EXPLANATION OF TABLES. 113 



Example. Find the log tan of 90 30' 50". 



q + I 15.314413 

 1800" + 50" = 1850* log 3.267172 



ATM. 12.047241 



To find the arc corresponding- to a given log 

 sin, cos, tan, or cotan which falls within the 

 limits of the first two pages of Table X. 



Find in the proper column two consecutive logarithms be- 

 tween which the given logarithm falls. If the title of the 

 given function is found at the top of that column read the 

 degrees from the top of the page; if at the "bottom read from 

 the bottom. 



Find the value of (q 1} or (q -f- 0, as the case may require, 

 corresponding to the given log (interpolating for the last figure 

 if necessary). Then if q = given log and I log of number of 

 seconds, n, in the required arc, we have at once I = q (q 1} 

 or I (q -[- q, whence n is easily found. 



Find in the first column two consecutive quantities between 

 which the number n falls, and if the degrees are read from 

 the left hand side of the page, adopt the less, take out the 

 minutes from the second column, and take for the seconds 

 the difference between the quantity adopted and the number 

 n. But if the degrees are read from the right hand side of the 

 page, adopt the greater quantity, take out the minutes on the 

 same line from the right-hand column, and for the seconds 

 take the difference between the number adopted and the num- 

 ber n. 



Example. 11.734268 is the log cot of what arc? 

 q + I 15.314376 



q 11.734668 



.-. n = 3802.8 "3.580108 



For 1 adopt 3780. giving 03' 



Difference 22". 8 



Ans. 1 03' 22".8 or 178 56' 37".2. 



J&cample. 8.201795 is the log cos of what arc? 

 q - I 4.685556 



q 8.201795 



/. n =t 3282". 8 3.51623d 



For 89 adopt 3300. giving 05 r 



Difference 17 ".2 



Ans, 89 05' 17".2 or 90 54' 42". 8. 



