

 Tn the cafe alfo of (ingle excavations and elevations, fuch 

 as thole confidered feci ion 3$ and feclion 38, we (hall have, 

 as already mentioned, R < K ; when fuch occur on any road 

 whatever. When thefejobtiacles are numerous, but not fo 

 near each other that the fore- and hind -wheels both experi- 

 ence a refinance at the fame time, four-wheeled carnages' 

 are for the mod part to be preferred to two- wheeled, without 

 taking into consideration the nature of the road in other 

 refpects. 



Sixth Division. 



More accurate Determination of -the Rcfijlance in tegard to- the* 

 Diretlion of the Pole or Shafts, 



Seclion, 46* 

 Tn the preceding refearches it has been fuppofed that the 

 direction of the pole of the carriage is parallel to that of the 

 road. In general, however, it deviates more or lefs from 

 this direction according as the breift leather or the collar of 

 the team horfe is higher or lower than the axles of the wheels. 

 This deviation depends alfo, befides the length of the pole, 

 on the kind of harnefs, on the'height of the cattle and the 

 method of yoking them, and on the fize of the wheels; and 

 when this is taken into confidcration the refiftance H and W 

 will certainly be fomewhat different from that found in the 

 preceding divifions. But though the difference is very fmall, 

 to render the examination of this queftion as complete as the 

 nature of the fubject will admit, I (hall take into conlidera- 

 tion in this.divifion the direction of the pole, and again de- 

 termine the values of R and R ; for each of the fuppofed three, 

 clafles of roads. 



I. Roads ef the frfi Clafs. 



Seclion 47. 

 Let the pole OT, fig. io. make with the direction of the 

 road AB or OM an angle MO I — K, the moving power Ol' 



= V = M f i — p- ) 2 is in this cafe not entirely employed,. 



but only the part OM — V cos. %:\ while the other part, ON 

 = V, (in. «, lefiens the prcfiurc on the fore axle, which is 

 only - P cos. a, — V, fin. «. Therefore the refinance from 

 frittion on the axle — ' wAP cos. a, — ntHV l 9 fki.^x ; and 

 the. whole: refinance, acting in the direction OP againit the 

 power OIVI == V cos. k is, ^ 



;:(» + «)>P cos. a 4- (P 4- p + P') fin. * Z 

 I — m\ V (in.x = V cos. * S 



If 



