568 
Proceedings of Royal Society of Edinburgh. [sess. 
of the problem of finding the motion in which the surface-pressure 
is that given in (74). 
§ 43. To understand thoroughly the constitution of the forcive- 
datum (74) for II, it is helpful to know that, n denoting any 
positive or negative integer, we have 
if 
27t(J + e cos 0 + e 2 cos 2 0 + etc.) = 
i = l!r l0g (1/ ^ 
X = ± 6 
2tt 
ba 
=-oo b 2 + (x-na ) 2 
• (78), 
• (79). 
This we find by applying § 15 above to the periodic function 
represented by the second member of (78). 
The equality of the two members of (78) is illustrated by fig. 11 ; 
in which ; for the case e = *5 and consequently, by (7 9), b/a = *1103; 
the heavy curve represents the first member, and the two light 
curves represent two terms of the second member ; which are as 
