there were an atmosphere capable of reflecting light up to a height represented by the greater circle, the Sun’s rays would strike the upper visible limit of this atmosphere, not at p’ but at s, sr being drawn parallel to the line from o to the Sun. The measured equatorial diameter, which is, of course, the projection of the arc d’b’s on the line d’h’, would be d’f instead of de, which it would be were there no atmosphere. It thus appears that owing to side-lengthening, as we may perhaps style this reverse of foreshortening, the fringe of atmosphere increases in apparent width with increase of phase, to an apparent increase of the equatorial diameter.
If, now, we take a third position for the Earth where Mars shows a yet greater phase, the third arrow, we find that in this case the resulting apparent increase in the equatorial diameter is mn, and we notice that mn is greater than ef, just as ef was greater than pp’ or cc’. That is, we see that the apparent increase in the size of the equatorial diameter varies directly, according to some law, with the increase in phase, or, as it is technically put, is a function of the phase.
This increase, being an increase in the measure itself, would in due course come in for its share of all the corrections applied to the diameter. In consequence, that diameter, instead of coming out simply the full equatorial diameter,