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Four-place logarithm tables contain tin- logarithms to four decimal 

 places of all numbers of three %mvs from i.oo to 9.99, and enable 

 one by interpolation to obtain the four-place logarithm of any t'our- 

 place number from i.ooo to 9.999. By merely prefixing tin- proper 

 characteristic n. therefore, the four-place logarithm of any four- 

 place number from o to oo is obtained, or, in other words, the four- 

 place logarithm of any number whatever from o to oo in so far as 

 this is governed by the first four significant figures of the number. 

 Four-place tables should not be employed upon work of an accuracy 

 exceeding one-half of one per cent. 



Five-place tables give directly the logarithms to one place further 

 than four-place tables, i.e. to five decimal places, for numbers from 

 i.ooo to 9.999, and thence, by interpolation, from i.oooo to 9.9999. 

 Thus, with the proper characteristic, these tables furnish the log- 

 arithms of all five-figure numbers from o to oo, that is, of any num- 

 ber whatever in so far as this is governed by the first five significant 

 figures of the number. Five-place tables should not be employed 

 in work of an accuracy exceeding one-twentieth of one per cent. 



Six-place tables are sometimes arranged with the same steps as 

 five-place, i.e. giving directly the logarithm to six decimal places 

 of numbers from i.ooo to 9.999 only. Such tables are of no prac- 

 tical service ; for it is entirely useless to employ six-place logarithms 

 in work on five-place numbers, and interpolation for six-place num- 

 bers in tables of so large steps as this, besides being less reliable, 

 is more laborious and annoying than is the use of the more bulky 

 tables of smaller steps. 



If six-place tables are desired, it is usual to employ, dropping 

 the last place, tables which give directly seven-place logarithms of 

 numbers from i.oooo to 9.9999 with convenient interpolation tables 

 for the next place. Of these, the Vega tables are among the most 

 convenient, legible, and reliable, being also comparatively inexpen- 

 sive. The seventh place is very rarely demanded by physical, 

 chemical, or engineering work. 



The relative labor in using four, five, and six place tables lies probably 

 between the ratios 1:2:3 an( i 2 : 3 : 4- Assuming the first estimate to hold, 

 the labor is doubled by using a five-place instead of a four-place table, and 

 is increased one-half by using a six instead of a five place table. Hence, as 

 there is no sensible gain from using an excess of places, it is obviously very 

 important to employ a table of the smallest admissible number of places. But, 

 on the other hand, the use of too few places must be guarded against. As an 

 instance of a somewhat dangerous practice may be cited the use of four-place 



