1002

THEORY AND PRACTICE OF ENGINEERING.

Book II.

and one axis passes through the side plate, to which is attached the winch or handle ; this,turning round, elevates the rack, and with it the claw which is applied to the load to beraised: that the weight should not have the power of running the pinion back, thehandle is secured by a hook fastened to the outside of the block.

There are several modifications of the jack; one of the most powerful is that in whichthe winch does not immediately act upon the rack, but first on a small pinion, thena large toothed-wheel, which carries a pinion that elevates the load: supposing R to bethe length of the winch, It' the radius of the wheel, r that of the first pinion, and r' that ofthe second, then

P : W' : : r : RW' : W : : r' : R'

PTW7: rr' : RR':

whence P =

R. R

. W

W

c

3 ;

TET

□

Fig. 1507.

Let r = / = l inch, R = 10 inches, and R' = 5 inches; then P = --, or 1 lb. power would be

50

a counterpoise to 50 pounds; and by exerting a force equal to an. hundred weight, or112 x 50 = 5600 lbs. might be raised.

A small power maythus elevate a con-siderable weight, butin so doing, the to-tal expenditure, inraising the weightthrough any height, isnever less than thatwhich Would be ex-pended if the powerwere immediately ap-plied to the weight,without the interven-tion of any machine:this arises from theuniversal property ofmachines, by which thevelocity of the weightis always less that that of the power, in exactly the same proportion as it is lessthan the weight, so that when a certain power is applied to raise a weight, the rate at whichit mounts is always slow, and in the same proportion as the weight is great; no machine,therefore, can be said to have the property of totally diminishing the expenditure of powernecessary to raise the weight or to overcome its resistance; all that a machine can effect isto enable the power to be expended at a slow rate, and more oeneficially in its duration,than if applied at once to the weight or its resistance; this common property refers to allthe mechanical powers, as the lever, the pulley, the inclined plane, screw, &c. &c.

The Screw is applied both to raise weights and press bodiesinto a more compact state; and sometimes to set in motionthe sun and planet wheels ; the worm of the screw workinginto the teeth of that wheel which drives the gear, and byits revolution compelling the wheel to move on its axis; itis also preferred to the jack wherever a delicate movement isrequired.

The working of the screw may be understood from theobservations made upon the inclined plane, and by con-sidering that the weights rest on the inclined face of thethread, whilst the power acts on the surface of the cylinderparallel to the base of the screw : equilibrium is obtainedwhen the power, is to-the resistance, as the distance betweenthe two threads of the screw, is to the circumference de-scribed by the point to which the power is applied.

P : W : h : 2rw,

and P=-^_ W:

2 wr

W being the weight or resistance to be overcome, h theheight or distance between the threads, and r the radiusof the screw. The space described by the power, is to

Fig. 1508.