462 Prof. Challis on the Source and 



adduced, which will serve to illustrate the subsequent reasoning. 

 It is a well-known fact that if vibrations are excited at one end 

 of a cylindrical tube open at both ends, by blowing across it, or 

 other means, there will be formed in the tube equidistant posi- 

 tions of minimum velocity and intermediate positions of minimum 

 change of density. These facts are accounted for by supposing 

 that two series of vibrations are propagated along the tube in 

 opposite directions. If the series are exactly alike and equal, the 

 velocity will be zero at the former positions, and at the other 

 there will be no condensation. In actual instances the vibrations 

 are not generally exactly equal when they originate in the man- 

 ner above mentioned. But for our present purpose we may 

 assume them to be so, taking no account of a slight excess of 

 the vibrations of one set above those of the other. Now the 

 vibrations propagated from the end where the disturbance is 

 made are clearly due to the disturbance itself. But what is the 

 origin of the returning vibrations ? The answer to this question 

 is, that the tube is at the other end relatively a cause of disturb- 

 ance by suddenly ceasing to confine the vibrations as they reach 

 it. At both ends the condition must be satisfied that the density 

 is permanently very nearly the same as in the surrounding air. 

 At the further end this condition is fulfilled by the relative dis- 

 turbance producing reflected waves, of which the condensation in 

 that position is just equal and opposite in sign to the condensa- 

 tion due to the direct waves. At the other end the same con- 

 dition is fulfilled by the condensation due to the reflected waves 

 being equal and opposite in sign to that impressed by the dis- 

 turbance. Under the circumstances supposed, the motion is 

 evidently alike on the two sides of a plane dividing the tube 

 transversely into two equal parts, and in the position of this 

 plane the velocity is zero. Conceive now the column of fluid in 

 the tube to be divided by an indefinitely thin partition placed in 

 that position. That half of the column which is furthest from 

 the disturbance will then become quiescent, and the vibrations 

 of the other half will remain just as before. Consequently the 

 total movement of the fluid will be only half as much in the case 

 of the closed tube as in that of the open tube, although the ori- 

 ginal disturbance is the same in the two cases. In fact, there is, 

 in the latter case, an additional relative disturbance, due to the 

 rigidity, or constancy of form, of the tube. We have thus been 

 conducted to a remarkable principle, peculiar to the motion of a 

 fluid, viz. that the effect of a disturbance impressed actively may 

 be subsequently increased by a relative disturbance due to a 

 passive rigid body. The above considerations are not merely 

 illustrative of the principle, but amount to a proof that it holds 

 good in aerial vibrations, and by consequence in setherial vibra- 



