1868.] from a Vibrating Body to a surrounding Gas, 471 



some curious experiments which show the singular incapacity of hydrogen 

 either pure or mixed with air, for receiving and conveying vibrations from 

 a bell rung in the gas. The facts elicited by these experiments seem not 

 hitherto to have received a satisfactory explanation. 



It occurred to the author of the present paper that they admitted of a 

 ready explanation as a consequence of the high velocity of propagation of 

 sound in hydrogen gas operating in a peculiar way. When a body is 

 slowly moved to and fro in any gas, the gas behaves almost exactly like an 

 incompressible fluid, and there is merely a local reciprocating motion of the 

 gas from the anterior to the posterior region, and back again in the oppo- 

 site phase of the body's motion, in which the region that had been ante- 

 rior becomes posterior. If the rate of alternation of the body's motion be 

 taken greater and greater, or, in other words, the periodic time less and 

 less, the condensation and rarefaction of the gas, which in the first 

 instance was utterly insensible, presently becomes sensible, and sound- 

 waves (or waves of the same nature in case the periodic time be beyond 

 the limits of audibility) are produced, and exist along with the local reci- 

 procating flow. As the periodic time is diminished, more and more of the 

 encroachment of the vibrating body on the gas goes to produce a true 

 sound-wave, less and less a mere local reciprocating flow. For a given 

 periodic time, and given size, form, and mode of vibration of the vibrating 

 body, the gas behaves so much the more nearly like an incompressible fluid 

 as the velocity of propagation of sound in it is greater ; and on this 

 account the intensity of the sonorous vibrations excited in air as compared 

 with hydrogen may be vastly greater than corresponds merely with the dif- 

 ference of density of the two gases. 



It is only for a few simple geometrical forms of the vibrating body that 

 the solution of the problem of determining the motion produced in the gas 

 can actually be effected. The author has given the solution in the two 

 cases of a vibrating sphere and of an infinite cylinder, the motion in the 

 latter case being supposed to take place in two dimensions. The former 

 is taken as the representative of a bell ; the latter is applied to the case of 

 a vibrating string or wire. In the case of the sphere, the numerical results 

 amply establish the adequacy of the cause here considered to account for 

 the results obtained by Leslie. In the case of the cylinder they give an 

 exalted idea of the necessity of sounding-boards in stringed instruments ; 

 and the theory is further applied to the explanation of one or two inter- 

 esting phenomena. 



