Chase.] 5 i 4: [Nov. 4, 



of one per cent, greater than Laplace's estimate and than the mean value 

 which is indicated by other photodynamic considerations. 



101. Earth's Rigidity. 



Sir William Thomson concluded, from investigations of tidal action and 

 equinoctial precession, that "the earth as a whole is much more rigid than 

 any of the rocks that constitute its upper crust," and that the mean tidal 

 effective rigidity must be greater than that of glass. The inconsistency 

 of this hypothesis with the belief of the internal fluidity of the earth led 

 many to question it. Gen. J. G. Barnard (Smithsonian Contributions, 

 240) applied the principles of the gyroscope to the explanation of preces- 

 sion, and endeavored to show that no increase in the rate of precession 

 arises from fluidity. Thomson subsequently modified his views (Brit. 

 Assoc. Kep., 1876) in accordance with his theory of vortex-atoms, by 

 considerations based on the quasi-rigidity introduced into a liquid by vor- 

 tex motion. The stress of the sethereal waves must have an important in- 

 fluence both upon the gyroscopic and upon the vortical tendencies, and 

 the rapidity with which they are propagated may perhaps furnish the sub- 

 stitute for the inconceivable rigidity which seemed to be required in the 

 first discussion of the problem. 



103. Sun's Internal Temperature. 



In Note 58, I gave two photodynamic estimates of solar temperature, 

 the second being 3.07 per cent, greater than the first. The second esti- 

 mate was based on the hypothesis that the whole mass of the Sun is either 

 fluid or gaseous, so that ever}^ particle is continually yielding to tendencies 

 toward Sun's centre, toward the centre of gravity of the solar system and 

 toward the immediate centre of gravity. If the whole mass could be 

 collected at Sun's centre, it would revolve about the centre of gravity of 

 the solar system in less than three hours, but the rotation on the axis 

 which partially compensates for the tendency to revolution, requires about 

 25.5 days. The orbital motion of the Sun about the centre of its stellar sys- 

 tem furnishes a slight additional compensation, but the photodynamic 

 stress seems to be mainly represented by radial oscillations which are syn- 

 chronous with the orbital revolution which Sun's centre would have if it 

 were free. The potential velocity which represents such radial oscillations, 

 is that which would be acquired by vertical fall through half of the diam- 

 eter, or perihelion parabolic velocity. 



103. Earth's Internal Temperature. 



The small mass of Earth interposes little opposition to orbital tenden- 

 cies, and its greatest velocity of axial rotation is only about g^^ as great as 

 its solar orbital velocity. If Earth's whole mass was homogeneous, gravity 

 within its mass would vary as distance from centre, and the mean tendency 

 to orbital velocity, in reaction against the stress of sethereal undulations, 

 would be represented by a virtual fall through \ of radius, or 990.7 miles. 



