221 
than in nature; and by assuming that the sea was relatively at 
rest close to the bottom and stuck to it, so to speak, the greatest 
possible effect of roughness of the bottom was obtained. These 
data being assumed, the problem became a simple but rather 
lengthy application of Professor Stokes’ equations of fluid 
motion; and the result of the investigation was to shew that 
the internal friction of the sea was too small to produce a 
sensible effect; the angle of lagging not being more than 2” or 
1 
100,000 
posed to vary so as to give a tidal range nearly on the scale of 
nature. The retardation due to this small value of X would not 
for an ocean of which the depth or latitude was sup- 
be more than enough to occasion an increase in the length of 
the day of one second in one hundred millions of years! Prac- 
tically none at all. Mr Rohrs admitted that close to shores 
and in narrow channels the retarding action of the sea would 
be greatly magnified, but he thought that this increased action 
would be more than counterbalanced by the entire absence of 
tidal retardation in the parts of the globe where no sea existed. 
Besides, the hypothesis of the sea “sticking to the bottom” 
gives an amount of retarding force due to the roughness of the 
sea-bed greater than what could be the case under any circum- 
stances; hence the value of X so obtained will be a superior 
limit. One second of retardation in 100,000,000 years would 
only make an error of 12 seconds in the date of an eclipse 
observed 2500 years ago; and as the error to be accounted for 
in eclipses then recorded is about an hour and a half, 450 times 
12 seconds is required; therefore tidal retardation cannot, as 
some have supposed it might, account for this discrepancy. 
The discussion of the second problem shews that if a globe, 
4000 miles in diameter, composed of a thin crust and imperfect 
fluid interior, be made to rotate under the action of a force 
going through its phases in 27000 years, and if w and w' be the 
angular velocities of the globe at its crust, on the hypothesis of 
17 
