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representative of an endless host of applicable and actually existent truths. For the objects of both sciences you must have inductive or observational evidence; but by a moral light in the one science, and a mathematical light in the other, we arrive at the ethics of the first science, at the mathematics of the second, without the aid of the inductive philosophy.
12. It is interesting to note if aught may have fallen from Lord Bacon himself upon this subject. In his English treatise on “the advancement of learning," he says, “that in mathematics I can report no deficience.”
So that this great author of the experimental method by which to arrive at a true philosophy of facts, had no improvement to propose on the methods of mathematical investigation. And in his more extended Latin treatise on the same subject, entitled, “De augmentis scientiarum," where he takes so comprehensive a view of all the possible objects of human knowledge, he says, speaking of geometry and arithmetic, “Quæ duo artes, magno certe cum acumine, et industria, inquisitæ et tractatæ sunt: veruntamen et Euclidis laboribus in geometricis nihil additum est a sequentibus quod intervallo tot seculorum dignum sit;" or so which two arts have certainly been investigated and handled with much acuteness and industry; notwithstanding which, however, nothing has been added to the labours of Euclid in geometry by those who have followed him, that is worthy of so long a series of ages." 13. The
discrimination then to be made in natural philosophy, is between the facts or data of the science, and the relations that by means of mathematics might be educed from these data. The former are ascertained by observation-after which no further aid is required from observation, while we prosecute that reasoning which often brings the most weighty and important discoveries in its train. It is well to consider how much can be achieved by mathematics in this process, and how distinct its part is from that of wide and distant observation; insomuch that by the light which it strikes out in the little chamber of one's own thoughts, we are enabled to proceed from one doctrine and discovery to another. From three distant points in the firmament, a triangle may be formed to which the very mathematics are applicable that we employ upon a triangle constructed upon paper by our own fingers. Whether they be the positions and the distances that lie within the compass of a diagram, or the positions and distances that obtain in wide immensity, it is one and the same geometry which, from a few simple and ascertained data, guides the inquirer to the various and important relations of both. After that observation hath done its office, and made over to mathematics the materials which it hath gathered—this latter science can guide the way to discoveries and applications innumerable; and without one look more upon the heavens, with nought but the student's concentrated regard on the lines and the symbols that lie in little room upon his table, might the whole mystery and mechanism of the heavens be unravelled.
14. Let those things, then, be rightly distinguished which are distinct from one another. They were not the objects of the science which gave the
observer his mathematics. These objects were only addressed to his previous and independent mathematics; and he, in virtue of his mathematics, was enabled rightly to estimate many important relations which subsisted between the objects. Nay, it is conceivable that the objects might have remained for ever obscure and unknown to him. He, in this case, would have wanted an application which he now has for his mathematics; but the mathematics themselves would have been still as much within his reach or his power of acquisition as before. His mathematical nature, if we may so speak, would have been entire notwithstanding; and he have had as clear a sense of the mathematical relations, and as prompt and powerful a faculty of prosecuting these to their results. Things might have been so constituted, as that every star in the firmament should have been beyond the discernment of our naked eye; or what is still more conceivable, the lucky invention might never have been made by which the wonders of a remoter heavens have been laid open to our view. But still they were neither the informations of the eye nor of the telescope which furnished man with his geometry; they only furnished him with data for his geometry. And thus, while the objects of astronomy are brought to him by a light from afarthere enters, as à constituent part of the science, the mathematics of astronomy, immediately seen by him in the light of his own spirit, and to master the lessons of which he needs not so much as one excursion of thought beyond the precincts of his own little home.
15. Now, what is true of the mathematical may be also true of the moral relations. We
have the faculty of perceiving these relations whether they be occupied by actually existent objects or not; or although we should be in ignorance of the objects. On the imagination that one of the inhabitants of the planet Jupiter had the mysterious knowledge of all my movements, and a mysterious power of guidance and protection over me; that he eyed me with constant benevolence, and ever acted the part of my friend and my guardian— I could immediately pronounce on the gratitude and the kind regard that were due from me back again : And should the imagination become a reality, and be authentically made known to me as such, I have a moral nature, a law within my heart, which already tells me how I should respond to this communication. The instance is extravagant; but it enables us at once to perceive what that is which must be fetched to us from without, and what that is which we have to meet it from within. The objects are either made known by observation; or, if they exist without the limits of observation, they are made known by the credible report or revelation of others. But when thus made known, they may meet with a prior and a ready made Ethics in ourselves. The objects may be placed beyond the limits of human experience; but though the knowledge of their existence must therefore be brought to us from afar, a sense of the correspondent moralities which are due to them may arise spontaneously in our bosoms. After the mind has gotten, in whatever way, its information of their reality
then within the little cell of its own feelings and its own thoughts, there may be a light which manifests the appropriate ethics for the most distant beings in the universe.
16. We are thus enabled to bestow a certain amount of elucidation on a question which falls most properly to be discussed at the outset of Natural Theology. On this distinction between the ethics of the science and the objects of the science, we can proceed at least a certain way in assigning their respective provinces to the light of nature and the light of revelation. But for this purpose let us shortly recur again to the illustration that may be taken from the science of astronomy.
17. Natural Philosophy has two great departments-one of them celestial, the other terrestrial; and it may be thought a very transcendental movement on the part of an inquirer, a movement altogether per saltum, when he passes from the one to the other. Now this is true; but only should it be remarked in as far as it regards the objects of the science. The objects of the celestial lie in a far more elevated region than the objects of the terrestrial; and it may certainly be called a transcendental movement, when, instead of viewing with the telescope some lofty peak that is sustained however on the world's surface, we view therewith the planet that floats in the firmament and at an inconceivably greater distance away from it. There is a movement per saltum when we pass from the facts and data of the one department, to the facts and data of the other. But there is no such move