polar flattening, which is the ratio borne by the difference of the equatorial and polar diameters to the equatorial diameter, would be seemingly increased.

The value of Mr. Douglass' measures is heightened by a certain happy event of an unprecedented nature,-- the first observed disappearance of the polar cap, and that at the very time the most important measures were made. The presence of the polar cap enters as a disturbing element into measures of the planet's disk, on account of the increased irradiation it causes at the extremity of the polar diameter, which makes the polar diameter measure more than it otherwise would. For the polar cap is the most brilliant part of the disk; and for the same reason that any bright body seems larger than a dark one of the same size, it dilates the planet unduly in that direction. The resulting effect is further complicated by the fact that the polar cap is eccentrically situated with regard to the pole of rotation, as we shall see later; and as the pole is tilted, the cap is sometimes on the edge of the disk and the irradiation in consequence large, and sometimes well on the disk itself where its irradiation is little or nothing. As the amount of its magnifying effect is not accurately known, there enters with it an unknown error. Now, last autumn Nature herself kindly eliminated this source of error.

The measures made by Mr. Douglass are thus entitled to special regard, not only because of their number (a great many of them were taken), but chiefly because Nature made the disturbing influence of the polar cap nil. When, in addition, the twilight arc is allowed for, the measures show a most satisfactory accordance and give for the value of the polar flattening 1/190 of the equatorial diameter.

Now, it is interesting that this value should receive corroborative support from two quite different directions. The first of these is that 1/190 is just about the flattening which would result from the most probable supposition we can make as to the past history of the planet. To show this we may take the case of the Earth. Investigations along several different lines all result in showing that the polar flattening of the Earth is almost exactly such as would result in a fluid body whose density from surface to centre increased according to the pressure and temperature of our Earth in the past, and which rotated with its present angular velocity. In the case of Mars, Tisserand has shown that the polar flattening under the influence of his present rotation would, if the increase of density in his strata were similar to the Earth's, be 1/227 of his equatorial diameter. If, on the other hand, his mass were homogeneous, his polar flattening would be 1/178. Now, in a fluid condition a body could not remain homogeneous, owing to the pressure exerted by the outer strata upon the inner ones, unless the matter of which it was composed were rigorously incompressible, which is certainly not the case with the Earth, and with quite equal certainty not the case with Mars. On the other hand, the increase of density from surface to centre is undoubtedly less in Mars than in the Earth, since the pressure depends upon the mass and the Earth's mass is nearly ten times that of Mars. Consequently, from this cause, the polar flattening should be somewhere between 1/178 and 1/227, not far therefore from the value found above, 1/190.

The second bit of corroborative testimony comes from the behavior of the satellites of the planet. Unlike a sphere, a spheroid acts unequally upon a body revolving about it in an ellipse inclined to its equator. The ring pulls the satellite now this way, now that, thus altering its nodes, that is, the points where the plane of its orbit crosses the planet's equator, and also its apsides, or the points in which the satellite's orbit is nearest and farthest front the planet. The effect of an equatorial protuberance tilted thus is to shift these points round the orbit, the line of nodes retrograding, while contrarily the line of apsides advances. From the speed with which these revolutions take place, it is possible to calculate the size of the bulge. Hermann Struve has just done this for the lines of apsides of the two satellites of Mars, and finds for the value for the consequent polar flattening of the planet 1/190 of its equatorial diameter. From these two independent determinations we may conclude that the value found at Flagstaff is pretty nearly correct.

We find, then, that Mars is a little flatter than our Earth, though not noticeably so, the polar flattening amounting to about 22 miles.

The value, 1/190, for his polar flattening, hints that at some past time Mars was in a fluid--that is, a molten-- condition, just as the Earth's polar flattening of 1/303, similarly shows her to have been, and that in both