In connection with this subject Dr. Mivart takes occasion to allude to Professor Helmholtz’s method of disproving the absoluteness of truth. He supposes “beings living and moving along the surface of a solid body, who are able to perceive nothing but what exists on this surface, and insensible to all beyond it. … If such beings lived on the surface of a sphere, their space would be without a limit, but it would not be infinitely extended; and the axioms of geometry would turn out very different from ours, and from those of the inhabitants of a plane. The shortest lines which the inhabitants of a spherical surface could draw would be arcs of greater circles,” etc. We have quoted enough from the professor to indicate the drift of his objection. He concludes: “We may résumé the results of these investigations by saying that the axioms on which our geometrical system is based are no necessary truths.” Such is the sorry mode of reasoning adopted by an eminent man of science in establishing a conclusion so subversive of the principles of science. Is it not evident that, no matter what name the inhabitants of the sphere described by Helmholtz might bestow on the “arcs of great circles,” these still would be “arcs,” and as such those beings would perceive them? As showing the lack of uniformity of views which prevail among men of science when it is question of super-sensible cognitions, Mr. Mill rushes to the opposite extreme from Herbert Spencer, and holds that there is nothing to prevent us from conceiving 2×2 = 5. In this arraignment of Spencer’s faulty view of the basis of certainty, Dr. Mivart proceeds with care and acumen, and adroitly pits his antagonists against each other, or invokes their testimony in support of his own views as against themselves.