COMPUTATIONS OF Z. COLBURN. 
1 7 
The unit figure of the cube being valued by inspection, the On numerical 
root is already found to be 7654. computations ; 
7 . particularly 
Explanation 1st. Use only three figures of the cube $ often thoseperforra- 
two will be sufficient The first root is known by inspection, z - Pol- 
and subtract its cube from the left-hand period. 
2d. Then the second root is to be assumed as correctly as the 
judgment can guess, taking it rather above than below the real 
value ; precision is not required, and very little practice will 
make this part of the process quite easy. Multiply the assumed 
figure by the first root ; add the product to the square of the 
first root ; and three times this last sum must be multiplied by 
the number that will bring it nearest to the remaining dividend,, 
This last factor will be the seeond root. 
3d. Deduct three times the product of the first and second 
roots multiplied by an assumed figure that you may conceive to 
be the next root wanted $ and deduct also the cube of the 
second root. In this stage, the divisor, which has been used int 
the second operation (there found to be 16 ) will give the third 
root correctly. 
The fourth root is known bv inspection. The cube of the 
second root may be neglected in most cases ; and always when 
the root is below 5 > only the left-hand figure of the cube is 
required. 
After a little exercise, all the divisors are readily found $ 
because each of them has been obtained in the second opera- 
tion, and there becomes known. The chief difficulty attends 
the explanation, to render the process intelligible. 
Illustration of the rule. 
Cube of m-\-n + p-\-q— or of 765 4 = 448 3 gg 7 62' 264 
Deduct m 3 - - - - - - - 343 
J05 
Deduct 3 (m 2 + m n) n - - • Q5‘760 
9-639 
Deduct 3 m n p and n 5 - - - - 846 
8 793 
Deduct 3 (m^+mn) p « - - - 7-980 
813702*264 
Vox.. XXXV. — No. 161. C The 
