EXPLANATION OF TABLES. Ill 



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. 



Example. 9.383731 is the log tan of what angle? 

 Next less 9.383682 gives 13 36' 



Diff. 49.00 -*- 9.20 = 05*.3 



An*. 13 36' 05".3 



Example. 9.249348 is the log cos of what angle? 

 Next greater 583 gives 79 46' 



Diff. 235 -5- 11.67 = 20M 



. Ans. 79 46' 20M 



The above rules do not apply to the first two pages of this 

 table (except for the column headed cosine at top) because 

 here the differences vary so rapidly that interpolation made by 

 them in the usual way will not give exact results. 



On the first two pages, the first column contains the number 

 of seconds for every minute from 1' to 2 ; the minutes are 

 given in the second, the log. sin. in the third, and in thefourfo 

 are the last three figures of a logarithm which is the difference 

 between the log sin and the logarithm of the number of sec 

 onds in the first column. The first three figures and the char- 

 acteristic of this logarithm are placed, once for all, at the head 

 of the column. 



To find the log sin of an arc less than 2 given 

 to seconds. Reduce the given arc to seconds, and take the 

 logarithm of the number of seconds from the table of loga- 

 rithms, and add to this the logarithm from the fourth column 

 opposite the same number of seconds. The sum is the log sin 

 required. 



