326 Prof. G. H. Darwin. [June 19, 



We next proceed to form XIII columns of cosine numbers, and 

 generally to operate exactly as though these numbers were heights ; 

 and then proceed with XIII columns of sine numbers in the same 

 way. 



The results are 



ScosV =-0-0522, S sinV =+0-0117, 



S*- cos iy m = -0-0168, S*' sin V = -0-0129. 



(n.) Formation of the Mean Sums of cos fV m and sin. fV TO . 



These maybe found with sufficient accuracy from the last Table (m) 

 of Sums, part of which is given. In that table lines are drawn dividing 

 the columns into three divisions of six each. These are treated in 

 the way shown in the following example : 



H. and L.W. $V m . 



Kefer to preceding 

 sorting (m). 



-1 st six of 2 nd -4 th . 



.-300 + 2 nd six of I 9t -3 rd . 

 -3+1 . + 3 rd six of 2 nd -4 th . 



2 nd_ 4 th .... _8 +1 . -3 



II. ...... -1 st six of 2 nd -4 th . 



. . . -3 + 2 nd six of 1 st 3 rd . 



+ 3 +3 . . . . + 3 rd six of 2 nd -4 th . 



+3 +3 . . . -3 



+ Tsixof I 9t -3 rd . 

 -2-3 + 2 nd six of 2 nd -4 th . 

 -1-2 -3 -2 . . -3 rd six of 1"- 3 rd . 



l"-3 rd +2 -3 -2 . -2 -3 



2 nd 5 th , rev. 3 . . +3 +3 



III. &c. &c. 



We have now only 6 instead of 18 sub-divisions of the quadrant, but 

 the cosine and sine numbers are found in exactly the same way as 

 before. 



The following example shows part of the treatment, and the cosine 

 factors are those marked * in F. 



