INVOLUTION. 147 



a. A grocer would mix teas at 1 2s. ros. and 6s. with 

 lo\h. at 4s. per pound ; how much of each sort must he 

 take to make the composition worth 8s. per lb ? 



Ans. 2olb. at 4s. 10 at 6s. 10 at los. and 20 at 12s. 



3. How much gold of 15, of 17 and of 22 carats fine, 

 must be mixed with 50Z. of 18 carats fine, so that the 

 composition may be 20 carats fine ? 



Axis. 50Z. of 15 carats fine, 5 of 17, and 25 of 22. 



INVOLUTION. 



A Power is a number produced by multiplying any giv- 

 en number continually by itself a certain number of times. 



Any number is itself called the Jirst power ; if it be 

 multiplied by itself, the product is called the second ponver^ 

 or the square ; if this be multiplied by the first power 

 again, the product is called the third power ^ or the cube ; and 

 if this be multiplied by the first power again, the product 

 is called the fourth power ^ or biquadrate ; and so on 5 that 

 is, the power is denominated from the rmmber, which ex- 

 ceeds the multiplications by i. 



Thus, 3 is the first power of 3. 

 3X311: 9 is the second power of 3. 

 3X3X3:::i:27 is the third power of 3. 

 3X3X3X311:81 is the fourth power of 3. 

 &c. &c. 



And in this manner is calculatecf the following table of 

 powers. 



TABLE 



