112 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 sm of 1 39' 14". 4. 



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



add (g-Z) 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 - 1) from the fifth column. 



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



52' 35" = (3120" + 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-\- 1} 

 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. 



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



(q-l) 4.685537 

 4740" - 12'.5 = 4727.5 log 3.674631 



Ans. $.360168 



