300 Mr. Challis on the Theory of the 



As the particles at the closed end must necessarily be at rest, 

 we may reckon x from B towards A, and date t from an instant 

 at which the condensation at B is o. Then v will be equal to o, 

 wherever x = n\, and as will = o, wherever x — {n + \)\. The 

 points obtained by putting n = o, l, 2, 3, &c. are in the first 

 case nodes, in the other loops. As tliese nodes and loops arise 

 solely from the reflection from the closed end, they cannot exist 

 in the tube open at both ends, at least not from the same cause, 

 and the two tubes in this respect are not circumstanced alike. 

 We have seen reasons in Art. 7, and shall give others hereafter, 

 to conclude, that the waves on returning back to the open ex- 

 tremity, will be transmitted into the circumambient fluid, causing 

 alternations of rarefaction and condensation in it, as frequent 

 as those generated in the tube. And as in this manner there 

 will be no cause at the open extremity of the closed tube to 

 affect its nodes and loops, so there will be none at the extremity 

 of the tube open at both ends to produce nodes and loops. Our 

 conclusion is also confirmed by the fact that when the cause 

 which produces the aerial vibrations ceases, the sound to which 

 they give rise ceases to all appearance instantaneously : — an efi'ect 

 which could scarcely take place if the particles were reduced 

 to rest solely by their inertia, and by their friction against the 

 sides of the tube. The vibrations of the air in a cylindrical 

 tube are analogous to those of an elastic chord, and the closed 

 ends correspond to the fixed points of the chord. If no point 

 be fixed in the direction in which the original motion impressed 

 on the chord is travelling, it will go on interruptedly without 

 being reflected ; so that according to the view I have taken, 

 as there is no ditference in theory between the two cases, there 

 will be none in practice. 



13. It does not appear from any thing that precedes, that 

 we can a priori assign a set of waves which a tube of given 



