On the Tides. 121 
into the results of the analysis as arbitrary quantities, which ought 
thus to represent the observations, if the universal gravitation is 
in fact the true cause of) the tides. The principle is this: The 
state of a system of bodies in which the primitive conditions of 
motion have disappeared by the resistance it meets with, is pe- 
riodical, as well as the forces which-animate tt. By reuniting 
this principle to that of the coexistence of very small uscillations, 
_ Ihave obtained an expression for the height of the tides, of 
which the arbitrary quantities comprise the effect of the local 
circumstances of the port. To deduce this, I have reduced the 
_ generating expression of lunar and solar forces acting upon the 
ocean into a series containing the sines and cosines of angles in- 
_ ereasing proportionally to the time. Each term of the series 
may be considered as representing the action of another object, 
which moves uniformly at a constant distance, in the plane of 
the equator. Thence arise several kinds of partial tides, the 
periods of which are about half a Innar day, a day, a month, a 
half-year, a year; and lastly, eighteen years and a half, which is 
the duration of the periodical motion of the uodes of ‘the lunar 
orbit. 
Ip the book which I have quoted of the Mécanique Céleste, 
I have compared this theory with the observations made at 
Brest at the commencement of the last century 5 and | have 
determined the constant arbitrary quantities relative to this 
port. I was curious to see whether these circumstances were 
found to be the same by the ebservations made a century after- 
wards, or whether, they ‘have experienced any alteration by the 
changes which the operations of nature and art have produced, 
d Sither at the bottom of the sea or in the port, and on the ad- 
jacent coasts. The result of this inquiry is, that the actual 
heights of the tides, in the port of Brest, surpass the heights 
_ determined by the old observations by about j4th. One part 
_ of this difference may arise from the distance of the points where 
these observations were made; another part may be attributed 
to the errors of the observations: but these two causes do not 
seem to me suflicient to produce the whole difference which in- 
_ dicate with great probability a secular change in the action of 
the sun and moon on the tides of Brest, if we could be well 
assured of the exactness of the graduations of the old scale, and 
taking into account its inclination to the horizon. But the un- 
certainty we are in with respect to this point, does not permit 
s to pronounce upon this change, which ought in future to 
x the attention of observers. In other respects the agreement 
$ surprising between the old and the modern observations, as’ 
‘Well as the theory; with regard to the variations of the heights 
the tides depending on the declinations and distances of the 
heavenly 
