Cuap. II., § 2.] 
Laplace’s dynamics than of astronomy, and to estimate all the 
Dynamical causes of movement of the particles of a heavy fluid, 
Theory. 
(74.) 
Its incom- 
pleteness, 
5. 
af? 
classes 
Tides. 
surrounding a spheroidal rotating nucleus exposed to 
the attractions of the sun and moon. This he did in 
a series of memoirs, more systematically condensed in 
the Traité de Mécanique Céleste, and it may safely 
be affirmed that no other mathematician of his day 
was equal to the labours and disappointments of an 
investigation attended with every species of difficulty, 
in which each result must be attained by a combina- 
tion of general sagacity with mathematical rigour, and 
for the verification of which observations were yet in 
a great measure wanting. The Theory of the Tides 
was, upon the whole, the most arduous and compli- 
cated problem which could well be conceived, in a 
branch of science (hydrodynamics) hitherto remark- 
ably little successful in predicting the results of the 
most simple and arbitrarily selected experiments. 
That Laplace has been in a measure successful 
in such an undertaking must be considered the highest 
test of his genius, especially in reducing his mathe- 
matics to practical application; but the result has 
been a treatise so profound and obscure (I mean as 
regards the tide theory), that very few persons have 
attempted to master its difficulties. Mr Airy, the 
present astronomer royal, has done a great service 
to men of science, and to that far wider community 
whom the laws of the tides nearly interest, by giving 
a connected and tolerably elementary view of La- 
place’s investigation, which he states confidently to 
be “ the most obscure of the Mécanique Céleste.” 
In this theory the figure of the ocean at any 
moment is considered as a dynamical problem ; and 
that figure as a momentary state arising from the in- 
ternal movements of the fluid itself, as well as from 
the variation of the external forces. The resulting 
, differential equations, expressing the attractions of 
the sun, moon, and earth, the rotatory movement of 
the earth, and the pressure of the water itself in mo- 
tion, are abundantly complex, and the solutions only 
partial and imperfect, The inferences from these 
solutions, too, partake not only of their imperfection, 
but, since they take no cognisance of the irregular 
distribution of land and water, present cases almost 
impossible to verify by observation. Some of the 
results are indeed so paradoxical, that without bet- 
ter evidence of their truth we do not further allude 
to them. 
The tidal effects are divided by Laplace. into three 
classes ; the distinction of which, however, cannot be 
called a discovery of his. The jirst class are inde- 
pendent of the earth’s rotation, and are practically 
insignificant. The second class includes the diurnal 
tide occurring once in about 24 hours. Concerning 
PHYSICAL ASTRONOMY—LAPLACE. 
817 
it, Laplace draws this conclusion, that its rise and fall 
(not, however, its horizontal motion) are insensible if 
the depth of the ocean is uniform ;* and being practi- 
cally insensible in most latitudes, we have thence an 
argument of more or less weight for a general 
tendency to uniformity in the depth of the sea, The 
third class of tides are the ordinary semi-diurnal 
tides. They afford, as Newton acutely perceived, the 
most direct and attainable measure of the relative at- 
tractions of the sun and moon. We have the sum of 
these attractions at the conjunctions and oppositions 
of the luminaries, and the difference when they are 
90° apart ; and a higher maximum when both bodies 
are without latitude. From the observation of the 
tides on the Severn near Bristol, Newton computed 
the relative action of the moon and sun to be as 
4'48 to 1; but this value is much too great, and 
gave far too large a relative mass to the moon. The 
result in the harbour of Brest, from observations made 
under Laplace’s direction, is about 2°90 to 1; and the 
moon’s mass 7;th that of the earth, agreeing almost 
identically with that deduced from the nutation of 
the earth’s axis caused by her attraction. Observa- 
tions at London and Liverpool reduced by Sir John 
Lubbock and Dr Whewell give about 2°66 to 1.? 
From the general theory of Laplace, the follow- 
(76.) 
ing results have been deduced with confidence :—(1.) Laplace's 
That the stability of the ocean is secure, whilst the ™*™!*- 
density of the ocean is inferior to that of the earth 
generally ; which it is about five or six times. (2.) 
That the phenomenon of precession is not modified 
by the fluid covering of the globe. 
In the application of his theory to special cases, 
Laplace is compelled to have recourse to an assump- 
tion entirely arbitrary—namely, that the periodic 
fluctuations, however otherwise modified by circum- 
stances, recur in the same periods as the causes to 
which they are due. In this manner he conciliates the 
results of observation with his theory, which the latter 
would have been altogether incompetent to predict. 
The general merits of Laplace’s theory we will sum 
(77.) 
(78.) 
up in the words of Mr Airy, who, of all his succes- Character 
sors, has probably most attentively studied it :—* If, 2 
La- 
lace’s in- 
putting from our thoughts the details of the investi- vestigation. 
gation, we consider its general plan and objects, we 
must allow it to be one of the most splendid works 
of the greatest mathematician of the past age. To 
appreciate this, the reader must consider—tirst, the 
boldness of the writer who, having a clear under- 
standing of the gross imperfection of the methods of 
his predecessors, had also the courage deliberately 
to take up the problem on grounds fundamentally 
correct (however it might be limited by suppositions 
afterwards introduced) ; secondly, the general diffi- 
1 Dr Young asserts that the conclusion will not hold unless the depth be also evanescent. Laplace has shown in his Fifth 
Book that the disappearance of diurnal tides will take place only when the nucleus is completely covered. 
* These ratios, however, being found to depend upon the configuration of the coast or estuary, cannot be used directly to de- 
termine the relative action of the sun and moon, 
VOL. I. 
See Phil. Trans., 1845, p, 42. 
5.1L 
