1874.] -'-^^ [Chase. 



in consequence of an explosion, a secondary centre of linear oscillation 

 should be established between the primary centre and the centre of 

 gravity, [| — | of (| - i) = f]. 



47. Planets and satellites, oscillating under the combined action of 

 centrifugal and centripetal forces, and subject to disturbances from 

 mutual interaction, should tend to arrangements analogous to those of 

 the particles in an exploded gas. 



48. The force of superficial gravity, at the Sun and at the principal 

 planets, should be in simple harmonic relations to other elements of 

 planetary motion. 



49. The laws of mechanical arrangement, in the particles of a homo- 

 geneous elastic aether, should give rise to polar forces. 



50. The velocity of primary oscillation (Theses 16, 25, &c.,) which 

 satisfies the foregoing theses, by explaining all velocities which are the result- 

 ants of gravitating force, is the velocity of light. 



These Theses seem to me to be all rigorously and mathematically 



connected vyith the hypothesis of a universal elastic aether. In my 



accounts of the successive tentative steps, inductive, deductive, and 



anticipative, by which I have been brought to their recognition, there has 



necessarily been much that was crude, and some things that were 



perhaps merely visionary, but the steps have all led towards the same 



goal. While endeavoring to learn caution from my mistakes, I 



have never ceased for a moment to believe that the many harmonies and 



coincidences which I have pointed out, were indicative of iinportant but 



unknawn laws. 



X ) 



The identification of v and v ', (Thesis 50), is perhaps the most 



important conclusiou of the whole, and its importance may render some- 

 what fuller details desirable. The common explanation of planetary 

 motions, assumes a primitive tangential impulse and a constant gravi- 

 tating pull, the resultant of the two forces determining the path at every 

 instant. But it should be remembered that the efficient tangential im- 

 pulse is by no means the one which was originally communicated ; that 

 it, as well as the pull of gravity, is continually shifting its direction, and 

 continually renewed ; and that all the known cosmical motions can be as 

 readily accounted for by the impulse of waves upon particles differing 

 in their relative amounts of inertia, as in any other way. 



In any case of free orbital revolution around a centre of gravity, every 

 infinitesimal pull of gravitation is assumed to be efficient, in some way 

 or other. If the orbit is circular, the orbital velocity (y'gr) is renewed, 

 as often as a portion of the orbit, equivalent to radius, has been described. 

 This fact is, of itself, suggestive of equal oscillations, either alternately 

 or simultaneously centripetal and tangential, and it may well justify us 

 in looking for some equally simple relationship to an invariable velocity 

 of primitive and continual impulsion. 



The only presumably invariable velocity that we know, being that of 



A. p. S. — VOL. XIV. S 



