REPORT ON ASTRONOMY. 
189 
useless. But it may be possible to choose functions for these ex¬ 
pansions, by the use of which the series may become convergent 
sin ^ * 
(such perhaps as b cps 6 instead of sin 0). At all events this 
may be fixed on as being at present the difficult problem of 
Physical Astronomy. 
In the preceding suggestions I have endeavoured to fix on 
definite points for the attention of astronomers. I need not 
mention that there are other subjects (the theory of Uranus, for 
instance,) in which the existence of difficulties is known, but in 
which we have no clue to their explanation. 
Observatory, Cambridge, 
May 2, 1832. 
G. B. Airy. 
Report on the Tides . By J. W. Lubbock, V.P. Treas. R.S, 
The connexion between the Tides and the motion of the moon 
was known to the ancients; but we are indebted to Newton for 
the discovery of the mechanical principles which regulate these 
phenomena. Newton contented himself with explaining the 
most obvious results of observation, and left all the details open 
to future inquiries. The subject was next taken up by Ber¬ 
noulli, Euler and Maclaurin, about the same time, in their seve¬ 
ral treatises which participated in the prize awarded by the 
Academy of Paris in 1740. Laplace afterwards undertook this 
difficult investigation, and succeeded in forming the differential 
equations from which the explanation of the phenomena is to 
be derived. The integration of these equations presents, how¬ 
ever, so many difficulties, that he confined his attempts to a very 
simple case, namely, that in which the depth of the ocean is 
constant, and the solid nucleus but little different from a sphere. 
Even in this case, his analysis is far from complete, andcon- 
tributes but little to unravel a question which he has character¬ 
ized, as “la plus epineuse de l’Astronomie Physique.” 
Finally, Laplace had recourse to the following indirect con¬ 
sideration, namely, “ that the state of any system in which the 
primitive conditions have disappeared through the resistances 
which its motion encounters , is periodical with the forces which 
act upon it” Hence he concludes, that if the system is dis- 
