EXPLANATION OF SOURCE AND USE OF THE 



TABLES. 



Tables i and 2 are copies of tables issued by the Office of Standard Weights 

 and Measures of the United States, edition of November, 1891. 



Table 3 is derived from standard tables giving such data. The arrangement 

 is that given in " Des Ingenieurs Taschenbuch, herausgegeben von dem Verein 

 ' Hiitte ' "* (nth edition, 1877). The numbers have been compared with those 

 given in the latter work, and also with those in Barlow's " Tables." The loga- 

 rithms have been checked by comparison with Vega's 7-place tables. 



Table 4 is abridged from a similar table in the Taschenbuch just referred to. 



Tables 5 and 6 are copies of standard forms for such table. They have 

 been checked by comparison with standard higher-place tables. The mode of 

 using these tables will be evident from the following examples : — 



(i.) To find the logarithm of any number, as 0.06944, we look in Table 5 

 in the column headed N for the first two significant figures of the number, which 

 are in this case 69. In the same horizontal line with 69 we now look for the 

 number in the column headed with the next figure of the given number, which is 

 in the present case 4. We thus find .8414 for the mantissa of the logarithm of 

 the number 694. To get the increase due to the additional figure 4, we look in 

 the same horizontal line under Prop. Parts in the column headed 4 and find the 

 number 2, which is the amount in units of the fourth place to be added to the 

 part of the mantissa previously found. Thus the mantissa of log (0.06944) is 

 .8416. The characteristic for the logarithm in question is —2 =8 — 10. Hence 

 log (0.06944) =8.8416 — I o. 



(2.) To find the number corresponding to any logarithm, as 8.8416— 10, we 

 look in Table 6 in the column headed L for the first two figures of the mantissa, 

 which are in this case 84. In the same horizontal line with 84 we now look for 

 the number in the column headed by the next figure of the mantissa, which is in 

 this case i. We thus find 6394 for the number corresponding to the mantissa 

 8410. To get the increase due to the additional figure 6, we look in the same 

 horizontal line under Prop. Parts in the column headed 6 and find 10, which is 

 the amount in units of the fourth place to be added to the number previously 

 found. Thus the significant figures of the number are 6944, and since the char- 

 acteristic of the logarithm is 8 — 10= —2, the required number is 0.06944. 



* Berlin : Verlag von Ernst & Korn. This work is an invaluable one to the engineer, archi- 

 tect, geographer, etc. 



