Page:Popular Science Monthly Volume 74.djvu/505
501
A FAMOUS ASTRONOMICAL PROBLEM
four planets. Satisfactory causes were looked for in a possible ellip- soidal form of the sun, in a hypothetical ring of small planets bet^yeen Mercun^ 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 investiga- tion. 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 deter- mined by IS^ewcomb in the second column. The ([uantities in the third column, which bear the sign ±:, are the " probable errors " as- signed by Xewcomb to his results; and, for the benefit of non-mathe- matical 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 All, AO and A/ 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 !N"ewcoml3 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.
AVe can not ascribe tliis remarkable agreement between Newcomb's
Seeliger
Newcomb
N-S.
' Mercury
-f 8.49
+ 8.48
±0.43
— 0.01
e-AIT*;
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
^ Mercury
+ 0.65
+ 0.61
± 0.52
— 0.04
sin t . AO -
Venus
+ 0.58
+ 0.60
±0.17
+ 0.02
Mars
+ 0.23
+ 0.0.3
± 0.22
— 0.20
' Mercury
+ 0.52
+ 0.38
±0.80
— 0.14
At J Venus
+ 0.17
+ 0.38
± 0.33
+ 0.21
- \Iars
— 0.02
— 0.01
± 0.20
+ 0.01
