118 



Sir J. W. Lubbock on some Methods of developing 

 Table IX. Indices of constant factors. 



Each operation moves the indices of the variable factor to the 

 numbers which are in the next horizontal row beneath in Table III. 

 The following table gives the indices of the sines which are intro- 

 duced by each operation when the products of two sines are substi- 

 tuted for the difference of two cosines. 



All the factors above the line which crosses the table are — , and 

 all beneath it + . 



