tJi Oc! 18, 



any regard to the \ ariety of possible or impossible tonus which i be tenden 

 cies may be supposed to assume or to indicate, in all mathema 

 physics an ideal completeness is assumed, such as is never found in nature. 

 The method in question is analogous to the one which lias been satisfac 

 torily adopted in investigating the laws of elastic undulation. 



It seems to have been generally admitted thai the third method may be 

 accepte 1 as lending probability to the indications of the other two, but it 

 involves the same question of dissociative velocity, and is, therefore, open 

 to the same criticism as the second method. For this reason it seems de- 

 sirable to see whether the problem can be successfully treated in some 

 other way. 



[f gravitating movements have any common limit, either of originating 

 efficiency or of ultimate tendency, which is uniform in all stellar systems, 

 that limit should evidently be sought in the direction of phenomena! 

 maxima, and with special reference to the principal center of the system. 

 If the sethereal hypotheses are correct, we may reasonably presume thai the 

 gravitating constant is dependent upon some sethereal constant. 



La Place established the general principle that the state of a system of 

 bodies becomes periodic when the effort of the primitive conditions of 

 movement has disappeared by the action of resistances. This principle, 

 which is a necessary consequence of the third law of motion, is well illus 

 trated in elliptical planetary orbits, in which the cyclical movement may 

 ba resolved into alternate oscillations, of approach to perihelion and re- 

 treat to aphelion. The duration of all such oscillations, whether circular, 

 slightly elliptical, or as nearly radial and rectilinear as the central nucleus 

 will allow, is determined by the length of the major axis, varying as the 

 | power of the length. If the major axes are equal, the oscillations are 

 synchronous. 



If orbital collisions of particles, in the neighborhood of the focus, shorten 

 the major axes, cosmical rotation may lie substituted for free planet- 

 ary revolution. But the limiting value, which is to be alternately over 

 come and renewed, will not be changed thereby ; the period for de- 

 stroying or acquiring that limiting value should still be one-half of the 

 cyclical period, or the period of a half rotation. 



The equation of constant velocity, in an elastic atmosphere or in an 

 sethereal medium, is 



v = v gh — gt, 



y denoting the wave-velocity ; g, the acceleration of gravity at the point 

 of observation ; A, the modulus of elasticity, or the height of a homogeneous 



atmosphere ; t, the time of rise or fall, through k h, under the constant re- 

 tardation or acceleration g ; / is also, as has just been shown, the time of a 

 half-rotation which is supposed to be t]\\c to sethereal impulses. Challis 

 has found* that if all the ordinary central forces are due to transformed 

 sethereal vibrations, -'the actions of such forces on atoms are in every in 

 stance attributable to mthereal currents, whether the atoms be immediately 

 acted upon by steady motions of the aether or by sethereal vibration." 

 Phil. Mag., Sep i . 1S72; Sept., 1S76: .tune, IS" . 



