Page:Popular Science Monthly Volume 74.djvu/505

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501
A FAMOUS ASTRONOMICAL PROBLEM

four planets. Satisfactory causes were looked for in a possible ellipsoidal form of the sun, in a hypothetical ring of small planets between Mercury and Venus, in an assumed minute variation in the law of gravitation from the Newtonian inverse square of distances, and in other assumptions, but in vain. One hypothesis, that the finely divided material which gives rise to the zodiacal light (by reflecting the sun's rays) is the responsible disturbing mass, has been discussed several times since the days of Le Verrier and as many times rejected, with one exception.

The exception is Professor Seeliger's recently published investigation. with great skill and with entirely reasonable assumptions as to the form of space occupied by the zodiacal material, and as to the density of the distribution of the material in this space, he establishes that there is sufficient mass to account for the discrepancies in the motions of all the four planets.

The following table exhibits the results of Seeliger's theory in the first column of figures, and the actual results of observation as determined by Newcomb in the second column. The quantities in the third column, which bear the sign ±, are the "probable errors" assigned by Newcomb to his results; and, for the benefit of non-mathematical readers, we may explain that these "probable errors," deduced from the observations themselves, are indications of the uncertainties existing in the quantities to which they are attached. In this table e and i are respectively the eccentricity of the orbit and the inclination of the orbit plane to the ecliptic; and ΔΠ, ΔΩ, and Δi are respectively the changes, per century, in the longitude of perihelion, in the longitude of node and in the inclination of the orbit plane, unaccounted for by the attractions of known masses, as in the second column, and produced by the attractions of the zodiacal matter as computed by Seeliger. In the last column are the differences between the Seeliger and Newcomb numbers: in other words, a comparison of theory with actuality. These differences are small. All are within the probable errors in the third column; with one exception, far within these probable errors.

We can not ascribe this remarkable agreement between Newcomb's

Seeliger Newcomb N -S.
αΔΠ Mercury +8.49 +8.48 ±0.43 -0.01
Venus +0.05 -0.05 ±0.25 -0.10
Earth +0.07 +0.10 ±0.13 +0.03
Mars +0.59 +0.75 ±0.35 +0.16
 
sin iΔΩ Mercury +0.65 +0.61 ±0.52 -0.04
Venus +0.58 +0.60 ±0.17 +0.02
Mars +0.23 +0.03 ±0.22 -0.20
 
Δi Mercury +0.52 +0.38 ±0.80 -0.14
Venus +0.17 +0.38 ±0.33 +0.21
Mars +0.02 -0.01 ±0.20 +0.01