proof." Gratry objects to Cournot speaking as if one process was less rigorous than the other. And, in fact, we are quite as sure what is the result of an "integration to Infinity," as of what is the answer to a Rule of Three sum.
Suppose that a marble is running round in an elliptical groove under our eyes. Geometry enables us to investigate the relations between the various portions of the course which we see it pursue. But we know its course by direct inspection. Geometry can but arrange into a convenient form, information which we have gathered by observation; or, at most, it shortens the processes by which we acquire information. But when an Astronomer has observed a small portion of the orbit of a heavenly body, it disappears from his ken. He has to construct in imagination its future path, guided by knowledge of the hidden law of its motion. In order to do so, he must resort to the method of the Infinitesimal Calculus; the method thus described by Gratry:—"We have analyzed the finite in order to know the infinitesimal. From the knowledge given by the study of the finite, we have eliminated the quality of finiteness; what remains is true for the infinitesimal; that is to say, for the analysis and knowledge of the Indivisible and the Infinite. We have analyzed the discontinuous, the divisible, the finite; and have found therein the law of the Continuous, the Indivisible, the Infinitesimal."
But when we know the theoretical law of the planet's course, how do we know that, when we have lost sight of it, it still continues to obey the Laws of Mathematics? No Syllogistic Logic can prove that it does not wander, lawlessly, into space. Yet the mathematician ventures
