330 G. B. AIRY, ESQ. SUPPLEMENT TO A PROOF OF THE THEOREM, &c. 



If 2r be a negative quantity = — /, then 



cos 80 = + 1, /o' = x. 



The combination of the different values of 6 which make cos 80 = ± l, properly carried out, 

 gives Cotes' Theorem. 



27. It will readily be seen that the process here used is perfectly general as regards the 

 order of the equation ; the adoption of the 8th order having been made merely for convenience 

 of writing. 



G. B. AIRY. 



EoYAL Observatory, Greenwich, 

 October 1, 1859. 



