\\vill LOGARITHMS. 



Interpolation Incomes more laborious and more liable to error, 

 if conducted mi'iitally. in proportion as the difference is large. It 

 is therefore great i-st in the iirst quarter of any logarithm table. But 

 it happens that in physical, chemical, and engineering computations 

 very often enter correction or reduction factors and other 

 terms of the form (i -fa) or i/(i a), where a is a decimal frac- 

 tion rarely as lar^e as o.i. The frequency of such terms calls for 

 a disproportionately large number of the more laborious interpola- 

 tions. To avoid this labor and increased chance of error, the excel- 

 lent practice lias been adopted in some five-place tables of inserting 

 two pages giving the logarithms from i.o to i.i, by steps only one- 

 tenth as large as in the rest of the tables, thus doing away with 

 all interpolation in this most used and most troublesome portion 

 of the table, without adding seriously to its bulk. Such a table 

 has here been prefixed to the five-place table. In the four-place 

 table the same result has been accomplished here, in a manner which 

 is perhaps novel, by the insertion of ten additional lines at the head 

 of the table. The Vega seven-place tables unfortunately lack this 

 feature. 



To find Logarithm of a Decimal Fraction. The procedure is 

 precisely the same as for a whole number. Note that the log- 

 arithm of a decimal fraction is always negative, and, conversely, 

 that a negative characteristic always denotes a decimal fraction. 



Difference = 14. 



Example. Desired the log of o.oo 306 2. 



log o.oo 306 2 = log 3.o62'io~ 8 



log 3.07 = .4871 



3.06 = .4857 



o. 2 of difference = 3 



. . log 3.062 = .4860 



log io- 3 = - 3. 



. '. log O.OO 306 2 = .4860 3. 



This is written either 3.4860 or 7.4860 - io. The latter form is obtained by 

 adding io to the characteristic and appending io to the whole. The num- 

 bers thus appended must in many instances, but not in all, be followed up in 

 the computation in order to correctly locate the decimal point at the close. 

 This is, however, usually very little trouble. The second method is the very 

 general practice and is based on the assertion that when several logarithms are 

 to be added, it is more convenient to have all the characteristics positive. The 

 author is, however, of the opinion that this conventional method serves almost 

 no useful purpose, and that it is better and less troublesome in every way to 

 retain the negative characteristic. It is almost as easy to add a column of num- 

 bers in which some are negative, and are therefore subtracted when they are 



