272 POPULAR LECTURES AND ADDRESSES. 



sound, and taking place with perfect regularity, 

 period after period. Noises and musical sounds 

 merge into one another. Musical sounds have a 

 possibility at least of sometimes ending in noise, 

 or tending too much to a noise, to altogether 

 please a fastidious musical ear. All roughness, 

 irregularity, want of regular smooth periodicity, 

 has the effect of playing out of tune, or of music 

 that is so complicated that it is impossible to 

 say whether it is in tune or not. 



But now, with reference to this sense of sound, 

 there is something I should like to say as to 

 the practical lesson to be drawn from the great 

 mathematical treatises which were placed before 

 the British Association, in the addresses of its 

 president, Professor Cayley, and of the president 

 of the mathematical and physical section, Pro- 

 fessor Henrici. Both of these professors dwelt on 

 the importance of graphical illustration, and one 

 graphical illustration of Professor Cayley's address 

 may be adduced in respect of this very quality of 

 sound. In the language of mathematics we have 

 just " one independent variable " to deal with in 



