44 
ME. K. TERAZAWA OX PERIODIC DISTURBANCE OF LEVEL 
and 
consequently we have 
2 e l®l — , /l = 
By (0 t) = —^T^o 2 (0 | Tj), 
4 
a/ V(0 tj) l 
j_4 + l°g^i 
. b 2 (o|t 1 ) 9r s ( 0 1 -7-0 Ji 
The q A series for the functions required here are 
3- 0 = l—2q 1 + 2q ] i — 2q{' + ... , 
S-" 2 = (1 + 3 V+ 5 V+7 V 2 + 
% = 2gd (1 + q? +g/ 3 +g, 12 + •••), 
^"3 = ~~ 8?r' (g, + 4g 1 4 + 9g 1 9 + •••), 
B *3 = 1 + 2 g 1 + 2 g 1 4 + 2 g 1 ' + ... . 
I 11 the accompanying diagram the courses of (u z ) 0 and its slope are exhibited as 
functions of the distance of the point of observation from the centre of the loaded 
circle, with the proper scale. The lower curve thus represents the vertical displace¬ 
ment and the upper one the corresponding slope outside of the loaded area. 
If we liken the North Atlantic to a circular basin of a large radius and determine 
the relative position of Potsdam or Chicago referred to the centre of it, the attraction 
effect and the tilting effect of the periodic filling and emptying of tide, which might 
