and Seeliger's results to fortunate chance, and it is scarcely possible to doubt that in the zodiacal-light materials lie the causes of the discrepancies referred to. I have little hesitation in venturing the opinion that Seeliger's investigation marks an epoch in the application of Newton's law of gravitation to the motions within the solar system. At one stroke he appears to have removed a group of discrepancies which served as bases for many inquiries as to the preciseness and sufficiency of the Great Law. With all respect to Seeliger's genius and labor, however, scientific caution will value confirmation of his results by other investigators.
Seeliger's assumptions as to the distribution and mass of the zodiacal material are of interest, especially when we recall that the zodiacal light within some 20 degrees of the sun is unobservable, on account of the glare, and that the brightness of the light is a poor index to the mass: a given quantity of matter, finely divided, would reflect sunlight more strongly than the same quantity existing in larger particles. For the mathematical development of the subject he assumed that the material is distributed throughout a space represented by a much-flattened ellipsoid of revolution whose center is at the sun's center, whose axis of revolution coincides more or less closely with the sun's axis, whose polar surfaces extend 20 or 30 degrees north and south of the sun (as viewed from the earth), whose equatorial regions extend considerably beyond the earth's orbit, and in which the density-distribution of materials decreases as a function both of the linear distance out from the sun and of the angular distance out from the equatorial plane of symmetry. According to these assumptions, surfaces of equal densities are concentric ellipsoidal surfaces, and the number of such ellipsoids can be increased or decreased according as the computer may desire to represent more or less closely any assumed law of density-variation within the one great spheroid. Practically, Seeliger found that the disturbing effects on the planets are almost independent of the law of distribution of the material, as related to distance from the sun, as far out as two thirds of the distance to Mercury. He made use of only two ellipsoids: One with equatorial radius 0.24 unit and polar radius 0.024, of uniform density; and the other with corresponding radii 1.20 and 0.24, of uniform but much smaller density. The total mean densities determined for his volumes, on the basis of unity as the mean density of the sun, are, respectively, and ; and the resulting combined mass of the two ellipsoids is of the sun's mass, which is roughly twice the mass of Mercury. The corresponding density of mass-distribution is surprisingly low. In the inner and denser ellipsoid, the matter, if as dense as water, would occupy 1 part in 30,000,000,000 of the space; if as dense as the earth, only 1 part in 160,000,000,000.
- The distance from the sun to the earth being 1.00.