277 



[Chase. 



The coefficients of a are, 5 X 8, 6 x 8, 9 x T, 10 X ", 10 X " + 8, 10 X 

 7 -|- 3 of 8^ being made up of multiples or sums of the phyllotactic num- 

 bers, 2, 3, 5 and 8, and the secondary phyllotactic number, 7. 



230. Relations of Central Force to Tliermal Constants. 



I have shown {Proc. A. P. S., xiv, 651) that the ratio of heat Under con- 

 stant volume to heat under constant pressure, as deduced from purely 

 theoretical considerations, is t:^ -f 4 : 2-^ or 1 : 1.4232. The elements for 

 computing this ratio are: 1, the synchronism of oscillations, under the 

 actio'n of central forces, in all orbits which have the same major axis ; 2, the 

 kinetic theory of gases, which supposes that all the paths of clashing particles 

 are rectilinear, and therefore in orbits of unitary eccentricity, one extremity 

 of each path corresponding with the centre of a synchronous circle ; 3, 

 the consequent ratio of mean rectilinear vis viva, or mean vis viva of con- 

 stant gaseous pressure, to synchronous mean circular vis viva,, or mean 

 vis viva of constant volume ; 4, the thermodynamic doctrine that equal 

 quantities of heat correspond to equal increments of vis viva and to equal 

 increments of temperature ; 5, the proportionality of mean vis viva to 

 mean distance of projection against uniform resistance ; 6, the determina- 

 tion of the radial locus at which the mean velocity of linear oscillation, 

 or of mean gaseous pressure, would be acquired both in centrifugal and in 

 centripetal motion. This theoretical determination of the ratio of specific 

 heats proceeds on the hypothesis of Boscovich, that central forces continue 

 to act, at all distances from the centre, with accelerations which vary in- 

 versely as the square of the distance. There are many reasons for be- 

 lieving that this law does not hold, even in the tethereal condition, within 

 the radius of inertial aggregation, and it seems likely that careful experi- 

 ments may bring to light many kinds of deviation from the theoretical 

 value, the study of which will greatly extend our knowledge of atomic 

 and molecular structure. The most accurate experimental determinations 

 of the ratio that have been published hitherto seem to range between 

 1 : 1.4053 and 1 : 1.421. These values indicate an orbital eccentricity of 

 from .9874 to .9985. 



230. Tests of Thermal Belations by Solar Mass and Distance. 



The estimates which I have hitherto made of the central energies of the 

 solar system, from measurable tendencies to equilibrium between gravi- 

 tating and explosive or centripetal and centrifugal energies (P?'oc. J.. P. S., 

 xii, 392-4, xix, 354, et al.), have been based upon the supposition that all 

 the calorimetric measurements were made under constant pressure. C. v. 

 TJian {Abstr. in, Jour. Chem. Soc, March, 18S2, p. 265.) gives five estimates 

 for the heat of combustion of H^O, from which estimates of solar mass and 

 distance mav be deduced hv the method of Note IG. 



