852 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
make the lao- f'' of the principal slow semi-diurnal tide, of speed 2n—2I2, equal to 
10°, 20°, 30°, 40°, 44°. (The curves thus correspond to the same cases as in §§ 7 
and 10). Values of sin 4f s , sin 2g x , sin 2xh x , sin 2g x , sin 4f x , when x=i, ii, iii were then 
computed, according to the theory of viscous tides. 
These values were then taken for computing values of <f>( iii), xp( i) with 
values of i=0°, 15°, 30°, 45°, 60°, 75°, 90°. The results were then combined so as to 
give a series of values of <1 logy dt or dejedt, and these values were set out graphically 
in the accompanying fig. 8. 
Fig. 8. 
Diagram stowing the rate of change in the eccentricity of the orbit of the satellite for various 
obliquities and viscosities of the planet when e is small^. 
In the figure the ordinates are proportional to dejedt, and the abscissae to i the 
obliquity ; each curve corresponds to one degree of viscosity. 
From the figure we see that, unless the viscosity be so great as to approach 
rigidity (when f“= 45°), the eccentricity will increase for all values of the obliquity, 
except values approaching 90°. 
The rate of increase is greatest for zero obliquity unless the viscosity be very large, 
and in that case it is a little greater for about 35° of obliquity. 
It appears from the paper on “ Precession ” that if the obliquity be very nearly 90°, 
the satellite’s distance from the planet decreases with the time. Hence it follows 
from this figure that in general the eccentricity of the orbit increases or diminishes 
with the mean distance ; this is however not true if the viscosity approaches very 
near rigidity, for then the eccentricity will diminish for zero obliquity, whilst the 
mean distance will increase. 
