1882.] 42 J [Chase. 



volved in its time-integral of rotary oscillation is slightly less than Jupi- 

 ter's corresponding velocity, being almost, or quite identical with plane- 

 tary velocity at the mean centre of gravity of Sun and Jupiter. These suc- 

 cessive accordances furnish data for a second " photodynamic problem of 

 three bodies," which is, perhaps, even more remarkable than the one given 

 in Note 254. The importance of the combined harmonies may be shown 

 by a simple recapitulation of the several harmonic velocities, viz. : 1. The 

 identity of Note 280 ; 2. The velocities which correspond with the respec- 

 tive time-integrals of rotary oscillation for the chief centre of nucleation 

 (Sun), the centre of nebulosity (Jupiter), and the chief centre of conden- 

 sation (Earth) ; 3. The limiting velocity of circular orbital revolution in 

 the system ; 4. The velocity of circular orbital revolution at the centre of 

 gravity of Sun and Jupiter. 



284. Instantaneous Action. 

 The case of gravitating action and re-action between Moon and Earth 

 {Thomsoyi and Tait, § 376), is the one which led Laplace to his highest 

 estimate of the velocity of gravitating transmission and to suppose that 

 the transmission might be absolutely instantaneous. K is also the case 

 which led Adams {lb. § 830) to the discovery of Laplace's error respecting 

 the theoretical invariability of the mean sidereal day and to the subsequent 

 discussions of tidal friction and retardation. That there is such a thing as 

 instantaneous action is so generally believed that it seems desirable that 

 attempts should be made to furnish some physical representation of its 

 possibility and to demonstrate its influence upon adjustments of equilib- 

 rium in cosmical actions and reactions. If friclional accelerations in onepor- 

 tion of a rotating globe can be compensated by frictional retardations in 

 another, or if elasticity (Note 217) aids tidal tendency and wave propaga- 

 tion in making the instantaneous changes which are required by tidal 

 action, our tidal theories need careful revision. The fads of harmonic 

 relation which are found on all sides, indicate activities which have been 

 at work in all time, and they should not be ignored for any merely theo- 

 retical considerations. 



285. "Harmonic Analysis of Tidal Observations." 

 At the last meeting of the British Association, a special grant of £.50 was 

 made to Mr. George H. Darwin, for a Harmonic Analysis of Tidal Obser- 

 vations. Mr. Darwin's success in developing Sir William Thomson's 

 views upon cosmical viscosity, and the beauty of many of his results, give 

 assurance of valuable additions to human knowledge from any work that 

 he may undertake. The accuracy of the conclusions which he has already 

 drawn from Delaunay's hypothesis, is unquestionable. My criticisms 

 CNotes 215-225) upon Prof. Ball's use of those conclusions, were based 

 upon the fact that they did not adequately represent all the elements of 

 the questions which were involved, the laws of intermolecular elasticity 

 and harmonic motion having been almost entirely overlooked. In the 

 absence of any positive evidence of tidal retardation, we have no right to 



