161 162 163 164 165 166 167 168 169 170 171
| |

and Stokes- Planck 165 aberration, i. e. <r= log5= 10*2, we shall have at the surface of the Sun, as already mentioned ina footnote, which means, no doubt, an enormous condensation *. The corresponding relative velocity ot* slipping v/v On the other hand, at the surface of a hydrogen atom, assumed for the moment to be a homogeneous sphere (and the only existing body), we shall have log 5=1*7 . 10“ indistinguishable from unity. Notice that for small cr the denominator in (2) reduces to Jo* For such bodies, therefore, as a hydrogen atom, or in fact any other atom, the ratio in question will be exceedingly nearly equal its limiting value 3/2, w therefore, by (2),which differs only by 0*35 from the full slip. Thusthe Selenites would obtain with a * Such fantastically large condensations need not frighten us. They can be reduced if Hoyle’s law is replaced by some other appropriate form of relation between pressure and density. Boyle’s law, which is by no means necessary, is here used only, as the simplest one, for the sake of illustration. | 166 Dr. L. Silberstein on the recent Eclipse Results Michelson-Morley experiment a pronounced positive effect. But enough has now been said in illustration of the formula* for the condensation and for the slip. 5. Before passing to consider the Eclipse result it may be well to generalize the condensation formula (3) for the case in which Boyle’s law is replaced by any relation between the pressure and the density of the aether. The corresponding generalization of the slip-formula (2), not required for our present purposes, may be postponed to a later opportunity. Let the pressure p be any function of the density p alone Then, in the state of equilibrium, and with dm written for any mass-element in astronomical units, where r is the distance of the contemplated point from dm is the velocity of propagation of longitudinal waves in any compressible non-viscous fluid *. This velocity is, in general,, a function of p, and becomes a constantfor the special case of Boyle’s law, namely, our previousUsing (7) and writing, as before,we have ## . . . . (5 a)the required form. The integral is to be extended from * This result, known as the formula of Laplace, holds also for the most characteristic kind of waves—to wit, for a wave of longitudinal discontinuity (Hugoniot, Hadamard), for which it follows directly, without integration, from the hydrodynamical equations of motion. Sec, for instance, my ' Vectorial Mechanics/ p. 169. |