STATISTICAL METHODS. 



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 - 1) 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. 



Example. Find the log tan of 52' 35". 



52' 35" = (3120" 4- 35") = 3155" log 5.498999 



add (q - I) 4.685609 



Ans. log tan 8. 184608 



To find the log cotangent of an angle less than 

 2 given to seconds. Take from the column headed ( q-{- Z) 

 the logarithm corresponding to the given angle, interpolating 

 for the last figure if necessary, and from this subtract the loga- 

 rithm of the number of seconds in the given angle. 



Example. Find the log cotan of 1 44' 22". 5. 



q + I 15.314292 

 6240" + 22". 5 = 6262.5 log 3.796748 



Ans. 11.517544 



These two pages may be used in the same way when the 

 given angle lies between 88 and 92, or between 178 and 180; 

 but if the number of degrees be found at the bottom of the page, 

 the title of each column will be found there also; and if the 

 number of degrees be found on the right hand side of the page, 

 the number of minutes must be found In the right hand col- 

 umn, and since here the minutes increase upward, the number 

 of seconds on the same line in the first column must be dimin- 

 ished by the odd seconds in the given angle to obtain the num- 

 ber whose logarithm Is to be used with (ql) taken from the 

 table. 



Example. Find the log cos of 88 41' 12". 5 



fe - J) 4.685537 

 4740" - 12".5 = 4727.5 log 3.674631 



Ans. 8.360168 



