EXPLANATION OF TABLES. 49 



Example. 9.383731 is the log tan of what angle? 

 Next less 9.383682 gives 13 36' 



Diff. 49.00 -f- 9.20 = 05".3 



Ans. 13 36' 05".3 



Example. 9.249348 is the log cos of what angle? 

 Next greater 583 gives 79 46' 



Diff. 235 -H 11.67 = 20M 



Ans. 79 46' 20".l 



The above rules do not apply to the first two pages of this 

 table (except for the column headed cosine at top) because 

 here the differences vary so rapidly that interpolation made by 

 them in the usual way will not give exact results. 



On tbe first two pages, the first column contains the number 

 of seconds for every minute from 1' to 2 ; the minutes are 

 given in the second, the log. sin. in the third, and in \kzfourth 

 are the last three figures of a logarithm which is the difference 

 between the log sin and the logarithm of the number of sec- 

 onds in the first column. The first three figures and the char- 

 acteristic of this logarithm are placed, once for all, at the head 

 of the column. 



To find the log sin of an arc less than 2 given 

 to seconds. Reduce the given arc to seconds, and take the 

 logarithm of the number of seconds from the table of loga- 

 rithms, and add to this the logarithm from the fourth column 

 opposite the same number of seconds. The sum is the log sin 

 required. 



The logarithm in the fourth column may need a slight inter- 

 polation of the last figure, to make it correspond closely to the 

 given number of seconds. 



Example. Find the log sin of 1 39' 14". 4. 



1 39' 14".4 = 5954".4 log 3.774838 



add (q-l) 4.685515 



Ans. log sin 8.460353 



Log tangents of small arcs are found in the same way, only 

 taking the last four figures of (q I) from the fifth column. 



