1449 
between this variation in the sea level and the change in the position 
of the pole. If the sea level always corresponded to the position of 
the pole, the lowest sea level at a given place would always 
correspond to the maximum of the latitude at that place. 
In the formula for the periodic variation in the water level p= 
for 1 Jan. 1855 = 2398585 Julian date, and as the change of g per 
day is 0°. 83478, we may represent the formula for the height of 
the sea level on a day for which the Julian date is ¢ by 
h = 4,42 Sin (t — 2398585 + 209,1) 0°,83478} 
h = 4,42 Sin {(t — 2398375,9) 0°. 83478}. 
The height of the sea level is a maximum when the expression 
under the sine is 90°; thus we find 
Maximum height of sea level for ¢ = 2398483,7, 
Minimum A NELE ed Wea a Shel rea es) 
and if we add to this 23 & 431,25 = 9918.7 we find 
Minimum height of sea level for ¢ = 2408618,0. 
According to Zwiers (These Proceedings XIV p. 211) the Julian 
date for the maximum latitude fer Greenwich is 2408580, and 
if we reduce this for the difference of longitude between Green- 
wich and Helder, the date for the maximum latitude at Helder is 
2408585,7 which gives a difference with the date of the minimum 
height of the sea level of only 32,3 days. 
If the latitude variation is really the cause of the variation in the 
sea level, some time will elapse between the maximum latitude and 
the moment of the lowest sea level; how much this will be, cannot 
be theoretically determined: it depends upon the configuration of the 
continents, but the small difference which has been found is an argu- 
ment in favour of the hypothesis that there is a connection between 
the two phenomena. 
We will now investigate the relation between the amplitude of 
the 431-days tide and the magnitude of the latitude variation. The 
distance from a point of the ellipsoid of the earth to the centre of 
the earth is approximately expressed by 
logo =C +"'/, Ma Cos 2 gp 
if a is the ellipticity of the earth, and the radius of the equator 
is taken equal to 1. If the pole moves through an angle Ap in the 
direction of the meridian of this point, so that the latitude becomes 
ptp, and the liquid and solid parts of the earth could immediately 
change so as to both acquire in relation to the new axis the same 
shape as they had to the original axis, then the distance from that 
point to the: centre of the earth would vary by the amount A g, 
