280 POPULAR LECTURES AND ADDRESSES. 



becoming shriller and shriller, before other ears 

 cease to hear it ; and, therefore, I can only say 

 in a very general way, that something like 10,000 

 periods per second is about the shrillest note 

 the human ear is adapted to hear. We may 

 define musical notes therefore as changes of 

 pressure of the air, regularly alternating in 

 periods which lie between twenty and 10,000 per 

 second. Well now, are there vibrations of thirty, 

 or forty, or fifty, or a hundred thousand or a 

 million of periods per second in air, in elastic 

 solids, or in any matter affecting our senses ? We 

 have no evidence of the existence in matter of 

 vibrations of very much greater frequency than 

 10,000, or 20,000, or 30,000 per second, yet we 

 have no reason to deny the possibility of such 

 vibrations existing, and having a large function 

 to perform in nature. But when we get to some 

 degree of frequency that I cannot put figures 

 upon, to something that may be measured in 

 hundred-thousands, if not in millions, of vibrations 

 per second, we have not merely passed the limits 

 of the human ear to hear, but we have passed 



