864 
MR. G. H. DARWIN ON THE SECULAR CHANGES IN 
§ 29. The change of eccentricity when the viscosity is large. 
I shall not integrate the equations in the case where the viscosity is large, because 
the solution depends so largely on the exact degree of viscosity. 
If the viscosity were infinitely large, then in the retrospective integration the eccen¬ 
tricity would be found getting larger and larger and finally would become infinite, 
when \ is equal to -§. This result is of course physically absurd. If on the other 
hand the viscosity were large, we might find the eccentricity diminishing, then 
stationary, and finally increasing until /V=f , after which it would diminish again. 
Thus by varying the viscosity, supposed always large, we might get considerable 
diversity of results. 
VII. 
SUMMARY AND DISCUSSION OF RESULTS. 
§ 30. Explanation of problem.—Summary of Parts I. and II. 
In considering the changes in the orbit of a satellite due to frictional tides, very 
little interest attaches to those elements of the orbit which are to be specified, in order 
to assign the position which the satellite would occupy at a given instant of time. 
We are rather here merely concerned with those elements which contain a description 
of the nature of the orbit. 
These elements are the mean distance, inclination, and eccentricity. Moreover all 
those inequalities in these three elements, which are periodic in time, whether they 
fall into the class of “ secular” or “periodic” inequalities, have no interest for us, and 
what we require is to trace their secular changes. 
Similarly, in the case of the planet we are only concerned to discover the secular 
changes in the period of its rotation, and in the obliquity of its equator to a fixed 
plane. 
It has unfortunately been found impossible to direct the investigation strictly 
according to these considerations. Amongst the ignored elements are the longitudes 
of the nodes of the orbit and equator upon the fixed plane, and it was found in one 
part of the investigation, viz.: Part III., that secular inequalities (in the ordinary 
acceptance of the term) had to be taken into consideration both in the five elements 
which define the nature of the orbit, and the planet’s mode of motion, and also in the 
motion of the two nodes. 
In the paper on “Precession” I considered the secular changes in the mean distance 
of the satellite, and the obliquity and rotation-period of the planet, but the satellite’s 
orbit was there assumed to be circular and confined to the fixed plane. In the present 
paper the inclination and eccentricity are specially considered, but the introduction of 
these elements has occasioned a modification of the results attained in the previous 
