between adjacent ones. It could, therefore, only be noted by its actual profile,--a very small affair, still further diminished by reason of the angle under which that profile was viewed. The resulting quantity in the case of Mars would be exceedingly minute. We perceive therefore, on the very threshold of our inquiry, reason to doubt the mountainous character of the irregularities. Such inference becomes the more probable on a more detailed investigation, into which we will now enter. This investigation depends upon a very important principle; namely, that if we have, as in this case, a great number of observations, it is possible, by dividing them into classes according to their kind and then taking the mean value of each class, to discover characteristics not otherwise exposed.

Means are very telling things. They are so from the fact of simplifying the effects of the factors at work. By taking the average of the series of observed values according to some definite principle, not only do we eliminate a very large class of errors, but we allow by so doing the various causes to unmask their separate results. The importance of reasoning upon averages could hardly be more strikingly exemplified than in the very case before us,--that of these depressions and projections seen on the terminator of Mars.

Of the 694 irregularities measured, 291 were projections and 403 were depressions. Here at the very outset, then, we perceive an objection to the theory that they are due to mountains, to wit, because the number of depressions so greatly exceeds the number of projections. As previously explained on page 64, mountains would produce on the average as many projections as depressions, for they would project the light on the one side as much as they would cut it off on the other.

Now let us classify these irregularities, and see if we can gain further information about them. There were two kinds of them,--the long and low, and the short and sharp. Each kind had its representatives among both the projections and the depressions. Of the short and sharp variety there were 95 projections. These averaged 0.276 seconds of arc in height. Of the same kind there were similarly 57 depressions which averaged 0.368 seconds of arc in depth. It will be noticed then, first, that the projections of this character exceeded in number the depressions of the same; secondly, that the average depth of the depressions exceeded the average height of the projections. Now, if the appearances had been due to mountains, both the number and size of the projections and of the depressions should have been substantially the same. They were emphatically neither. Consequently mountains fail to explain them. But there is another possible set of phenomena that will; namely, clouds. For, in the first place, clouds would cause apparent depressions and projections, since the light would linger on them as it does on mountain tops, and they would cast shadows as mountains do. But furthermore their two effects, of extending or curtailing the limit of vision along the terminator, would not necessarily be equal, as would be the case with hills. Because it is a peculiarity of mountains that they are attached to the soil, and are commonly permanencies; while clouds are not. The latter form and dissipate, dissipate and reform, and their metamorphoses are phenomena depending upon the time of day. Consequently they may appear in one place at one time, in another the next; and what is no less important, they may form at different heights at different times. They therefore not only account for irregularities on the terminator, but they account also for irregularity in the plus or minus character of these irregularities. Clouds, therefore, are capable of explaining the case before us, although mountains are not.

From what we have just shown let us mark now just what clouds are here required to account for what we see. The clouds that cause depressions are those within the terminator,--those, that is, that form before sunset or after sunrise; while those that cause projections are those that gather after sunset or before sunrise. As the observed projections in this case exceed the depressions in number, we infer, then, that there are more clouds after nightfall than before it, and similarly more before daybreak than after it; next, as the average depression is greater than the average projection, we likewise infer that the day clouds lie at a higher altitude. Now, this is precisely what we should expect would be the case, just as it is the case on the Earth.

Of the other class of irregularities, the long and low, there were observed 196 projections and 346 depressions. The projections averaged 0".136 in height; the depressions, 0".125 in depth. Here, then, we have an