With a vertical axis the daylight and darkness in all parts of the earth would be of equal duration, being always twelve hours. There would be no seasons, and the climate would approach the average condition now experienced at the two equinoxes. On the whole the climate of high latitudes would give the impression of being milder than now, for there would be less opportunity for the accumulation of snow and ice with their strong cooling effect. On the other hand, if the axis were tilted more than now, the winter nights would be longer and the winters more severe than at present, and there would be a tendency toward glaciation. Thus Cordeiro accounts for alternating mild and glacial epochs. The entire swing from the vertical position to the maximum inclination and back to the vertical may last millions of years depending on the earth's degree of elasticity. The swing beyond the vertical position in the other direction would be equally prolonged. Since the axis is now supposed to be much nearer its maximum than its minimum degree of tilting, the duration of epochs having a climate more severe than that of the present would be relatively short, while the mild epochs would be long. Cordeiro's hypothesis has been almost completely ignored. One reason is that his treatment of geological facts, and especially his method of riding rough-shod over widely accepted conclusions, has not commended his work to geologists. Therefore they have not deemed it worth while to urge mathematicians to test the assumptions and methods by which he reached his results. It is perhaps unfair to test Cordeiro by geology, for he lays no claim to being a geologist. In mathematics he labors under the disadvantage of having worked outside the usual professional channels, so that his work does not seem to have been subjected to sufficiently critical analysis.