The speed and period together easily give the radius of the circular orbit as about 8 million miles.

Equating centrifugal and centripetal forces

mv / r = ? m / (2r)

and comparing the value of 4r / T so obtained with the r / T of the earth, we find the ma.s.s of each body must be about 30,000 times that of the earth, or about 1/10th that of the sun.

(This is treating them as spheres, though they must really be pulled into decidedly prolate shapes. Indeed it may seem surprising that the further portions can keep up with the nearer portions as they revolve.

If they are of something like solar density their diameter will be comparable to half a million miles, and the natural periods of their near and far portions will differ in the ratio (17/16)^{3/2} = 11 approximately. Tenacity could not hold the parts together, but gravitational coherence would.)

This, however, is a digression. Let us continue the calculation of the gravitative pull.

We have ma.s.ses of 3 104 6 10 tons, revolving with angular velocity 2p 4 days, in a circle of radius 8 106 miles.

Consequently the centripetal acceleration is 4 p 8 106 / 16 miles per day per day; which comes out 32 / 22 ft. per sec. per sec., or nearly half ordinary terrestrial gravity.

Consequently the pull between the two components of the double star Aurigae is

_g_ / 2.2 18 105 tons,

or equal to the weight of

80 104 tons on the earth,

which is more than twenty million times as great as is the pull between the earth and our sun.

Simple calculations such as these could have been made at any time; there is nothing novel about them, as there is about the estimate of the ether's density and vast intrinsic energy, in Chapters VI and VII.

But then there is nothing hypothetical or uncertain about them either; they are certain and definite: whereas it may be thought there is something doubtful about the newer contentions which involve consideration of the ma.s.s and size of electrons and of the uniform and incompressible character of etherial const.i.tution. Even the idea of "ma.s.siveness" as applied to the ether involves an element of uncertainty, or of figurativeness; because until we know more about ether's peculiar nature (if it is peculiar), we have to deal with it in accordance with material a.n.a.logies, and must specify its ma.s.siveness as that which would have to be possessed by it if it fulfilled its functions and yet were anything like ordinary matter. It cannot really _be_ ordinary matter, because ordinary matter is definitely differentiated from it, and is presumably composed of it; but the inertia of ordinary matter, however it be electrically or magnetically explained, must in the last resort depend on something parentally akin to inertia in the fundamental substance which fills s.p.a.ce. And this it is which we have attempted in Chapters VI and VII to evaluate and to express in the soberest terms possible.

CHAPTER X

GENERAL THEORY OF ABERRATION

In Chapter III the subject of Aberration was treated in a simple and geometrical manner, but it is now time to deal with it more generally.

And to do this compactly I must be content in the greater part of this chapter to appeal chiefly to physicists.

The following general statements concerning aberration can be made:--

1. A ray of light in clear s.p.a.ce is straight, whatever the motion of the medium, unless eddies exist; in other words, no irrotational disturbance of ether can deflect a ray.

2. But if the observer is in motion, the apparent ray will not be the true ray, and his line of vision will not truly indicate the direction of an object.

3. In a stationary ether the ray coincides with wave-normal. In a moving ether the ray and wave-normal enclose an aberration angle e, such that sin e = v/V, the ratio of the ether speed to the light speed.

4. In all cases the line of vision depends on motion of the observer, and on that alone. If the observer is stationary, his line of vision is a ray. If he moves at the same rate as the ether, his line of vision is a wave-normal.

5. Line of vision depends not at all on the motion of the ether, so long as it has a velocity-potential. Hence if this condition is satisfied the theory of aberration is quite simple.

_General Statement as to Negative Results in the Subject._

It is noteworthy that almost all the observations which have been made with negative results as to the effect of the Earth's...o...b..tal motion on the ether are equally consistent with complete connexion and complete independence between ether and matter. If there is complete connexion, the ether near the earth is relatively stagnant, and negative terrestrial results are natural. If there is complete independence, the ether is either absolutely stationary or has a velocity-potential, and the negative results are, as has been shown, thereby explained. Direct experiment on the subject of etherial viscosity proves that that is either really or approximately zero, and substantiates the "independence" explanation.

_Definition of a Ray._

A ray signifies the path of a definite or identical portion of radiation energy--the direction of energy-flux. In other words, it may be considered as the path of a labelled disturbance; for it is some special feature which enables an eye to fix direction: it is that which determines the line of collimation of a telescope.

Now in order that a disturbance from A may reach B, it is necessary that adjacent elements of a wave front at A shall arrive at B in the same phase; hence the path by which a disturbance travels must satisfy this condition from point to point. This condition will be satisfied if the time of journey down a ray and down all infinitesimally differing paths is the same.

The equation to a ray is therefore contained in the statement that the time taken by light to traverse it is a minimum; or

?{A,B} ds/V = minimum

If the medium, instead of being stationary, is drifting with the velocity _v_, at angle ? to the ray, we must subst.i.tute for V the modified velocity V cos e + _v_ cos ?; and so the function that has to be a minimum, in order to give the path of a ray in a moving medium, is

Time of journey = ?{A,B} ds / V(cos e + a cos ?) = ?{A,B} (V cos e - v cos ?) / (V(1-a)) ds = minimum

where a is the ratio v/V.

_Path of Ray, and Time of Journey, through an Irrotationally Moving Medium._

Writing a velocity-potential f in the above equation to a ray, that is putting

v cos ? = df/ds,

and ignoring possible variations in the minute correction factor 1-a between the points A and B, it becomes

Time of journey = ?{A,B} cos e / (1 - a) ds/V - (f - fa) / V( 1-a) = minimum.

Now the second term depends only on end points, and therefore has no effect on path. The first term contains only the second power of aberration magnitude; and hence it has much the same value as if everything were stationary. A ray that was straight, will remain straight in spite of motion. Whatever shape it had, that it will retain.

Only cos e, and variations in a, can produce any effect on path; and effects so produced must be very small, since the value of cos e is

v (1 - asin?).

A second-order effect on direction may therefore be produced by irrotational motion, but not a first-order effect. A similar statement applies to the time of journey round any closed periphery.