10 Trans. Acad. Sci. of St. Louis. 



We conclude therefore that if all the planets fell into the 

 sun they could not maintain his heat for a great length of 



i = S 



time, since ^j Eh i* small compared to T. We may observe 



that by the previous suppositions E k has been made to assume 

 very nearly the value of (7, as the neglected value of E p is 

 very small. 



But in order to estimate the total kinetic energy we should 

 take account of the rotations of the sun and planets and of the 

 orbital motions of the satellites. 



The energy of rotation of the satellites and of their orbital 

 motions is relatively insensible, and we may also disregard the 

 rotations of the planets ; but an accurate estimate of the en- 

 ergies of the planetary system would require us to consider 

 the energy of the sun's rotation. The moment of inertia of 

 the sun depends upon the law of density, and unfortunately 

 this can be inferred only approximately from certain hy- 

 potheses resulting from the theory of gases. Accordingly, it 

 does not seem worth while to pursue further the subject of 

 the energy of solar rotation. 



We have seen that a contraction of 69723 metres in the 

 sun's radius, the mass being supposed of homogeneous den- 

 sity, would maintain the observed radiation for 2180 years, 

 or that an annual shrinkage of 35 metres per year would 

 account for the observed output of light and heat.* Such a 

 rate of contraction would affect the diameter of the sun less 

 than a tenth of a second of arc in a thousand years, and 

 would be wholly inappreciable during the period covered by 

 exact observations. The fact that ancient and modern eclipses 

 are sensibly of the same duration, taken in conjunction with 



* Ritter has computed this annual shrinkage on the supposition that the 

 mass is heterogeneous and in convective equilibrium; and finds a value of 

 about 90 metres. If, therefore, the density follows the laws treated in the 

 next section, the shrinkage in the sun's diameter would be less than six- 

 tenths of a second of arc since the days of Hipparchus. Were even the 

 most refined measures available for the whole of this period, there would 

 still be no hope of confirming the shrinkage by observations made within 

 historical time. 



