10 PHYSICS. 
the weight (fig. 4). A man pushing open a gate by applying his hand 
near the hinges, gives an example of a lever of this class; another 
is furnished by the common fire-ongs, the fulcrum being at the joint, 
and the lever being double, as in the case of the scissors. 
Having now described the different kinds of levers, we proceed to 
explain the principle upon which they work ; and although the practical 
use of a lever is to move a weight, yet, to values aceutately its manner 
of working, we must consider it in that state in which the power balances 
the weight, Sailich is called the state of equilibrium [Latin, equus, equal, 
uibra, a balance]. The whole principle will be understood at once if it 
be kept in mind that the lever 
>? does not, of itself, give rise to 
A eis oe B any force, but merely affords 
| te Ne [] the means of applying it. Let 
ete. the lever AB (fig. 5), which is 
seat three feet long, be supported 
Fig. 5. . on the fulcrum F, with two 
feet of its length on one side, 
AF, wal one foot, FB, on the other; and let a weight ae four pounds be 
sigpended at B, al one of two Mec at A. These two weights balance 
each pier thee is, the lever is in equilibrium. But suppose it to 
move into another position, CD. By a simple proposition in mathematics, 
we know that AF, being twice as great as FB, the distance AC, through 
which the small weight moves, is twice as great as BD, the distance through 
which B moves. We see, then, that the reason why a smaller weight or 
force is equivalent to a greater weight is, that the smaller force is exerted 
over a larger space. Thus, when a man wishes to overtum a large 
stone, and, finding that it is too heavy for him, takes a lever to assist 
him, he os not get any additional strength foun the lever; it merely 
coables him to concentrate the strength he,has. If his strength be 
sufficient to enable him to press dow the end of the lever, the raising 
power at the other end will be greater exactly in the proportion that the 
distance through which the one end is pushed down is greater than the 
distance through which the other end is moved, or in the proportion 
that the end a the lever next him is longer than the end next the 
stone. The principle of the lever then is, that the farther from the fulcrum 
the force is applied, the less it ene to be; and this principle applies 
to all kinds of levers. 
Sometimes the object in making use of a lever is not to get a greater 
power applied, as when a man wishes to raise a stone as described above, 
but to get greater speed of motion. It will be observed that in fig. 5, the 
long end of the lever A, since it moves through a distance twice as great 
as that moved by the short end B, must move twice as fast. If then speed 
