1882.] ^^* [Chase. 



tional exponent f ; the actions and reactions of elasticity and inertia in nu- 

 cleation, assign, as I have shown, the product of two phjilotactic expo- 

 nents, 2 X 1= f. in the ratio of variability between the nucleal radius 

 and Laplace's limiting radius ; the relations between density and distance, 

 in elastic media, change exponential to numerical coefficients. All of these 

 phyllotactic relations spring from simple and elementary mathematical 

 principles, to which the actions of central force must yield. If we call 

 the fundamental force radiodynamic, we may' be continually reminded of 

 its alternating centripetal and centrifugal tendencies. If we call it photo- 

 dynamic, the term will be naturally suggestive of the all-pervading elas- 

 ticity or quasi-elasticity which propagates the rays of light and thus be- 

 comes the medium through which we get all our knowledge of heavenly 

 bodies, as well as the largest portion of our knowledge of all earthly phe- 

 nomena. 



190. Phyllotaxy of Virtual Areas. 



The planetary virtual areas. Notes 159 and 164, are jointly related 

 through the last two of the elementary phj'llqtactic principles of the fore- 

 going note. Beginning with the largest and primitively central planetary 

 mass, the laws of nucleation and elasticit5% acting first outwardly from the 

 Sun and then inwardly, help to determine the reactionary vis viva of Saturn, 

 Neptune, Uranus, Earth, Venus, Mars and Mercury, in regular succession. 

 In passing from the extra-asteroidal to the intra-asteroidal group, another 

 phyllotactic succession of phyllotactic ratios shows itself, the ratio between 

 the harmonic areas* of Uranus and Earth being, within less than 1;^ per 

 cent., (f)", the exponent being the phyllotactic product 2x3. This is 

 also the coefficient of orbital retarda:tion at the centre of the belt of great- 

 est condensation ; it is the f power of the ratio between the harmonic 

 areas of Jupite;- and Earth, thus pointing to Uranus as a nucleal locus for 

 which Jupiter represents Laplace's limit ; the locus of secular perihelion, 

 or incipient rupture, for Uranus, is nucleally central between the mean loci 

 of Jupiter and Neptune ; Uranus and Earth are at opposite extremities of 

 a major-axis which would be traversed by light in the same time that 

 Sun would rotate, if it were condensed until its present equatorial radius 

 became Laplace's limiting radius. These five accordances present a chain 

 of phyllotactic and photodynamic influences which seems worthy of fur- 

 ther study. 



191. Optical and Thermal Relations in Organic Liquids. 



Briihl {Ber. Berl. Chem.. Ges. x'lv, 2533, Nov. 1881 ; cited in Am. Jcur. 

 Sci. [3], xxiii, 234), finds that progressive oxidation has the same influence 

 on the optical as on the thermal properties of organic liquids, the refractive 

 power diminishing as the amount of oxygen is increased, precisely as the 

 heat of combination diminishes. Removal of hydrogen or its replacement 

 by oxygen produces the same effect, so that both the above physical values 

 *The ratio of the actual virtual are.as is within xj of one percent, of (f )*• 



