210 C. A. Young—Diameters of Mars. 
than 45°, we get for the mean (by weights) 20’°687=-0’-028 at 
a mean angle of 72°-4. The nine nearly vertical measures, 
give 20’780-+0’-044 at a mean angle of 19°°3. Similarly the 
ten nearly horizontal measures of the Polar diameter give 
20’°608+-0’'031 at a mean angle of 73°°8, while the nineteen 
nearly vertical measures give 20'°706+0°926, at a mean angle 
of 16°9. No sensible difference appears between results ob- 
tained when the measured diameter inclines to the right, and 
those obtained when the inclination is toward the left. 
It is not certain what causes produce this difference between 
horizontal and vertical measures, but it is probably due in part 
to atmospheric dispersion, and partly to a known vertical astig- 
matism of the observer’s eye. In either case the effect would 
be proportional to the cosine of the inclination, and we may 
therefore assume with sufficient approximation, that the correc- 
tion required to an observation is I=axXcosf; f being the 
angle with the vertical, and a a constant to be determined from 
the observations themselves. 
strongly attests the reality of the correction. 
t is not, however, strictly correct to treat these groups as 
sp observations. ‘The more legitimate course is to regard 
each observation, (corrected for refraction and phase and re- 
duced to opposition) as furnishing an equation of condition of 
the form 
measured diameter = true diameter+a cos f. 
This has been done, and from the equations of condition, 
using the weights given, normals have been formed, in several 
different ways. 
us we may take as the unknown quantities z, e, (the polar 
and equatorial diameters) and a. Or calling c=e—z, we may 
take as the unknowns a, z and c, or a, € and c. Or finally, 
‘ etna : 
putting mat", we may form our normals with m, ¢ and @ 
Whichever of the four sets of normals we use, we get for the 
unknown quantities involved, the following values, weights and 
probable errors, viz: 
é (Equatorial Diam., Nov. 12, 1879) =20"-6342.0'-034 ; wt. 8°92 
x (Polar Di m., oo “« Jo 20°552-+ 07043; wt, 5°85 
eta y 
mat — 20°593-+ 0°035; wt. 8°85 
e, = (e-7) = 0°0818+0°0348 ; wt. a 
a coefficient of inclination correction = 0°168 -+ 0°050; wt. 41 
