To see exactly how this is possible, let us consider the effect an illuminated atmosphere would have upon the measurements in question. To make matters more obvious we will introduce a diagram. The inner circle represents a section of the planet in the plane of the ecliptic; the arrows, the directions in the same plane of the Sun and Earth from the centre of the planet, in the different positions to be considered; and the outer circle, an atmosphere surrounding the planet, at the limit at which it is dense enough to reflect light.
At opposition the Earth lay very nearly in the same line from the planet as the Sun. This is shown by the left-hand arrow. The illuminated semi-circumference of the planet’s surface, at that time also the semi-circumference seen from the Earth, was gabp, and gop was the equatorial diameter; g’a’b’p’ and g'op’ the semi-circumference and equatorial diameter, upon the supposition of an atmospheric envelope encircling the surface. As the Earth and Mars passed along their orbits, the line from Mars to the Earth shifted into its second position, the Sun remaining as before. The illuminated part of the surface of Mars continued, therefore, to be gabp; but the portion of this illuminated surface visible from the Earth was only dbp, the part gd being invisible from the Earth, and the part ph lying in shadow. If, however,