Chase.] 3^ [July 21, 



taueous rotation and transmission,* will doubtless contribute to the proper 

 determination of data for finding the practicable equivalent, in any given 

 case. 



According to tlie dynamical theory of gases, the average radial velocity, 

 which is found by Prop. Ill, is the velocity which represents constancy 

 of volume, in any aggregation of a homogeneous elastic fluid. 



We liave alread}' seen (I) that dynamic constancy of pressure produces 

 the velocity of circular revolution ; and by the principles of thermody- 

 namics, specific heat varies as vis viva. Prop. IV, tlierefore, furnishes an 

 exact mathematical accordance with the empirical ratio betAvecn heat of 

 constant volume and heat of constant pressure,! the representative of con- 

 stant pressure in a perpetual radial oscillation, being the radius of mean 

 excursion ; the representative of constant volume, the radius of mean 

 velocity; while the vires vivce, of circular revolution due to constant pres- 

 sure and of circular revolution maintaining constant volume, are inversely 

 as their respective radii. Newcomb showed^: that if there is actual collision 

 of particles, they can neither be perfectly hard and spherical, nor hard 

 and not spherical. There must, therefore, be elasticity or something 

 analogous to elasticity, either in the gaseous particles themselves, or 

 in their relative motions. Peirce's views, together with the fact that 

 vis viva varies as the quantity of motion, (the quantity of motion, in 

 perpetual oscillation under uniform resistance, being proportional to the 

 average velocity), seem to involve the probability that there is no absolute 

 collision, but the phenomena are due to simple motions, and are independ- 

 ent of the nature of the particles themselves. The vis viva of constant 

 circular velocity varying inversely as radius, the product of such vis viva 

 by radius, for any given central force, is a constant quantity. § 



Prop. V may perhaps prove suggestive, in the study of the mechanical 

 differences between fluidity and solidity, and of the laws of chemical com- 

 bination, as well as in the elucidation of the nebular hypothesis, of which 

 some illustrations are given below. I have already shown || that Alexan- 

 der's planetary ratio, 1.8, which is the | power of the thermodynamic 

 ratio 1.4233, appears in the explosive energy of H.p, and that this energy 

 is directly traceable to the limiting velocity of synchronous rotation and 

 revolutionT[ under the same primitive impulses (I, III). 



If the central force/, in Prop. VI, is solar gravity, the limiting velocity 

 (n Tt i/Tv ) of uniform impulses which account for solar and planetary 



*loc. cit., Feb. 4, 1851. ^ 



t The principal estimates of — are: Guthrie, Rcgnault, 1.41; Masson, 1.419; 

 Tyndall, 1.421. 



J loc. cit , 1801. 



g The various vires vivce considered In the present paper are : 



V. V. of Interior nucloal rotation in an unchanging nucleus, varying as r-: 



V. V. at any point within a homogeneously e.xpanding or contracting nucleus, 

 varying Inversely as r2; 



V. V. of free revolution communicable by Interior nucleal rotation in an un- 

 varying nucleus, varying as r; 



V. t'. of free revolution due lo fall towards, or repulsion from centre, varying 

 Inversely asr. 



IProc.S. P. A., xll,394. 1[ lb., and xlil, 142. 



