380 LECTURE XXXII. 



aliquot part of the length; but a stopped pipe cannot be divided into any 

 even number of similar parts; its secondary sounds being only those of a 

 pipe of which the proportion is determined by the odd numbers, its length 

 being, for example, one third, one fifth, or one seventh of the original 

 length. These secondary notes are sometimes called harmonics; they are 

 not only produced in succession from the same pipe, but they are also often 

 faintly heard together, while the fundamental note of the pipe continues to 

 sound. When the pipe has a large cavity connected with it, or consists 

 principally of such a cavity, with a small opening, its vibrations are usually 

 much less frequent, and it is generally incapable of producing a regular 

 series of harmonics. 



J . _ It is obvious from this statement of the analogy between the velocity of 



/ U^.^lt^'^-^ sound and the vibrations of the air in pipes, that they must be affected in 



a similar manner by all alterations of temperature. Thus, the frequency of 

 the vibrations of a pipe must be increased nearly in the ratio of 33 to 34 by 

 an elevation of 30 degrees of Fahrenheit's thermometer ; and if this change 

 be accompanied by a transition from dampness to simple moisture, the sound 

 will be still more altered. 



/ / Dr. Chladni has discovered that solids of all kinds, when of a proper form,. 



*"*** are capable of longitudinal vibrations, exactly resembling in their nature those 



f^^^-f 



of the air in an organ pipe, having also their secondary or harmonic notes 

 related to them in, a similar manner. These vibrations are always far more 

 frequent than those of a column of air of equal length, the velocity, with 

 which an impulse is transmitted by a solid of any kind, being usually from 5 

 to \6 times as great as the velocity of sound in air; so that the longitudinal 

 sounds are always extremely acute, when they are produced by substances^ 

 of moderate length. These sounds afford perhaps the most accurate mode 

 of determining the velocity of the transmission of an impulse through any 

 elastic substance, and of obtaining from that velocity the exact measure of 

 its elasticity : they may be easily exhibited by holding a long bar or wire of 

 iron or brass in the middle, and striking it at one end witli a. small hammer^ 

 in the direction of its length. , 



The vibrations by which solid bodies most usually produee sound are» 

 however, not longitudinal, but lateral, and they are governed either by a 



