110 STATISTICAL METHODS. 



The number derived from a six-place logarithm is not 

 reliable beyond the sixth figure. 



At the end of Table XI is a small table of logarithms of 

 numbers from 1 to 100, with the characteristic prefixed, for 

 easy reference when the given number does not -exceed two 

 digits. But the same mantissas may be found in the larger 

 table. 



TABLE XII. The logarithmic sine, tangent, etc., 

 of an arc is the logarithm of the natural sine, tangent, etc., of 

 the same arc, but with 10 added to the characteristic to avoid 

 negatives. This table gives log sines, tangents, cosines, and 

 cotangents for every minute of the quadrant. With the 

 number of degrees at the left side of the page are to be read 

 the minutes in the left-hand column; with the degrees on 

 the right-hand side are to be read the minutes in the right-hand 

 column. When the degrees appear at the top of the page the 

 top headings must be observed, when at the bottom those at 

 the bottom. Since the values found for arcs in the first quad- 

 rant are duplicated in the second, the degrees are given from 

 to 180. The differences in the logarithms due to a change 

 of one second in the arc are given in adjoining columns. 



To find the log. sin, cos, tan, or cot of a given 

 arc. : Take out from the proper column of the table the log- 

 arithm corresponding to the given number of degrees and 

 minutes. If there be any seconds multiply them by the ad- 

 joining tabular difference, and apply their product as a cor- 

 rection to the logarithm already taken out. The correction is 

 to be added if the logarithms of the table are increasing with 

 the angle, or subtracted if they are decreasing as the angle in- 

 creases. In the first quadrant the log sines and tangents in- 

 crease, and the log. cosines and cotangents decrease as the 

 angle increases. 



Exampk. Find the log sin of 9 28' 20". 



Log sin of 9 28' is 9.216097 



Add correction 20 X 12.62 252 



Ans. 9.216349 

 Example. Find the log cot of 9 28' 20". 



Log cotan of 9 28' is 10.777948 



Subtract correction 20 X 12.97 259 



Ans. ~10777689 



