Logarithms. 207 



page on the same horizontal line with 2596 until we come to the 

 column headed 4, at which place will be found the figures 3716, 

 which are the last four figures of the required mantissa. The first 

 three figures are found in the column headed o and are seen to be 

 414. Whence the mantissa of the logarithm of 25964 is .4143716, 

 and therefore 



log 25964=4.4143716. 



Of course a decimal point belongs before the mantissa of each 

 logarithm, and since this fact is understood, it is unnecessary to 

 print the decimal points in a table. 



Inasmuch as the first three figures of the mantissa are only 

 printed in the column headed o, it is necessar}^ to mark the point 

 at which these first three figures change. This is done by an 

 asterisk {^) standing in the place of a cipher in the last four fig- 

 ures. Thus to find the logarithm of 25646 we must note that the 

 three figures change from 408 to 409 at the point 25645 (which is 

 indicated b}^ printing ^027 in place of 0027), and consequently 

 log 25646=4.4090196. 



The dagger ( t) which appears in column o is intended to cau- 

 tion us that the first three figures change at some place in the 

 same horizontal line with it. 



If we wdsh to find the logarithm of a number consisting of more 

 than five figures, say 25705.84, then we must take the nearest 

 number whose logarithm is given in the table, that is to say, 

 25706.00. Thus 



log 25705.84=4.4100345, nearly. 



Greater accuracy may be secured by means of tables of dif- 

 ferences and multiples, as is explained in connection with any 

 good table of logarithms. 



A table of logarithms of numbers from i to 1 00000 can be used 

 to find the logarithm of any number consisting of five significant 

 figures. Thus to find the logarithm of 25.964 we entirely neglect 

 the decimal point- in finding the mantissa, as the decimal point 

 affects the chjiracteristic alone. Thus 



log 25.964=1.4143716. 



A table of logarithms also enables us to find the number corre- 

 sponding to any given logarithm by a mere reversal of the process 

 already explained. Thus all numbers the mantissas of whose 



