252 Mb HOPKINS ON AERIAL VIBRATIONS 



IV. Sonorous vibrations, whatever be their period, may be main- 

 tained in a tube of any length, except that of which the length does 

 not approximate too nearly to something less than an even multiple 



of J in the closed tube, or to an odd multiple of - in the open one. 



(Arts. 11, 12.) 



V. The intensity of the general vibrations in the tube varies with 

 the length of the tube, being greatest for the lengths just mentioned, 

 and least in the closed tube when its length is rather greater than an 



odd multiple of -; and in the open one, when it is something less than an 

 even multiple of -r . (Art. 10.) 



VI. In these latter cases also of both tubes, the opposition afforded 

 by the vibratory motion of the air within the tube, to the vibrating 

 of the plate, is least; and greatest for the lengths which approximate 

 to those mentioned in (IV.), as those with which the vibrations cannot 

 be maintained. (Art 13.) 



VII. When the cause producing the vibrations in a tube ceases, 

 the vibrations themselves may cease, not instantaneously, but in a period 

 of time not exceeding the small fraction of a second, supposing the 

 tube not to exceed a few feet in length. (Art. 14.) 



VIII. If we suppose the original disturbance to produce an un- 

 dulation different in any respect to those produced by the cause which 

 afterwards maintains the vibratory motion of the aerial column, this 

 original disturbance will cease to affect the form of subsequent undula- 

 tions in a period of time not exceeding the small fraction of a second, 

 depending on the length of the tube*. (Art. 14.) 



* Similar inferences to the above may be drawn equally from M. Poisson's investigations, 

 except that the phenomena according to his solution would take place for lengths of the open 

 tube materially different from those above-mentioned. 



