PRESIDENT’S ADDRESS. 53 
motion have disappeared through the resistance which this 
motion experiences is coperiodic with the forces which 
animate it.”’ In other words, the ocean is forced to oscillate 
eypchronously with the tide-generating forces. “ From this 
I concluded,” says Laplace, “ that if the sea is actuated by a 
periodic force expressed by the cosine of an angle which 
increases uniformly with the time, there results from it a 
partial tide, expressed by the cosine of an angle increasing 
in the same manner, but in which the constant involved in 
this angle and the co-efficient of this cosine may be, by virtue 
of accessory circumstances, very different from the same 
constants in the expression for the force. and can be deter- 
mined oniy by observation. The expression for the actions 
of the sun and. moon upon the sea can be developed in a con- 
vergent series of similar cosines. Whence arise as many 
partial tides as, by the principle of the co-existence of small 
oscillations. being added together, constitute the tide which 
is observed at a port.” Laplace determines three principal 
classes of oscillations—lIst, those independent of the rotary 
motion of the earth; 2nd, those dependent on the earth’s 
rotation, and having a period of about one day; 3rd, chose 
dependent on the earth’s rotation, and having a period of 
about one half-day. The excess of one high-water over the 
adjacent one, which we have already referred to as the 
diurnai inequality, he shows is-due to oscillations of the 2nd 
class. According to Newton’s theory, this difference in 
height between the two daily tides should be large at such a 
port as Brest, where, as a matter -of facr, it 1s scarcely: sen- 
sible. Newton explained the discrepancy by the inertia of 
the water, whereby the effects of ona oscillation were. so to 
speak, carried over into the next. But Laplace showed 
that it really depends upon the law of the depth of the sea, 
and that, if the ocean were of uniform depth over the whole 
earth, it would vanish complecely. It was thought at the 
time that this gave the explanation of the non-existence of 
diurnal mequality im the European perts whose tides had 
been recorded; but. as tides in other parts of the -world 
came to be examined, it was found that the North Atlantic 
tides were peculiar in this respect, snd that elsewhere, as a 
general rule, the two daily tides are of unequal height. So 
that this result differs as much from actuality as Newton's. 
Amengst other important deductions made by Laplace m 
the ccurse of his work was the proposition that the move 
ments of the earth’s axis are the same as they would be if 
the sea formed with the earth a solid mass. This was ‘con- 
trary to the opinion of most mathematicians at that time, 
