NEW OBSERVATIONS OF THE PI. ANFT MERCri;v. 4^3 
the cusps in consequence of which 
1 
f light throughout, we see at once tliat the micromo 
,' 
dichotomy^ show a less loss of phase tlian tlie drawhigs, flion^li ila^y iiiny ^linw mow; 
in other words, that no correction for irradiation at the liinl) Icsb limn {hni lUwc .*.v 
to reduce the equatorial diameter to such a ratio is aJiiiissi]ile,yyy>/iw/ci/?/( ffn il,,.'!..j 
with a sphere. 
For such a difference hctween the niicrometric mcn^urcs and the drawiiu i-* 
just what an ellipsoid would cause whose longest axis pointed to the Sun. Nor 
would such ellipticity be more directly revealed. For when ihc planet i« in 
transit his greatest axis would be pointed directly at the Earth, fclnce llic Siui 
h his centre. It is only 
and the Ea 
o 
at the times mentioned above, at and near dicliotomy, that the (•nii)tioi(y wuuM 
show itself. 
47. Spheric and Ellipsoidal Phase. — This is not all. There is another curious 
fact to be found on comparing Tables I. and VI. 
If an ellipsoid be illuminated by the light from a point in a principal plane con- 
taining its longest axis, and an observer be placed in that plane at an nngle from the 
of light, the phase sliown by the ellipsoid will not In general be 
I 
be 
that shown by a sphere whose diameter is one of the two sbortcr axc.^ of the 
ellipsoid. It will only be so in the particular case uhere both the terminator ai " 
observer are in the line of the minor axis of the ellipse made hy the plniie. 
other positions it will be greater or less than the spheric phase, acrordin- 
terminator is on one side or the other of the minor axis, provided tlie ob-;r ^ 
between the line joining the tangential points on the circle and ellipse n iH-ctivcly 
and the minor axis. If we suppose the source of light to be in the third quadrant 
with the major axi^ to its left, which were the conditions in the case of Murcury m 
February, and call the angle a between the source of light and the mnjur axis of the 
ipse t + w, we see that, if 
c + O 90°, then the phase shown by the ellipse > than that shown by the .phere. 
t 4 CO = 90% 
t + CO < 90% 
a u 
« « « 
« u a 
a " < 
tc il « ** 
t is the phase angle ; while a> is the angle of libration. . , , t,^ 
To an observer, then, placed nearly in the line of the minor axis, the pha- =ho 
by an ellipsoid would suddenly change from being greater than thnt .hown 
sphere to bein. less as . + a, passed through 90°. This would cause, in 
Vol. XII. No. 4. — 5. 
\ 
