A NEW DETERMINATION OF THE DIAMETER OF MARS. 3) 
The discrepancy between these and the value obtained from the heliometer 
is shown in the following table. In the eolumn ‘‘ Diameter” the angular value of 
the diameter for distance unity is given: 
Value used in the Nautical Almanac and Berliner Yahrbuch, 11”. r00 
Valweiusediini the American) Ephemenrisqy 0.) 2) 2 ros Tos 
Bessel’s value from the Heliometer, .. . 9.328 
Hartwig’s value from Heliometer ‘observations of Bessel, 
Kaiser, Main and himself: - - . . Bi ee te 9-352 
we difference Here shown between the largest ail eine values amounted 
to 4” at the time of opposition. The value used in the American Ephemeris was 
derived from observations with the Mural Circle (aperture 4.1 in.) of the Naval 
Observatory during 1845-46, and is subject to the large probable error +-0”.203. 
In the observations made at this observatory the diameter of the disc was meas- 
ured in four different directions : 
1. From position angle 143° to 323°, corresponding to the polar diameter. 
2. From position angle 8° to 188°. 
3. From position angle 98° to 278°. 
4. From position angle 53° to 233°, corresponding to the equatorial diameter. 
The observations extended from October 27 to November 24, the opposition 
occurring on November 12, and the nearest approach of the planet to the earth 
on November 4. After correcting the separate observations for incomplete illu- 
mination and reducing to distance unity, the results of the measures are shown in 
the following table: 
DIRECTION. |NO. OBSER’TION.| DIAMETER. | PROBABLE ERROR. 
143°—323° ir? g’”.422 + 07.024 
8°—188° 9 he OA AS Bac, 1043 
Oa eion 8 Or e5L7 IL © ,ORe 
Ban 258), 17 g .638 + © .044 
If these separate results are considered as independent measures of the same 
diameter, and combined according to the method of least squares, there will result 
finally, Diameter=9”. 486-+-0”.033, which, combined with Newcomb’s value of the 
solar parallax, gives for a mean value of the diameter of the planet 4248 miles, 
with a probable error of 15 miles. ‘This value, as will be seen, agrees quite closely 
with the determinations of the heliometer, and shows conclusively that the values 
in use in the Ephemerides are much larger than would be given by any good in- 
strument of good definition and moderate size. 
The difference between the polar and equatorial diameters being so much 
greater than the probable error would indicate, seems to show an ellipticity of the 
apparent disc. This systematic difference was noted in the individual observa- 
tions from day to day, and is confirmed by the measures of the intermediate di- 
ameters. The observations would then assign to the planet the form of an ellip- 
soid of revolution, with a polar diameter of 4220 miles and an equatorial diame- 
ter 4317, the amount of compression being 1-45. Very varying results have been 
arrived at for the amount of compression of Mars. Sir Wm. Herschel -gives it 
1-16; Schréeter less than 1-80; Arago, from Paris observations extending over 36 
