• November 2 to 21 inc. 9".53
• The measure of the 12th of October and those of the 24th to 30th are taken
together, because equidistant from opposition on October 20.

The agreement of this table with that deducible by theory from the effect of an atmosphere is striking. But the agreement is even more exact than appears. For, as the polar axis was not in the same line as the axis of phase, the twilight arc to some extent affected the polar diameter at all times, but specially during November. This becomes evident, numerically, on applying the correction for an atmosphere, which gives the following values:

Polar Diameters:      
     

• October 15 to 23 inc. 9".32
• October 12 and 24 to 30 inc. 9".31
• November 2 to 21 inc. 9".32

Equatorial Diameters:

• October 15 to 23 inc. 9".37
• October 12 and 24 to 30 inc. 9".36
• November 2 to 21 inc. 9".37
• The middle values are evidently somewhat too small, since they affect both the
polar and equatorial diameters alike. Otherwise the variation in the values of the same diameter is less than the probable errors of observation. Taking the mean of all but the middle ones, we deduce the value for the polar flattening given above, 1/190 of the equatorial diameter.

From the correction for the effect of the atmosphere, we find the amount of the twilight arc upon the planet visible from the Earth to be about 10 degrees. That of the Earth, as seen from the Earth's surface, is 18 degrees but it is to be noticed that here the point of view is important From the topmost layer of our air of sufficient density to be capable of reflecting light we are but forty miles away; from the corresponding layer of the Martian air we are forty millions of miles off. We cannot, therefore, expect to detect the one to the same extent that we can the other. The value, then, for the Martian twilight arc of 10 degrees is simply a minimal value, not an absolute one. The twilight arc cannot, from the observations, be less than this, but it may be much more.

The large number of measures from which the above means were deduced not only renders error in the result less likely, but shows that result to be due to air pure and simple. This appears from the fact that the observed increase is systematic. For its systematic character proves it due to something largely transparent. It is because it is chiefly not seen that it is seen at all. At first sight this deduction seems paradoxically surprising. But, in considering the problem, we shall realize that it must be so.

If what was seen were opaque, as, for example, a mountain, then in certain positions it would indeed be seen projecting beyond the terminator,--for example, if it were at s in the diagram; if, on the other hand, it were in the position r , it would, instead of apparently increasing, decrease the diameter. Now, as the rotation of the planet would bring it eventually into all possible positions, it would be as likely on any one occasion to be measured in a position to decrease the diameter as to increase it. From but a few measures, therefore, it might appear that there was an increase in the calculated diameter, or it might seem that there was a decrease from it, and either would be equally likely to happen. If, however, many measures were made, and just in proportion as they were many, those decreasing the diameter would offset those increasing it, and the mean of all would show no trace of either. In the mean the minus quantity would wipe out the plus. Indeed, owing to the fact that both the Sun and the Earth are not infinitely far off from Mars, and in consequence that all the lines to them are not strictly parallel to one another, the decreasing effect would actually slightly exceed the increasing effect, but this would be too small to be perceptible.