48 STATISTICAL METHODS. 



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. 

 Example. 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. 10-777689 



To find the angle or arc corresponding to a 

 given logarithmic sine, tangent, cosine, or co- 

 tangent. If the given logarithm is found in the proper 

 column take out the degrees and minutes directly; if not, find 

 the two consecutive logarithms between which the given 

 logarithm would fall, and adopt that one which corresponds to 

 the least number of minutes; which minutes take out with the 

 degrees, and divide the difference between this logarithm and 

 the given one by the adjoining tabular difference for a quo- 

 tient, which will be the required number of seconds. 



With logarithms to six places of decimals the quotient is 

 not reliable beyond the tenth of a second. 



