As the two planets, Mars and the Earth, turn on their axes the parts of their surfaces they present to each other are constantly changing. For a feature on Mars to be visible from a given post on earth, observer and observed must confront each other, and, furthermore, it must be day there when it is night here. But, as Mars takes about forty minutes longer to turn than the Earth, such confronting occurs later and later each night by about forty minutes, until finally it does not occur at all while Mars is suitably above the horizon; then the feature passes from sight to remain hidden till the difference of the rotations brings it round into view again. There are thus times when a given region is visible, times when it is not, and these succeed each other in from five to six weeks, and are called presentations. For about a fortnight at each presentation a region is centrally enough placed to be well seen; for the rest of the period either ill-placed or on the other side of the planet. If a marking were always salient enough it would appear in every drawing made of the disk during the recurrent fortnights of its display. If it were weaker than this, it might appear on some drawings and not on others, dependent upon its own strength and upon the definition at the moment, and we should have a certain percentage of visibility for it at that presentation. While if it changed in strength between one presentation and the next, the percentage of its recording would change likewise. Definition of course is always varying, but if its value be noted at the time of each drawing this factor may be allowed for more or less successfully. Making such allowance, together with other corrections to produce extrinsic equality, such as the planet’s distance, which we need not enter upon here, we are left with only the marking’s intrinsic visibility to affect the percentages; that is, the percentages tell of the changes it has successively undergone and give us a history of its wax and wane. From drawings accurately made it is possible to add to the accuracy of the percentage by noting in each, not only the presence or absence of the marking, but the degree of strength with which it is represented. This was done on the final investigation in the present case, and it was interesting to note how little difference it made in the result.