INTRODUCTION. 81 



is incompatible with the fission hypothesis, it is found necessary to 

 conclude that, at least for a part of the earth-moon history, the viscosity 

 of the part of the earth distorted by tides has been small. Hence that 

 viscosity which best explains the inchnation of the lunar orbit causes 

 trouble when considering its eccentricity. Since numerical details were 

 not worked out in the discussion of the eccentricity for large viscosities, it 

 is not known to what quantitative extent the two things are antagonistic, 

 and it may very well be that a viscosity could be assumed which would 

 explain largely the inclination and not be particularly unfavorable to the 

 eccentricity. There were so many partial contradictions and so much 

 uncertainty that Darwin attempted to draw no final conclusion from this 

 discussion (3, p. 879). 



Another question, still more critical, is the distance from the earth to 

 the moon when the day and month were of equal length. In 2, section 18, 

 neglecting part of the action of the sun, Darwin found that the day and 

 month were equal at 5*^ 36™, corresponding to a distance between the centers 

 of the earth and moon of 10,000 miles. In 3, section 22, including all the 

 action of the sun, he found that the initial period and distance were less. 

 The numerical results were not obtained, but he stated (3, section 22, p. 835) : 



It is probable that an accurate solution of oiu- problem would differ considerably from 

 that found in "Precession" (5'^ 36™), and the common angular velocity of the two bodies 

 might be very great. 



In the summary of this same paper, p. 877, he said: 



In section 22 it [the sun's action] is only so far considered as to show that when there 

 is identity of periods of revolution of the moon and earth, the angular velocity must be much 

 greater than that given by the solution in section 18 of "Precession." 



Computations given at the end of the present paper, section 14, show 

 that the difference is actually unimportant. 



Apparently, in order to make this fission hypothesis workable it must 

 be shown that if the day and month ever were equal they had such a period 

 that the distance from the earth to the moon was much less than 10,000 miles. 



There are many places where it would be easy for a careless reader 

 of Darwin's work to lose the connection between the conclusions and the 

 hypotheses upon which they were based. For example, taking approxi- 

 mately that viscosity which would produce the most rapid tidal evolution, 

 he found ^ that 57,000,000 years ago the day was 6'' 45"" long, and that 

 the length of the month was 1.58 of our present days. Notwithstanding 

 the fact that this is quite a different thing from having proved that 

 the earth-moon system has actually gone through this series of changes, 

 undoubtedly many first-hand and more second-hand readers of Darwin's 

 work have supposed that this computation gives a fairly certain and 

 definite account of the evolution of these bodies. But it is interesting to 

 find in the same memoir, section 14, under the hypothesis that the observed 

 secular acceleration of the moon's mean motion is due entirely to tidal 

 friction, and also that the earth is purely viscous, the conclusion that the 

 length of the month is now being increased at the rate of only 2** 20" in 



> 2, Section 15, Table IV, and pp. 529-531. 



