PROFESSOR O. H. DARWIN ON ELLIPSOIDAL HARMONIC ANALYSIS. 
557 
7 = 5 (OEC) 
= 1 — 7/8 cos 2(^+Yf/3'Cos 4<^] 
Note that in this table 
= (1 — /8 cos 2(f))-. 
A table of P ( v ) and Q { v ) up to 7 = 5, s = 5 is contained in Professor Bryax’s 
paper (‘Proc. C'amb. Phil. Soc.,’ vol. vi., 1888, p. 297). The functions there 
tabulated as (i^) and U* ( 7 .-) in the notation here adopted, would be Pf, ( 7 ’) (with the 
factor - 1)^*) and (-)’Q^^). 
The formula for Q/ (v), where s is greater than 7, is given in ^ 10 above. 
