While the favourable reception which the Astronomical Theory of the Ice Age has met with among scientific men has been chiefly due to the writings of Dr. Croll, its more general acceptance, especially among the semi-scientific public, has been greatly assisted by the lucid and vigorous exposition by Sir Robert Ball, in his “Cause of an Ice Age,” published in 1891. But notwithstanding the apparently exhaustive way in which Croll discusses the problem, and the fact that Sir Robert Ball's work has been published in the “Modern Science” Series (indicating that the theory has secured a place among the permanent acquisitions of science), I venture to think that a careful examination of the problem will show that the theory is but a vague speculation; clothed, indeed, with a delusive semblance of severe numerical accuracy, but having no foundation in physical fact, and built up of parts which do not dovetail one into the other. The following pages contain what I hope will be admitted to be a justification of this sweeping condemnation. The first portion of my paper deals with Croll's form of the theory; the second, to be published next month, deals with Sir Robert Ball's form.