2$ S - On the Re ft fiance experienced by 



II. Two-wheeled Carriages. 

 Seel ion 20. 



The refinance found in the preceding divifion, fe&ion 12, 

 for carnages of this kind, acquires here an increafe, which, 

 if we make the angle GOG 7 - 2a, will be found in the lame 

 manner as in the preceding fe&ion (P +7r) cos. a tang. a. 

 The whole refinance for two-wheeled carriages on roads of 

 the fecond clafs will therefore be expreifed as follows : 

 R'^- /*xPcos.« + (P+ £ P + v ) fin.al 

 -i- (P -f- u) cos. a tang, w j 



III. Comparifon of the two Kinds of 'Carriages \ 

 Seclion 21. 



If the comparifon be made in general according to the five 

 different points of view mentioned in the 1 6th fe<5ion, it will 

 be found that four-wheeled carriages are preferable to two- 

 wheeled when any of the five following conditions take place: 



iK + n — 2p (fP + tf— /— />' tan. a+ (P-f tt) tan c/j" 

 lit, j < ^ — 



-(5P+0) tang.p-(iP+/> ; ) tang. ^ 

 AP 



a d^+^~^< £ P^ ( "^- 2/X)|AP+(P ^ )tang - 

 7 c c ^ tang, a 



-(£P+^) tang. <g-(i P + p') tang. * 



tang, a 



, p (^-f-^ 7 —tf) tang. a-f/> tang. <p - f /> y tang-.<I/- - 7Ttang.a; 



3 ' £ tang, a-j- tang, w — \ tang. <f> — - ^ — | A(;« + « — 2/x) 



(^ + »~2^)^xP4-(/!»+^ 7 --7r)tang. ft-K* P+/>) 

 P tang, a 

 tang. <p -f ( ^ P+/> 7 ) tang. <|/-(P+ tt) tang, q; 

 P tang, a 



5th , Tang, a > (»+»-^U* P+ (*»»+/> *■*•? 

 + (jP+/ y ) tang.j / - (P + *f) tang, cq - 



Example I. 

 Seclion 22. 

 Let the road be compofed of round pieces of timber fix 

 inches in diameter laid acrofs it, and let a - o. Let the 

 mean diameter of the fore and hind axle-trees of the four- 

 wheeled carriages be 3! inches; that of the axles of the two.- 

 wheeled carriages 3J3 and the diameter of the wheels in the 



9 fam* 



4th, 



i 



