On Wheel Carriages. 257 



For good figures of the C. cancellous, Micheli may be re- 

 ferred to, and for the two latter, Curtis' s Fl. Lond. and Sower- 

 by's Englifli Fungi, called in both publications Phallus. 



I am not aware that any other Fungus will arrange with 

 the above three fpecies, although fome have been placed un- 

 der the genus Phallus, by Linnaeus and other botanifts, 

 which have very little agreement with the P. impudicus and 

 P. caninus of thole authors. 



XLIII. An Attempt towards a Theory of the Rejiflance experi- 

 enced by two ami four -wheeled Carriages on different Kinds 

 of Roads ; and to determine the Circumjlances under which 

 the one are prefer able to the other. By Nicholas Fuss, 

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

 ber of the Imperial Academy of 'Sciences , &$> 

 [Continued f;on p. 122.] 



Second Division. 



Of the Rejiflance en folid and uneven Roads, 



I, Four-wheeled Carriage*. 



— Section 19. 



XF the road AB, Plate II. fig- 4. be naturally rough and 

 (tony, or paved artificially, or covered in fome places with 

 trees laid acrofs it, new impediments arife from thefe ine- 

 qualities, and the refi fiance found in the preceding divifion, 

 fection 9, which takes place here alfo, acquires an increafe, 

 which is determined in the following manner : 



Let the wheel touch in G and G / two equally large and 

 folid inequalities of the road, and for the fore-wheels let the 

 angle GOG' = o,$ 3 but for the hind-wheels GOG— 2^. 

 Now as a part of the moving power OV, which we mall call 

 OLT K, 11111ft be employed to overcome a part of the power 

 of gravity acting in a direction perpendicular to AB, which 

 is (* P + p) cos. a, and to raife the fore-axle together with 

 its part of the load over the fixed point G, the momentum 

 of thefe powers OU.GU and OR.GR muft be equal to each 

 other; that is, K.GO cos. <p *= (^P+/>) cos. a. GO fin. <p\ 

 fo that the increafe of refiftanee arifing from this impediment 

 will be for the fore-wheels K (-^P -+•/>) cos. a tang. <p. A 

 (imilar increafe will be found for the hind-wheels ({-P+/ )/ ) 

 cos. a tang. -vj/. Confequentlv the whole refinance on roads 

 of the fecond clafs for four-wheeled carnages is : 

 R I (m + n)AP cos. a+ (P-4- p -f- p') fin. a 7 



+ (s-P+jp) cos. a tang, (p + (r P+/0 cos. a tang. ^ > 



II. Two- 



