The same thing will apply if our symbols are more numerous, and if they express relations of motion as well as of space, or, in fact, any relations which are governed by fixed laws expressible by equations. If I have succeeded in conveying to the readers any idea of this celebrated calculus, they will perceive what an analogy it presents to the idea of modern physical and chemical science, that of molecules, atoms, and ether, forming differentials of successive orders of the infinitely small. It is certainly most remarkable that while the former was a purely intellectual idea based on mathematical abstractions, and which was invented and worked as an instrument for solving the most intricate astronomical problems for nearly two centuries, without a suspicion that it represented any objective reality: the latter idea, based on actual experiment, seems to show that differentials and integrals have their real counterpart in nature and represent fundamental facts in the constitution of the universe. Those who are of a mystic or metaphysical turn of mind may discern in this, arguments for matter and laws of matter being after all only manifestations of one universal, all-pervading mind; but in following such speculations we should be deserting the solid earth for cloudland, and passing the limit of positive knowledge into the region where reflections of our own hopes, fears, religious feelings, and poetical sentiments form and dissolve themselves against the background of the great unknown. For the present, therefore, I confine myself to pointing out how these undoubted truths of mathematical science, which have verified themselves in the practical form of enabling us to predict eclipses and construct nautical almanacs, correspond with and throw light upon the equally certain facts of this succession of infinitely small quantities of successive orders in the constitution of matter.