1876.] *^^^ [Chase. 



quired as is actually exhibited in the resulting rotation. The same argu- 

 ment may be derived in another form from the vibrations of elastic 

 bodies." 



The "Mathematical Monthly," for January, 1859, contained an ex- 

 haustive discussion of "The Motions of Fluids and Solids relative to the 

 Earth's surface," by Professor William Ferrel, some of the results having 

 been published about two years before, in the "Nashville Journal of 

 Medicine and Surgery." The recent great advance in meteorological 

 knovifledge and in successful weather prediction is due, in great measure, 

 to the publication of Ferrel's laws. 



In 1861, Professor Simon Newcomb presented to the American Acade- 

 my, a compendious review of the dynamical theory of gases.* His 

 paper contains, among other matters of interest, the following first approxi- 

 mation towards a theoretical establishment of the empirical ratio between 

 the temperatures under constancy of pressure and under constancy of 

 volume : "7. If the particles were perfectly hard and spherical, the specific 

 heat under constant volume would be to that under constant pressure as 

 3 to 5. If they were hard, but not spherical, this ratio would be that of 3 

 to 4. The latter result follows from an elegant theorem given by Professor 

 Maxwell in Vol. XX, of the Philosophical Magazine, viz., that if the parti- 

 cles are hard, but not spherical, the sum of their vires vivm of translation 

 will be equal to that of their vires vivce of rotation." 



My first attempt at applying the foregoing principles was made in 1863,f 

 when I showed that the daily fluctuations of the barometer are of such 

 form and magnitude as can be explained by the combined action of 

 atmospheric inertia, terrestrial resistance, and motion relative to the Sun. 

 I also showed that the tendencies to equality of areas, in the daily and 

 yearly fluctuations, furnish the data for a close approximation to the solar 

 distance. :f 



In 1864, Professor James Edward Oliver made a practical investi- 

 gation of the best approximate representation of all the mutual ratios of 

 k quantities by those of simple integers, drawing illustrations especially 

 from phyllotaxis and planetotaxis. His investigation assumed that 

 "Nature, while obeying with absolute precision the resultant of her effi- 

 cient laws, such as Inertia, Attraction, etc., falls into forms which com- 

 monly both utility and taste, often independently of each other, would pre- 

 scribe. "§ 



In 1865, Ferrel described an annual variation in the daily mean level of 

 the ocean, the greater part of which he attributed to "a tangential force 

 arising from the motions of the ocean combined with the motion of the 

 Earth's rotation. It was first brought out in its most general form in [his] 

 paper on the motions of fluids and solids relative to the Earth's surface."! 



* Proc. A. A. S., v, 112. 

 t Proc. Soc. Phil., Amer,, ix, 283. 



X lb., loc. cit., and x, 376. See, also, Ferret's paper of 1865, to which reference 

 is made below, 

 gib., vi, 288. llb.,vii, 35. 



PROC. AMER. PHILOS. SOC. XVI. 98. 2l 



