422 Mr. G. A. Darwin on the Bodily Tides [May 23, 



Lunar Semi-diurnal Tide. 



Coefficient of 

 viscosity 

 x 10- 10 '. . 



Retardation 

 of bodily 

 tide. 



Height of 

 bodily tide is 

 tide of fluid 

 spheroid mul- 

 tiplied by 



Height of ocean 

 tide is tide on 

 rigid nucleus 

 multiplied by 



Acceleration of 

 high water 

 of ocean tide. 



Fluidity 

 96 

 721 



Eigidity oo 







41 min. 



2 hr. 25 min. 



3 hr. 6 min. 



1-000 

 •940 

 •342 



•ooo 



000 

 •342 

 •940 

 1-000 



3 hrs. 6 min. 

 2 hrs. 25 min. 

 41 min. 

 





Fortnightly Tide. 





1,200 

 12,000 

 Eigidity oo 



9 hrs. 



2 days 6 hrs. 



3 days 10 hrs. 



•985 

 •500 



•ooo 



•174 



•866 

 1-000 



3 clays 1 hr. 

 1 day 3 hrs. 

 



A comparison of the numbers in the first column with the viscosity 

 of pitch at near the freezing temperature (when I found by rough 

 experiments that its viscosity was about 1*3 X 10 8 ), shows how enor- 

 mously stiff the earth must be to resist the tidally distorting influence 

 of the moon. It may be remarked that pitch at this temperature is 

 hard, apparently solid and brittle ; and if the earth was not very far 

 stiffer than pitch, it would comport itself sensibly like a perfect fluid, 

 and there would be no ocean tides at all. It follows, therefore, that 

 no very considerable portion of the interior of the earth can even 

 distantly approach the fluid condition. 



This does not, however, seem conclusive against the existence of 

 bodily tides in the earth of the kind here considered ; for, under the 

 enormous pressures which must exist in the interior of the earth, even 

 the solidest substances might be induced to flow to some extent like a 

 fluid of great viscosity. 



The theory of the bodily tides of an " elastico-viscous " spheroid is 

 next developed. The kind of imperfection of elasticity considered is 

 where the forces requisite to maintain the body in any strained con- 

 figuration diminish in geometrical progression, as the time increases in 

 arithmetical progression. There are two constants which define the 

 mechanical nature of this sort of solid : first, the coefficient of rigidity 

 n, at the instant immediately after the body has been strained ; and 

 second, "the modulus of the time of relaxation of rigidity" t, which 

 is the time in which the force requisite to maintain the body in its 

 strained position has diminished to e~ l or "368 of its initial value. I 

 am not aware that there is any experimental justification for the 

 assumption of such a law ; but after considering the various physical 



