fixed limit to the acuteness of sounds which we can hear; some individuals can hear sounds too shrill for other ears, and as there is nothing in the nature of the atmosphere to prevent the existence of undulations far more rapid than any of which we are conscious, we may infer, by the principle of continuity, that such undulations probably exist.
There are many habitual actions which we perform we know not how. So rapidly are acts of minds accomplished that analysis seems impossible. We can only investigate them when in process of formation, observing that the best formed habit is slowly and continuously acquired, and it is in the early stages that we can perceive the rationale of the process.
Let it be observed that this principle of continuity must be held of much weight only in exact physical laws, those which doubtless repose ultimately upon the simple laws of motion. If we fearlessly apply the principle to all kinds of phenomena, we may often be right in our inferences, but also often wrong. Thus, before the development of spectrum analysis, astronomers had observed that the more they increased the powers of their telescopes the more nebulæ they could resolve into distinct stars. This result had been so often found true that they almost irresistibly assumed that all nebulæ would be ultimately resolved by telescopes of sufficient power; yet Huggins has in recent years proved by the spectroscope, that certain nebulæ are actually gaseous, and in a truly nebulous state.
The principle of continuity must have been continually employed in the inquiries of Galileo, Newton, and other experimental philosophers, but it appears to have been distinctly formulated for the first time by Leibnitz. He at least claims to have first spoken of “the law of continuity” in a letter to Bayle, printed in the Nouvelles de la République des Lettres, an extract from which is given in Erdmann’s edition of Leibnitz’s works, p. 104, under the title “Sur un Principe Général utile à l’explication des Lois de la Nature.”23 It has indeed been asserted that the doctrine of the latens processus of Francis Bacon involves the principle of continuity,24 but I think that this doctrine, like that of the natures of substances, is merely a vague statement of the principle of causation.