264 
DR. HAROLD JEFFREYS ON TIDAL FRICTION IN SHALLOW SEAS. 
is equal to fit — n, which is sufficiently near to H for our present purpose. Hence the 
friction of the tide will have a damping effect on this component of the earth’s 
rotation, which is not altered by the other couples acting, since none of these have a 
notable effect in diminishing the amplitude of the motion. If the average value of 
the dissipation is taken to be 5 x 10 18 ergs per second, this being rather more than was 
found in the South China Sea, and we remember that the average of sin 2 $ is sin 2 i, 
where i is the obliquity of the ecliptic, we find that the amplitude of fl sin § would he 
reduced to l/e of its value in 2 x 10 M years. This is of the same order as the probable 
age of the earth. If H remained constant this would show that the inclination ot 
the Equator to the ecliptic would be reduced by in about 2 x 10 4 years. Actually 
D is decreasing, so that if the rate were maintained it would be reduced to l/e of its 
value in about 10 10 years, a longer time than was found, on the assumption stated, to 
be enough for a similar reduction in the obliquity. Thus we can infer that the 
obliquity is at present diminishing, though there is no reason to believe that there 
has been any observable change in it in historic times. Even if there were as much 
dissipation in the diurnal tides as in the semi-diurnal ones this would hardly be 
possible. 
[Note added September 16. —Mr. Taylor asks me to point out certain errata in 
his paper “ Tidal Friction in the Irish Sea.” On p. 2, 1-is twice written for 
V r 
1 the correct form is used in equations (4) and (5). On p. 9, line 9, is 
v r 
Greenwich mean time of high water at full and change of the moon at the place 
considered, whereas the “ establishment ” is the local mean time of this event. In 
equation (16), £ + T x should be t — T 1( and in equation (18), £ + T 0 should be t — T 0 . On 
pp. 19 and 20, sin 2 </> 0 is consistently written for sin 20 o ; equation (33) is correct. 
In this paper, as in Taylor’s, integrals over a period are always determined as if 
the current velocity and the tide height varied harmonically. This could be strictly 
correct only if the frictional force was proportional to the velocity, which is not the 
case. It appears, however, that the departure from the harmonic variation is not 
enough to produce any great alteration in these integrals. 
I wish to express my thanks to Mr. H. W. Braby for drawing the maps in this 
paper.] 
