HARMONICS. 81 



if it is a large and heavy bell besides the general vibra- 

 tion which emits the principal and dominant tone, there 

 are always a great many others which blend with the 

 principal one, and combine with it in the effect of produc- 

 ing the general sound. These subordinate tones are called 

 the harmonics. It is so with a musical string or wire ; it 

 has its harmonics as well as its principal sound, and they 

 all come together through the air to the ear without in- 

 terfering with each other. So, when a band of one hun- 

 dred performers is playing, it is wonderful to think what 

 an immensely complicated mass of vibrations, produced by 

 so many kinds of instruments and playing so many differ- 

 ent parts, must come to the ear through the air at the same 

 time ; and though many of them may mingle and blend so 

 as to produce a delightful harmony, they do not disturb 

 or derange each other at all, for if they did so the result 

 would be only a discordant noise. 



"Such cases as these," said Lawrence, "make it just pos- 

 sible for us to conceive that the emanations of light, mov- 

 ing constantly, as they do, with such amazing velocity, and 

 in every direction through the starry heavens, without in- 

 terfering with each other at all, may be propagated, as sci- 

 entific men now suppose, by undulations or oscillations ir 

 a very subtle and highly elastic medium. 



"At any rate," he added, "this much is certain, that 

 these emanations are propagated, in some way most mys- 

 terious to us, in right lines, diverging in every direction 

 from the centre ; that they expand in two dimensions as 

 they advance, and so each portion of them occupies a 

 space that increases as the square of the distance, and, of 

 course, that the intensity on a surface of given magnitude 

 diminishes as the square of the distance, or, as the mathe- 

 maticians say, is inversely as the square of the distance ; 

 and, finally, that these rays are wholly invisible to us, ex- 

 D2 



