182

FRICTION OF CARRIAGES

not the same at all velocities, then the frictionis not an uniform retarding force, but increasesin the ratio of the velocity ; for instance, whenthe body is moved forward at twice the velo-city, if the pressure indicated by the dynamo-meter be twice as great as when moving athalf the velocity, then the aggregate amountof force required to move the body over agiven space with twice the velocity, will betwice that required to move the body over thesame space, with half that velocity; and, con-sequently, by traversing that space in half thetime, the moving power will also travel attwice the velocity ; and, therefore, the mecha-nical power required will be four times theamount, acting half the time ; and the under-mentioned diagram will shew the mechanicalforce required at different velocities:—

U-

VelocitiesSpares

Times - - -

Resistance

Mechanical force required,acting for the above timeMechanical force required,for any given distance

Again, if the resistance increases in the ratioof the square of the velocity, then the amount of

12 3 4111 !111112 3 4

1 4 9 16

12 3 4