Oct. 1 and Dec. 3, 18T5.] 



651 



r Chase. 



FURTHER DYNAMIC CO-ORDINATIONS. 



By Pliny Eakle Chase, 



Professor of Mathematics in Haverpord College. 



{Bead before the American PMlosopMcal Society, October 15, and December 



3, 1875.) 



A further extension may be given to my co-ordination of the great 



natural forces, by means of the thermodynamic rehxtions which subsist 



between constancy of pressure and constancy of volume. 



In central forces, varying inversely as the square of the distance, a 



perpetual oscillation through a linear ellipse 



AC, with foci at the centre of a circle and at 



2?', would be synchronous with a perpetual 



revolution around the circle. The complete 



linear-elliptical orbit being = 2d, the mean 



velocity of linear oscillation, or the velocity of 



2 

 constant mean gaseous pressure = — of the 



velocity of revolution ; a velocity which would 



be attained, both in the centripetal and in the 



centrifugal phase of the oscillation, at lA2d2r 

 o 

 2- r 



The ratio of heat under eon- 



stant volume to heat under constant pressure, as experimentally deter- 

 mined, is 1 : 1.421.* 



Let f = radius of a gaseous nucleus which is sufficiently condensed to 

 allow of chemical combinations, or the radius of constant volume ; r = 

 radius of constant mean pressure. The vis viva of free revolution in a 

 circular orbit varying inversely as radius, the ratio of the mean nucleal 

 and atmospheric forces riiay be represented by the proportion 

 r : r : : 1 : 1.4232 



In elastic media, as the distances from the centre increase in arith- 

 metical progression, the densities decrease, in geometrical progression if 

 the central force is constant, in harmonic progression if the central force 

 varies according to the law of inverse squares. Whatever may have 

 been the beginnings of cosmo-taxis, whether through nebular condensa- 

 tion, meteoric accumulation, explosive rupture, or other unknown pro- 

 cess, the secular mean actions and reactions between opposing forces 

 should lead to similar numerical and harmonic results. In the lan- 

 guage of Herscheljf " Among a crowd of solid bodies of whatever size, 

 animated by independent and partially opposing impulses, motions oppo- 

 site to each other must produce collision, destruction of velocity, and sub- 



*Tynclall, Heat a Mode of Motion, 4th Ed., Sect. T4. 

 f Outlines of Astronomy, Sect. 872. 

 A.. P. S. — VOL. XIV. 4f 



