Logarithms. 205 



logarithm must be a number such that it can be made by sub- 

 tracting I from o n times ; that is, it must be — ;/. 



20. Examples. The above enables us to tell by inspection 

 the characteristic of the common logarithm of any number. Thus 

 the characteristic of the logarithm of 237945.834 is +5, because 

 2, the first significant figure, stands in the fifth place to the left 

 of units place. In the same wa}^ the characteristic of the log- 

 arithm of .0007423 is —4, because 7 stands in the fourth place to 

 the right of units place. 



In determining the characteristic, care must be taken that we 

 count from the units place and not from, the decimal point ; for the 

 decimal point stands to the right side of units place. 



Find the characteristic of the logarithms of the following num- 

 bers : 



T. 1888. 1 19 5. 3000.0303 



2. .3724 6. .00000000849 



S- 783294.009 7. .00010000849 



y. .0084297 8. 3.00007 



21. Tables of Common Logarithms. The nature of the 

 work in which logarithms are to be used determines the size and 

 accuracy- of the tables which should be employed. For some pur- 

 poses a table of the logarithms of all numbers from i to loooo, 

 given to five or six decimal places, is sufficient. For many pur- 

 poses a table of the logarithms of all numbers from i to 1 00000 

 to seven decimal places is desirable, and this may be said to be 

 the standard table. We print herewith a sample page from such a 

 table. This page contains the logarithms of all numbers between 

 25600 and 26100, or, more correctly, the mantissas of the log- 

 arithms of these numbers. For, since the characteristic of the 

 common logarithm of anj- number can always be found by inspec- 

 tion, characteristics are never printed in such tables. 



Suppose we wish to find the logarithm of 25964. Then know- 

 ing that the characteristic of the logarithm of 25964 is 4, we will 

 find the mantissa from the table. We run down the column headed 

 N^iim. until we come to the figures 2596. We then run across the 



