On Wheel Carriages, 363 



proofs of that unity of dejign which pervades the great 

 Temple of Nature. 



" Some men feem deftined to obferve and record naked 

 fa£ts; others, of a fuperinr genius, follow after and apply 

 them. Some future Franklin may do with thefe dejiderated 

 facls what Newton did with thofe collected by Kepler and 

 Galileo, and therewith form a fyftem which may teach us to 

 bridle the winds themfelves, and render them further fubfer- 

 vient to human ivies." 



LXI. An Attempt towards a Theory of the Refinance experi- 

 enced by two and four-wheeled Carriages on different Kinds: 

 of Roads ; and to determine the Circumflances under which 

 the one are preferable to the other. By Nicholas Fuss, 

 Profejfbr of the higher Mathematics at Peter/burgh, Mem- 

 ber of the Imperial Academy of Sciences, &c. 

 [Concluded from p. 266 ] 



Fourth Division. 



On the Refjlance experienced from frngle Obflacles. 



* Seclion ^. 



jljLMONG thefe obftacles I include, as already mentioned, 

 fe&ion 2, fingle excavations and elevations which here and 

 there occur on roads, fuch as ridges, (lones, channels, cavi- 

 ties, broken pavement, and bridges, 8cc. When fuch impe- 

 diments frequently occur, an examination of the increafe of 

 refinance which thence arifes cannot be a matter of indiffer- 

 ence to the object of the queftion, and therefore I fhall treat 

 of them in particular in the prefent divifion. 



I. Roads worn into Sinuofities, 

 Seclion 34. 

 Let AB, PI. TT. fig. 7. be a road of this kind where the 

 finuofities are pretty regular. Required the refiftance which 

 arifes to four as well as two- wheeled carriages at a given point 

 F of the road, the tangent to which, FM, forms with the di- 

 rection of the road AB an angle — 7. In this cafe, when 

 the road is folid, and otherwife tree from inequalities, the re- 

 fiftance for the fore- wheels will be found by the fame method 

 as that employed fecYion 7 and feclion 8 to be : 



l-m xPcos. a (a + 7) + ( f P+/>) fin. (a +7) 

 And for the hind-wheels, when the angle which the tangent 

 FM' forms in F with the direction of the road is exprefled 

 by £, the refiftance in this point will be: 



4^ a P cos. (« + *) + Q-P+^fin. (« + 3). 



For 



