row 



PRA 



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, bu*. have neverthe- 

 less thought proper to give the above cau- 

 tion. See MECHANICS. 



POWER of attorney, an instrument, or 

 deed, whereby a person is authorised to 

 act for another, either generally, or in a 

 specr c transaction. 



This power is always revoked by the 

 death of the grantor, and no person who 

 has a power of attorney can grant a pow- 

 er 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 2 , 3, a-*, 

 &c. the powers of the quantity ; which 

 operation is called involution. Powers 

 of the same quantity are multiplied by 

 only adding their exponents, and making 

 their sum the exponent of the product : 

 thus, 4 x s = a4 * 5 = a9 - Again, the 

 rule for dividing powers of the same 

 quantity is, to subtract the exponents, 

 and make the difference the exponent of 



a 6 



the quotient : thus, _ = a 6 * =. a*. 

 aft 



Negative powers, as well as positive, 

 are multiplied by adding, and divided by 

 subtracting, their exponents, as above. 

 And, in general, any positive power of a, 

 multiplied by a negative power of a, of 

 an equal exponent, gives unit for the pro- 

 duct ; for the positive and negative de- 

 stroy each other, and the product is a, 



which is equal to unit. Likewise, - 



of a ; and X 



a 5+ 2 



a-3 



. G 1 



and 



a 5 



==03= ^ZJ 1 And, in general, any quan. 



tity placed in the denominator of a frac- 

 tion may be transposed to the numerator, 

 if the sign of its exponent be changed : 



thus, ~- = G~ 5 , and _ = 3. 



The quantity a m expresses any power 

 of a, in general ; the exponent m being 



undetermined: a m expresses ' or a 



tl m 



negative power of , of an equal expo- 

 nent : and a m X &~ m = a m ~ m = a = 

 1. Again, a n expresses any other power 



a m+n t and = 

 an 



To raise any simple quantity to its se- 

 cond, third, or fourth power, is to add 

 its exponent twice, thrice, or four times, 

 to itself; so that the second power of any 

 quantity is had by doubling its exponent ; 

 and the third, by tripling its exponent ; 

 and, in general, the power expressed by 

 ?n, of any quantity, is had by multiplying 

 the exponent by m : thus the second pow- 

 er, or square of , is a 2 l = a- ; its third 

 power. a>* ' = 3 ; and the mth power of 

 , is am* l = u m . Also the square of a% 

 is z * = a 8 ; the cube of n*, is a3*4 = 

 a 1 - ; and the mih power of 4 , is a**m. 

 The square of a b c, is a 1 b 1 c 1 ; its cube 

 n3 63 C 3 ; and the with power, am bm c. 



POX, or SMALL-POX. See MEDICI XE. 



PRACTICE, in arithmetic, or rules of 

 practice, are certain compendious ways 

 of working the rule of proportion, or gol- 

 den-rule. 



I. When a question in the rule of three 

 being duly stated, and the extremes are 

 simple numbers of one name ; whether 

 the middle term be simple or mixed ; if 

 the extreme, which by the general rule is 

 the divisor, be 1, and the middle term, 

 an aliquot part of some superior spe- 

 cies; then divide the other extreme by 

 the denominator of that aliquot part, the 

 quote is the answer in that superior spe- 

 cies ; and if there is any remainder, it 

 must be reduced, and its value found. 

 Example. What is the price of 67 yards 

 of cloth at 5s. per yard ? The state of the 

 proportion is, as 1 yard : 5s. : : 67 ; and 

 because the divisor is lyard, and the mid- 

 dle term 5s. which is a fourth part of one 

 pound. Therefore divide 67 yards by 4, 

 the quote is 16/. and 3 remains, which 

 reduced to shillings, and divided by 4, 

 quotes 15s. 



The reason of this practice is obvious ; 

 for if 1 yard cost one-fourth of 11. 67 yards 

 must cost 67th parts, or, which is the 

 same thing, the fourth part of 671. 



II. If the price of an unit is an even 

 ntnnber of shillings, multiply the other 

 extreme (of the same name with the unit) 

 by the half of that number ; double the 

 first figure of the product for shillings, 

 and the remaining figures to the left are 

 pounds in the answer. Example. What 

 is the value of 324 yards at 6s. per yard : 

 Multiply 324 by 3 (the one-half of 6) the 

 product is 972, which according to the 

 rule, is 971. 4s. which is the answer. And 

 it is very easy to set down the shilling's 



