COMPUTATION OF Z. COLBURN. 
15 
error, whenever it can happen, becomes immediately obvious ; On numerical 
and, by taking the relative quotient a single unit less than the computation*, 
fallacious multiplier, the second root will be always obtained those C perfiu in- 
correct Jy. This incident may unfrequently retard the calcula- 
tion for a moment j but ought never to defeat the accuracy of 
the final result. 
Example. 
Square 5g05Q2 25 
Deduct square of the first root 7 4 9 
Twice the first root, 7x6= 84 
Square of 6 36 
100 
87 
Twice the first and second roots 
v say 
13 
76 X 8 
15 X 8 12 
5 must be the fourth root, without any trial, 7685 is therefore 
found to be the root of the given square. In rhe second opera- 
tion twice 7 will go 7 times in 100, which is the case of nicety 
alluded to ; but it must be instantly perceived that the square 
of 7 added to 98 would raise the sum too high for the dividend 
of tQO ; therefore, the next lower digit is adopted; and the 
very first substitute will always be right, as the same divisor is 
employed in the third and fourth operations (where both are 
accessary) the work is completed with expedition and accuracy. 
Practical 
