618 THE PKINCIPLES OF SCIENCE. [CHAP. 



to be made at intervals which we gradually diminish until 

 the separate strokes coalesce into a uniform hum or note. 

 With great advantage we approach, as Tyndall says, the 

 sonorous through the grossly mechanical. In listening to 

 a great organ we cannot fail to perceive that the longest 

 pipes, or their partial tones, produce a tremor and fluttering 

 of the building. At the other extremity of the scale, there 

 is no 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 nebulae 

 they could resolve into distinct stars. This result had 

 been so often found true that they almost irresistibly 

 assumed that all nebulae would be ultimately resolved by 

 telescopes of sufficient power ; yet Huggins has in recent 

 years proved by the spectroscope, that certain nebulae 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 Rdpub- 

 lique des Lettres, an extract from which is given in 

 Krdmann's edition of Leibnitz's works, p. 104, under the 



