ARISING FROM THE LOAD OF NEIGHBOURING OCEANIC TIDES. 
45 
assist in producing- the extra east-west force, in observations of lunar disturbance of 
gravity, may be computed. If we suppose the place of the observation to be not very 
near to the circular basin, the effect, as we see from the above diagram, is of course 
small, but it increases rapidly as the edge is approached. 
For example, suppose the radius of the North Atlantic basin to be 2000 km., 
the position of Chicago to be 3000 km. from the centre*and the level of the water 
in this area to be raised one meter, then 
— = 1'5, q x = 0-00255, 
a 
and 
act 2 — > 7 j) = 0'8639. 
Further assume that the density of sea water is 1, and in c.g.s. units, 
y = 6'65 x 10~ 8 , g — 980, 
A + 2 
ft 
3 
M = 6x 10 u , 
then we shall have 
2 (a + ft) 
v > = 1*17 X 10- 8 = 0 ,/- 0024, 
cjj = 3*37 -F 1 0- 8 = (ff'0069. 
Accordingly the total effect amounts to 
+ 0 = 4‘54 x I0~ 8 = 0"-009. 
It will be noticed that the effect of tilting is about three times as great as that of 
the attraction, so far as the material constants are assumed as above. According to 
Lord Kelvin,* who initiated these investigations, the direct lunar effect on the 
deviation of a plumbline is a maximum when the moon is at the altitude 45 degrees and 
amounts to 0"’0L7 nearly. The total effect of a tide of amplitude one metre (which 
is possibly two or three times the actual amount) found here is not small enough to 
be neglected compared with the direct effect of the moon, the former is nearly half 
the latter. As the tilting effect and the attraction effect of the tide wave are 
directly proportional to the height of the tide, the total effect oscillates in time in 
accordance with the law which the tide obeys. There is, in general, a difference in 
phase between the lunar effect and the tidal effect, which is worthy of closer 
investigation.! But we must bear in mind that the calculation adopted here is 
nothing but a rough estimation of order of magnitude, since the North Atlantic is far 
from circular, the tidal loading in it is never uniform. 
* ‘Natural Philosophy,’ Part II., p. 383. 
t Fortunately, the phase difference of both effects in Michelson’s experiment may be neglected in a 
rough estimation, owing to the relative position of Chicago and the centre of the North Atlantic. 
H 2 
