two and four-wheeled Carriages. 2,6 1 



be b inches broad, we (hall have for both wheels : 



i^pl&* _ ■ fin. GOG') = ^ 



V l8o° % J q 



Hence we find, 



*".GO R r rnrf &££,. 

 — ^5 fin. G0G=^ 02 ; 



from which equation the angle GOR neceflary for deter- 

 mining the refinance is found. 



I. Fair- wheeled Carriages. 



Seclion 26. 



As the wheels in this cafe have funk to the points G,G f 

 of their circumference, there arifes in the point G an impe- 

 diment to the motion, which will be greater or lefs according 

 as the furface of the road is covered with more or lefs fluid 

 matter; that is, according to the greater or lefs extent of the 

 angle which the fides of as fteep an accumulation as poflible 

 of this matter forms with the level furface. This angle, 

 which gives the moft convenient meafure of the fluidity, I 

 fhall in future call 0. 



Now if GFG' were an excavation in a perfectly folic! road, 

 G would oppofe the moving power OV in confequence of 

 the power of gravity OQ. = S with a power OR = S cos. a, 

 the momentum of which is OR.GR=S cos. a. GO fin. 

 GOR. If the part of the moving power employed for this 

 purpofe be K, its momentum KAjU = K.GO cos. GOR; 

 fo that K = S cos. a. tang. GOR. If the angle for the fore- 

 wheels be GOR = I, and for the hind-wheels GOR = n, 

 the refinance for the former ~ ( T P + p) cos. a. tang. |, and 

 for the latter — (\V + p') cos. a tangr?; consequently, 

 the increafe of refinance for the four-wheeled carriages = 

 cos. a [({ P -f- p) tang. £ + (A. P 4- p') tang. *]. With this 

 power G oppofes a refiftancc as a fixed point, but, as a fluid, 

 it yields and oppofes a lefs power the greater its fluidity, the 

 coefficient of which is fin. j3. The increafe. of refiftance on 

 roads of this kind is therefore = cos. a fin. [(^P4-/>) 

 tang, i + (4 P + />') tang, ri] ; confequently the whole refift- 

 ance for four-wheeled carriages : 



R = J (m + n) * P cos. a + (P + p +p') fin. a % 



+ cos. a fin. |8 [(£ P + p) tang. £ + (i P + p ) tang. ».] J 



II. Two-wheeled Carriages. 



Seclion 27. 



If we make the angle GOR ss h> it will be found in th^e 

 Vol. XIII. No. 51. S fame 



