two and four-wheeled Carriages. $6$ 



IV. Comparifon between the two Kinds of Carriages, 

 Section 29. 



On roads of this clafs, four-wheeled carriages are to be 

 preferred to two-wheeled^ when one of the five following 

 conditions takes place t 



m+n—2 [j, ^ (gP-f-Tr-^— p 1 ) t.a + fin./3 [(P + ir)t.^' 

 lit, - <; — — 1 { 



j . rt (w + »-2a)^P + fin./3[(P+ir)t.&-| 



gd, 6+a — a-<gp— 1 ■ •' ■ -— - / 



tang. & I 



-(jP + rt tang^-dP + zOtang.^] f 

 tang, a J 



. p> ( P + P'-*) t.* + fin./3 fct-g+l't. q-gt .&) 



3 ' £t.a-Min./3[t.^— it.J-lt.^]-f A^ + ^-2^) 

 4th £ > Qk+k-2/x) ^xP + (; + /-tf) tang, g+fin.ff <| 



4 * P tang, a " J- 

 1(1 P+p) tang.g+ qP+/ Q tang. 7; -(P + ir) tang. S] J 



P tang, a 



5thj Tang . a > («. + «-^)^p +fin . ) sc( i P ±gL t. 



+ (1- P + />') tang, q - (P + it) tang . 



£ P + 7T— />— p 7 



That thefe five conditions are general, and contain the con- 

 ditions found for the two claffes before treated, feclion 16 and 

 fe&ion 17, it is fuperfluous to mention, after what has been 

 faid in the firft two remarks of the preceding feelion. 



Application to fome determinate Cafes. 



Example I* 



Section 30. 



I poured very dry coarfe red fand, PI. II. fig. 6. after 

 I had found the angle zr 3O 42' (that is to fay, AB = 16 

 inches and CD = 4 J inches), into a veffel, and, fmoothing 

 the furface of it after each experiment by making it fo as to 

 obtain the fame degree of foftnefs, I took a fteel rod weighing 

 5 lib., which I had caufed to be conftru&ed for magnetic 

 experiments, and which was juft an inch fquare, and puflied 

 it feveral times into the fand in a gentle manner, to prevent 

 the acquired velocity from making it fink deeper than the 

 equilibrium fought for. Sixteen experiments of this kind, in 

 which the greateft difference did not amount to half a line, 



S g gave 



3 



