THE PLANET MAES IN FEBRUARY 1869. 
41 
It will be well in tbe first place to examine the exact relations 
which Mars will exhibit as respects the presentation of his polar 
axis towards the earth during the approaching opposition. A 
general impression can be obtained of his presentation by con- 
sidering the indications of my chart of the orbits of the four 
interior planets. But as some persons find it difficult to grasp 
with clearness and distinctness the results which follow when 
two globes like Mars and the earth have a certain relative 
position — that is, to gather how one of them would appear to 
an observer situated on the other — I have thought it well to 
calculate the exact presentation of Mars with relation to the 
declination circles and parallels of the celestial sphere, because 
the knowledge of this point enables the observer to at once 
interpret the meaning of his observations without reference to 
the hour of observation or to the position of the planet with 
respect to the horizon. 
The following table presents all that is necessary to be known 
respecting the presentation of the planet, at bi-monthly inter- 
vals. Here d is the apparent diameter of the planet; is the 
apparent angle at wffiich the northern extremity of the planet’s 
polar axis is inclined to a declination-circle (towards the east 
in the present case) ; and I is the angle at which the line of 
sight from the earth to the planet is inclined to the plane of 
the planet’s equator (this line being on the northern side of the 
equator in the present instance). 
P 
d 
1 
December 16, 1868 
11-2 
12 29 E. 
24 33 X. 
December 31, „ 
130 
13 50 „ 
24 26 „ 
January 14, 1869 
14-6 
13 36 „ 
23 50 „ 
January 29, „ 
15-8 
11 28 „ 
22 50 „ 
February 13, „ 
164 
7 39 „ 
21 39 „ 
February 28, „ 
16-8 
3 52 „ 
20 24 „ 
March 15, „ 
14-4 
1 18 „ 
20 7 „ 
March 30, „ 
12-8 
0 37 „ 
20 32 „ 
April 14, „ 
11-2 
1 9„ 
21 36 „ 
Since the apparent path of the planet across the field of view 
of the telescope indicates the position of the declination- 
parallel, there can be no difficulty in interpreting these results, 
and thus assigning the spots seen in the planet to their proper 
position on the globe of Mars. 
Figs. 1 , 2, and 3 (PI. XXXIX.) indicate the presentation of the 
planet on December 16, February 13 (opposition), and April 24, 
respectively, as seen in an inverting telescope. They will 
assist in interpreting the table given above. It will be noticed 
