2Z6

Mechanics.

able to make the Wheel rest on the Top of the Obsta-cle at E, without suffering any Part of its Weight torest on the horizontal Plane at G.

4. Now this Force must be increased if it acts inany other Direction but that of CM; for let it drawthe Wheel in the Direction Cot, between M and E,then the Force may be resolved into two others C r, andr ot, of which C r draws the Wheel directly againstthe Top of the Obstacle E, and so is destroyed by equalRe-action of the Point E ; what therefore remains todraw it upwards in a Direction parallel to O K, is m r,which is less than Cm orCM; and to be made equalthereto, (as it must be to support the Wheel on theTop of the Obstacle E) it must be increased in the Ra-tio of Cot to tot, which let be as R to S (or as Ra-dius to the Sine of the Angle which the Direction of theForce makes with C E). But it is plain, the Force r mcannot be increased, but the whole Force C M must beincreased in the same Proportion ; that is, when r tn be-comes— X f m, CM will become — X C M — X

W X y/iRH-H 1 _ W X v /7 RH-H*

K " b

5. In order that the Wheels may be drawn over theObstacle F E, it is necessary the Direction of the Forceshould lie between C E and CA; for if it were in theDirection C E, it could only draw the Wheel upon oragainst, but not over the Obstacle; and if it acted inthe Direction C A, it would not make it press againstthe Obstacle, and consequently, could never draw itover.

W X v/aRH —H 1S

— the Force sof-

6. LetF =

ficient to sustain the Wheel on the Top E of the Ob-stacle, it is evident if W, R, H, continue the same, F —

the Force will always be less as the Sine of

the Angle E C ot is greater, till r m — C M, when {hesaid Force will be least of all.