328 
Mr. Manning’s new Method 
examining parts taken at random, we may in some cases 
satisfy ourselves of its accuracy, as well as by examining the 
whole.* 
Among the various methods of computing logarithms, 
none, that I know of, possesses this advantage of forming 
them with tolerable ease independently of each other by 
means of a few easy bases. This desideratum, I trust, the 
following method will supply , while at the same time it is 
peculiarly easy of application, requiring no division, multipli- 
cation, or extraction of roots, and has its relative advantages 
highly increased by increasing the number of decimal places 
to which the computation is carried. 
The chief part of the working consists in merely setting 
down a number under itself removed one or more places to 
the right, and subtracting, and repeating this operation ; and 
consequently is very little liable to mistake. Moreover, from 
the commodious manner in which the work stands, it may be 
revised with extreme rapidity. It may be performed after a 
few minutes instruction by any one who is competent to sub- 
tract. It is as easy for large numbers as for small ; and on 
an average about 27 subtractions will furnish a logarithm 
acccurately to 10 places of decimals. In general £x^-p- 
subtractions will be accurate to 2/1 places of decimals. 
In computing hyperbolic logarithms by this method it is 
necessary to have previously establised the h. logs, of y , 
=^2, &c. of 2 and of 10. 
999 
* For example, we may wish to know whether the editor of a table has been 
careless. We examine detached portions here and there to a certain extent; if we find 
no errors, we have a moral certainty that the editor was careful, and consequently a 
moral certainty that the edition is accurate. 
