52 _ PROCEEDINGS OF SECTION A. 
weight of a body, so that, at a point on the equator directly 
under the moon, a mass of one ton has its weight diminished 
by about 1°85 grains, owing to this cause. Such a slight 
vertical force cannot produce any raction, as it will. net lift. 
_a body away from the surface. On the other hand, the 
horizontal component, although it is also very smaU, and its 
maximum value is only chree-fourths of the vertical force 
just noted, is unresisted by gravity, and is thus capable of 
preducing movement im the waters of the ocean. Similar 
tide-producing forces are set up on the same principle by the 
action of the sun. The sun, however, being so far away, 
exerts upon the different parts of the earth an attraction 
which is much more wniform than that of the moon, so that 
the tide-preducing forces due te it are smaller. Newton, 
and, after him, Pernoulli, Euler, and Maclaurin, in their 
developments and extensions of his theory, assumed that the 
surface of the ocean at any instant is one of equilibrium 
under the action of gravity and the tide-producing forces. 
On this assumption the ocean, under the influence of the 
moon alone, would take the form of an ellipsoid of revolution 
with its major axis pointing towards the moon; similarly, 
the sun alone would cause it to take the form of a some 
what less elongated ellipsoid with iis major axis directed 
towards the sun. The actual tide is given by the super- 
position of the two ellipsoids. In this form, however, the 
Newtonian theory fails very considerably when compared 
with actuality, and, as has been pointed out by Lord Kelvin, 
the conditions assumed could only be satisfied by an earth 
completely covered with ocean. With a constanc amount 
of water in the oceans, the theory could not Hold with a dis- 
tribution of land and water such as we actually have. 
According to the theory, at spring-tides the morning - and 
evening tides should be of nearly equal height at a point on 
the equator, but very different in height for ports in other 
latitudes. We find, however, that this “diurnal inequality ”’ 
is very small indeed at ports in the North Atlantic—nothing 
approaching what the equilibrium theory would lead us to 
expect. Moreover, spring-tides occur at an interval after 
full and change of moon, instead of exactly at the full and 
change. : 
Laplace, in 1774, attacked the problem in his Mécanique 
Céleste. He investigated the nature of the waves set up 
in am ocean covering the entire earth by the action of the 
tidal forces. As the basis of his work, he stated the 
principle of Forced Oscillations ‘‘That the state of osciliation 
of a system of bodies in which the imitial conditions of 
