SUN AND PLANETS FOR DECEMBER, 1883. 497 
planet is allowed to enter the calculation. The error is perceptible in the case 
of Jupiter, but the combined mass of all the planets is so small in proportion to 
the Sun, that very iQ.vii writers care to waste additional words when quoting the 
law. In view of the fact that late astronomical works make such frequent use of 
ratios, and since Kepler's laws are so well known, we here present four sentences 
whose differences are almost infinitely small. "The squares of the periodic 
times of any two planets are to each other in the same proportion as the cubes of 
their mean distances from the Sun." — Herschel. 
The squares of the periodic times of any two planets are to each • other in 
the same proportions, when their masses are considered, as the cubes of their 
mean distances from the Sun. 
The squares of the times are equal to the cubes of distances, when ratios are 
considered. 
The squares of the times are equal to the cubes of distances. 
And these ratios are units formed by the same hand that made the solar 
system; and should never be forgotten, whether by student or skilled astronomer. 
With due deference to Prof. Pritchett, we make these explanations and cor- 
rections. 
In November issue " Axis" should have read Axes, and " .1 " as i. 
New Windsor, III., November 20, 1883. 
SUN AND PLANETS FOR DECEMBER, 1883. 
W. DAWSON, SPICELAND, IND. 
The Sun's R. A. is 16 hours 30 minutes on December rst, and 18 hours 42 
minutes on December 31st. About 9 P. M., of the 21st, the Sun will arrive at 
his greatest declination south, 23° 27'; a point called the winter solstice — the 
astronomical beginning of winter season. It is 18 hours 00 minutes of R. A. — 
the solstitial Colure, and 6 hours west of the Vernal Equinox. This will be the 
shortest day of the year — 9 hours 10 minutes long in 40° north latitude. After 
that the Sun will decline northward and the days grow longer. The Sun will be 
nearest the Earth on January rst. Solar spots are not so numerous as they were 
in October; ninety-five spots is the greatest number yet observed in Novembery 
on the ist and 17th. Two were visible without telescope on the 17th, o.ne near 
the west edge of the Sun, the other in southeast quadrant. 
Mercury is evening Star, but will not be visible until near the last of the 
month, when it may be seen in evening twilight near where the Sun sets. Venus 
is also evening star, and will be somewhat conspicuous by the end of the month, 
about half an hour above Mercury. Saturn will be a lovely object all through 
December; rising at 4:30 on the ist, it will be high enough for observation soon 
after dark. As stated on former occasions, a good sized spy-glass will show the 
ring and one or two moons; and a large telescope brings out a magnificent ap- 
