Chase.] 



596 



[Jan. 19, 



the mean length or exceeding it. The simplicity of thermodynamic rela- 

 tions in central force {Proc. Amer. Phil. Soc, xiv, 651), suggests an equally 

 simple means of estimating the proportionate number of mean excursions. 

 Peirce's views respecting the vis viva of rotSit'ioa. (see Proc. Amer. Phil. Soc, 

 xvi, 300), involve the consideration of the mean moment of inertia, which 



2 7-2 



is represented by -g-, the momentum being represented by r j/i = 



.632455 r, which differs from the estimate of Clausius by less than ^V o' 

 one per cent. 



370. Cosmical Influence of Botary Inertia. 



"We may naturally suppose that, among the many harmonic influences 

 which have combined in fixing the relative positions of the several planets, 

 rotary inertia should be represented Among the evidences which 

 strengthen such a supposition, are the following: 



The ratio of the rotating radius to the projectile radius of mean rotary 

 vis viva is 2.5 ; the reciprocal ratio gives the vector-ratio in opposition, 1.5 ; 

 the ratio of the rotating radius, less that of the projectile radius is .6 ; the 

 reciprocal of 1.5 is §, which also represents the centre of linear osciHation 

 and the radius of subsidence-collision ; the viscous rupturing radius of 

 subsidence is ^. 



371. Reaction of Botary Vis Viva. 



A fact which has an important bearing on Delaunay's hypothesis, as 

 well as on the second law of thermodynamics, is shown by the recipro- 

 cal ratios of the foregoing note, and more strikingly, by the reactionary 

 influence of Neptune. If we look to a like reaction on the part of the 

 other planets, we find the following harmonic ac^cordauces : 



