1882,] 419 [Chase. 



nate Moon's mass and semi-axis major l)y m^ and p^, this approximation 

 gives us the following proportion : 



'"o ■• Pa - (^ — 1) '»*o : pz"- 

 Substituting m^ = 331776 m^, p^ = 92785700 miles, p^ = 388869 miles, we 

 get, ???3 = 82.486 m^. The values which were found in Notes 8 and 246 

 seem likely to be subject to fewer modifications than this, but every ad- 

 ditional indication of approximation to anticipated harmonies lends new 

 interest to the discussion of elastic influence and furnishes new material 

 for future analytic research. 



266. Rarmonic Tidal Cycles. 



The tendency of the solar- and lunar tidal disturbances to cyclic har- 

 mony, is shown by the approximate equality of the solar disturbance, 

 during the interval which would give terrestrial particles orbital velocity, 

 to the lunar disturbance, during a sidereal revolution about the Earth. 

 The approximation may be expressed by the equation : 



, m. 1 yr "^a 

 -„z X -g- =—3X1 mo. 



Substituting the same values as in the foregoing note for w^, ^3 and p^, 

 we get the approximate value, mj = 83.025»i^. The closeness of these 

 various approximations may be attributed, with great likelihood, to 

 original influences of central-belt condensation, aided by the natural sta- 

 bility of harmonic oscillations which have once been set up. The slight 

 discrepancies between different estimates are probably owing to subordi- 

 nate rhythmic disturbances, such as nutation, precession, and other oscilla- 

 tions, the exact influence of which we may reasonably hope to understand 

 when we have a fuller knowledge of tethereal elasticity. 



267. Subterranean Tides. 



My views regarding the influence of elasticity upon tidal adjustments, 

 (Proc. Amer. Ph..8oc., ix-Siv ; xvi, sq. ; Phot. Notes 215-8), are confirmed 

 by the subterranean tides in the flooded mines at Dux, in Bohemia. In a 

 communication to del et Terre (copied in Ann. de Gliim. et de PJiys., xxv, 

 533-46), M. C. Lagrange cites the discussion, hy Grablowitz {Boll, della 

 Sac. Adv. di Sci. Nat. in Trieste, vol. vi, fasc. I, 1880), of Klonne's obser- 

 vations. The observations seem- to show conclusively that the ebb and 

 flow in the mines is due to combined solar and lunar action, but that it can 

 be satisfactorily explained only l)y the direct attraction of the two bodies 

 upon the solid mass of the Earth. Lagrange refers to previous investi- 

 gations, by himself and by George H. Darwin, which go to show that if 

 cosmical bodies have any elasticity, they must undergo continual and 

 periodic changes of form. Grablowitz infers that those changes should 

 lead to oscillations of various intensitj^ so as to produce mechanical 

 effects which difier according to the nature and degree of local elasticity, 



PROC. AMER. PHILOS. SOC- XX. 112. 3a. PRINTED NOVEMBER 15, 1883. 



