650 On the “ Rigid Earth ” Paradox. [November, 
The beginning, so far as I know, of this “ rigid ” paradox, 
was a mistake of Sir W. Thomson’s, which Sir Edmund 
Beckett copied into one edition of his capital “ Astronomy 
without Mathematics that the rate of precession would 
not be the same in a fluid earth as in a rigid one, and that 
the actual rate (commonly explained on the assumption of 
an unyielding solid ball) would not apply to a perfect fluid. 
Now in the “ Philosophical Transactions ” for 1880 (p. 464) 
we find this entirely retracted. Prof. Darwin there italicises, 
as both his own result and Sir W. Thomson’s, that “ The 
precession of a fluid spheroid is the same as that of a rigid one 
which has an ellipticity equal to ” the fluid one’s. But mean- 
while, as they were correcting this slip, an exactly similar 
one was made about the tides. These are commonly ex- 
plained on the same easy idea of a rigid ball covered with 
sea ; and everyone may readily infer (though they would be 
quite wrong) that, if the Earth’s interior be as fluid as the 
sea, both would be deformed alike, and thus, every spot oi 
sea-surface preserving its distance above the bed unchanged, 
there would be no marine tide. They would err, because it 
is a thing “ not generally known ” that the school-book dia- 
grams all exactly reverse, as regards high and low water, 
the real effects in a general ocean as shallow as our actual 
ones. The Moon’s (or Sun’s) pull direct , that would, as they 
show, heap the waters under the pulling body, and pull the 
Earth from the further sea surface, would thus aCt were the 
ocean thousands of miles deep ; but as it is only 2 or 3 miles, 
this effeCt is vastly excelled and quite masked by another, 
namely, that the eastward rotary movement, common to the 
ground and waters, is retarded by the moon wherever they 
are going from her meridian, but accelerated where they are 
returning to it, — i.e., retarded during the six hours before 
moonrise or moonset, and accelerated during the six after 
those events. This heaps them up at moonrise and moon- 
set, making — were the ocean universal and friChionless — - 
high-water at those times, and low-water under the moon: 
the contrary of what the popular diagrams show. But as 
these would be correct for an ocean enormously deeper, so 
are they for Prof. Darwin’s “ bodily tides.” Accordingly the 
observations of Palmieri, when Vesuvius is most open, find 
low-lava , at moonrise and moonset, and high-lava following 
her upper and lower transits. Now when Prof. G. Darwin 
said, in 1879 (“ Phil. Trans.,” p. 28), “ Unless the viscosity 
were very much larger than that of pitch, the viscous sphere 
would comport itself sensibly like a perfect fluid, and the 
ocean tides would be insignificant,” this meant that the 
