PO w 
move rapid, but the explosion is less violent. 
With three parts of nitre, one of sulphur, 
and one of saw-dust, well mixed together, 
what is called powder of fusion is formed. 
If a little of this powder is put into a wal- 
nut-shell, with a thin plate of copper rolled 
up, and the mixture set fire to, it detonates 
rapidly, and reduces the metal to a sul- 
phiiret, without any injury to the shell. 
POWER, in mechanics, denotes any 
force, whether of a man, a horse, a spring, 
the wind, water, &c. which being applied to 
a machine, tends to produce motion. 
The intensity of a power is its absolute 
force ; that is, its force, supposing its velo- 
city equal to its weight : for its moving or 
acting force may be greater or less accord- 
ing as its velocity is increased or diminished, 
in respect of that of the weight. As for 
example, if a man be the power, and can 
raise from the ground a certain.weight, that 
weight will express or be equal to the in- 
tensity of the power; for in this case, what- 
ever engine be made use of, that part of the 
engine, where the weight is duly applied, 
will move just as fast as that on which a 
man acts with his whole force. A power 
may act in any direction whatever ; but a 
weight has only one directioil, viz. towards 
the centre of the earth. 
When we speak of the mechanical pow- 
ers, the word power is taken in a very dif- 
ferent sense from that above laid down ; 
since, in this case, it signifies only an organ 
or instrument, whereby a power of a known 
intensity is made to act upon a weight; and, 
therefore, we must take care not to attri- 
bute any real force to any simple or com- 
pound machine, as many are apt to do 
merely because the name power has been 
given to mechanical organs, not from their 
etfect, but from the effect which the power 
produces by their means. For how much 
soever the force of a power is thereby in- 
creased, in order to sustain or raise a weight 
far superior to it in intensity ; yet this can- 
not be done without losing in space and 
time what is gained in force ; contrary to 
what some have vainly imagined, because 
the vulgar commonly speak of a machine as 
they do of an animal ; attributing that effect 
to the machine, which is only the effect of 
the power by means of the machine : thus, 
it is usual to say, such a machine raises such 
a quantity of water, or performs such and 
such work ; when we should say, if we 
would speak philosophically, such a running 
stream, such a fall of water, the wind, or so 
many men, horses, oxen, &c. raise so much 
VOL, V. 
POW 
water in such a time, &c. by means of such 
or such a machine. It were, therefore, to 
be wished that the word power were to be 
confined to its proper sense, and not used 
to signify one of the mechanical organs ; 
however, as it has been customary to use it 
in that sense, we have done so too, but 
have nevertheless thought proper to give 
the above caution. See Mechanics. 
Power of attorney, ah instrument, or 
deed, whereby a person is authorised to act 
for another, either generally, or in a specific 
transaction. 
This power is always revoked by the 
death of the grantor ; and no person who 
has a power of attorney can grant a power 
under him. 
Powers, in arithmetic and algebra, are 
the products arising from the continual 
multiplication of a number, or quantity, 
into itself: thus, 2, 4, 8, 16, 32, &c. are the 
powers of the number 2; and «, a*, a’, a\ 
&c. the powers of the quantity a ; wliich 
operation is called involution. Powers of the 
same quantity are multiplied by only add- 
ing their exponents, and making their sum 
the exponent of the product : thus, a4 x 
= Again the rule for dividing 
powers of the same quantity, is to .subtract 
the exponents, and make the difference the 
exponent of the quotient: thus, 
Negative powers, as well as positive, are 
multiplied by adding, and divided by sub- 
tracting, their exponents, as above. And, 
in general, any positive power of a, multi- 
plied by a negative power of a, of an equal 
exponent, gives unit for the product ; for 
the positive and negative destroy each other, 
and the product is a", which is equal to unit. 
a~^ r 
Likewise, — = a-^+4=;a-’= a^; and 
|^^=a-='+^ = a’=^ 3 . And,ingene. 
ral, any quantity placed in the denominafor 
of a fraction, may be transposed to the 
numerator, if the sigh of its exponent be 
changed: thus, = a-^, and ak 
d d i 
The quantity a® expresses any power of 
a, in general ; the exponent m being unde- 
termined : and a “ “ expresses -^, or a ne- 
gative power of a, of an equal exponent; 
and a® x a— a’"-™ = a° = 1. Again, 
a" expresses any other power of a ; and a’’ 
am 
X a” = 0 ®+", and — = a®-”, 
G g 
