12 PHYSICS. 
weight of the earth in lbs. will then be 1,961,701,537,649,784,000,000 - 
Dividing this by 30 = 65,390,051,253,772,800,000 inches=arc described by 
the long arm while the short arm is moved an inch. Reducing this to feet, 
and considering that, at ten hours per day, 3,650,000,000 feet would be tra- 
versed in a century, we shall have for the final result, 1,473,973,790 centuries 
as the time required to raise the earth one inch. 
The wheel and axle 1s a simple machine which consists of a cylinder (the 
axle) and a wheel, both having a common axis, at whose extremity are pins 
or gudgeons on which the whole can turn. The power operates generally 
at a tangent to the circumference of the wheel, the resistance being 
attached to a cord around the axle. Pi. 16, fig. 33, shows the ordinary 
construction of the machine, where the gudgeons of the axle are at FE, 
turning in the parts of the frame HF and AE; the weight, W, is raised by 
the cord, G, wrapped about the axle, and the power is applied to the wheel, 
ISB, either by the cord I, or the hand-pins 8, S, S. Sometimes, instead of 
the wheel, arms only, like spokes, are fastened to the axle, or else a winch is 
employed ; the effect, however, is the same. The axle may be vertical, or 
in any other position, without changing in the least the principle of its 
operation. The wheel and axle is sometimes called an endless or constant 
lever, as it is in fact a lever on whose arms power and resistance act always 
normally, although the lever rotates about its fulerum, and weights can 
therefore be raised to any height. In the simple lever, the space traversed 
by the power is always limited. A catch wheel is attached at D. 
The same conditions apply to the wheel and axle as to the common lever. 
The radius of the wheel is the power arm of the lever, the radius of the axle 
is the resistance arm, and equilibrium takes place when, in the normal 
action of the two forces, the power is to the resistance inversely as the radii 
(arms of the lever) on which they act. It is evident that an increase of 
power is brought about either by diminishing the radius of the axle, or by 
increasing that of the wheel, or the winch on which the power acts. This 
must, however, be within certain limits, as the axle may become too thin 
and break, and the wheel or winch may become inconveniently large for 
use. Another obstacle is found in the principle, that the greater the diffler- 
ence between the two arms of the lever, the greater will be the space 
traversed by the power in proportion to that traversed by the resistance. 
To obviate the first difficulty, the construction represented by pl. 16, fig. 35, 
has been employed. The credit of the invention has been ascribed to the 
renowned George Eckardt, although its date is more than a hundred years 
before his time. Here the part A of the axle is stronger than B, and the 
rope, I, I’, which passes round a pulley and supports the resistance, W, is 
wrapped about two parts of the axle in opposite directions. When the 
winch, P, is turned in such a manner that the rope winds up on the stronger 
cylinder, at each revolution a portion of rope is unwrapped from the smaller 
cylinder equal to the circumference of the greater. The part of the cord 
wrapped up, therefore, diminishes by the difference of the circumference of 
the two cylinders: here the resistance or weight is to the power as the arm 
of the winch to the half difference of the radii of the cylinder. 
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