288 Mr. Challis on the Theory of the 



generating- a portion cd (Fig. 3.) of a primary wave, suddenly stop. 

 The particles in contact with it, which were moving with a 

 velocity represented by ac, are suddenly reduced to rest, because 

 they cannot separate for any appreciable time from the diaphragm, 

 on account of the great force which jiresses them against it. 

 Now in whatever manner the other particles are affected, we 

 may be sure that as soon as the diaphragm ceases to move, 

 the law of condensation given by the curve cd will begin to 

 change, and the change will be accompanied by a movement 

 of the particles regulated by the laws of propagation demon- 

 strated in the foregoing Articles. By referring to Art. 6, it will 

 be seen that the movement will proceed as if reflection were 

 taking place at ah, and that the curve cd gives the compound 

 condensation arising from the incident and reflected portions 

 of the wave. Also the equations 



V = F{x-at) +f{x + at), 



as = F{x — at) —f{x + at) 



shew, that where u = o, that is, at the reflecting surface, 



F{x-at) = -f{x + al), as = 2 F{x-a1). 



Hence, bisect ac in e, describe some curve ef, (the nature of 

 which will hereafter be considered,) to represent the incident 

 portion of the wave, and diminish the ordinates of cd by quan- 

 tities equal to those of ef, so as to form the curve en. Then the 

 particles will move in such a manner that the ordinates of the 

 broken curve end, will represent the velocities in the direction 

 ad, and the curve ef those in the contrary direction. The 

 l)articles in contact with the diaphragm will have no motion 

 .at all, but will undergo the condensations indicated by double the 

 ordinates of the curve ef. When the condensation becomes o, 

 these particles will have no more tendency to change their state, 



