550 
MR. G. H. DARWIN ON PROBLEMS CONNECTED 
dn JD 
But the equation of tidal friction is — = ——. Therefore 
at C 
Now 
Therefore 
d|_i 
dt fM Gn () 
d L wa? iS 
7t=Tv c 008 
dL wr o/i 
(19') 
All the quantities on the right-hand side of this equation are constant, and there¬ 
fore by integration we have for the change of longitude 
wa~ 
A L=im 0 —(i— 1) cos ~9. 
But since (o 0 =n 0 — S2 0 , and tan 2e 0 =f-• -- VC °p , therefore in degrees of arc, 
( xwcc* 
T 180 19 n 0 —fl 0 , n t u x I. 
aL=“ pm 09() —-— 5 cot 2e 0 (^— 1) cos'-#. 
In order to make the numerical results comparable with those in the paper on 
“ Precession,” I will apply this to the particular case which was the subject of the first 
method of integration of that paper.* It was there supposed that e 0 =l7° 30', and it 
was shown that looking back about 46 million years ^ bad fallen from unity to ‘88. 
Substituting for the various quantities their numerical values, I find that 
— aL= 0 o, 31 cos 3 #=19' cos' 2 9. 
Hence looking back 46 million years, we find the longitude of a point in latitude 
30°, further west by 4§' than at present, and a point in latitude 60°, further west by 
14j/—both being referred to a point on the equator. 
Such a shift is obviously quite insignificant, but in order to see whether this 
screwing motion of the earth’s mass could have had any influence on the crushing of 
the surface strata, it will be well to estimate the amount by which a cubic foot of the 
earth’s mass at the surface would have been distorted. 
The motion being referred to the pole, it appears from (17) that a point distant p 
from the axis shifts through — in the time Bt. There would be no shearing if 
* “ Precession,” Section 15. 
