4^8 Mr, Herschel on various points of Analysis. 
If there be m roots equal to we have 
(D — py^: or(D — pY' : ux.r'^^zzzo. 
Now, ( D — py ^ : u . | u . = o. 
Therefore, integrating m times 
and «= [°C+ 'Cx+ . . . .“-■C.x”’— 
which is the part of the integral ai'ising from the equal roots/*. 
JOHN F. W. HERSCHEL. 
London, Jan. 29, 1814, 
