298 Mr. Challis on the Theory of the 



and velocities. Afterwards it will be represented for any length 

 of time by a straight line c'z, parallel to the axis and distant 

 from it by dc'; for this motion was shewn in the preceding 

 Article to be pos.sible. Hence it appears, that if a piston be 

 made to move uniformly in an open cylinder, the resistance it 

 meets with from the air varies as its velocity, if the velocity 

 be small compared with that of sound. Also as the rarefaction 

 on one side of the diaphragm is just equal to the condensation 

 on the other, it may be concluded that if a column of air be 

 made to move uniformly through a cylindrical tube, it will either 

 be condensed or rarefied proportionally to its velocity. As this 

 is a case in which no extraneous force acts, the equation v= ±as 

 should apply. 



If the diaphragm after a while suddenly stop, the resulting 

 wave will take the type, fecc'e'f, (Fig. 10.). If it move but for 

 a very short time, fq'qf (Fig. 11) will be its type. In these 

 two cases mm' = aT, t being the time during which the diaphragm 

 moves, and the area mm'n'n represents the condensations it ge- 

 nerates. Reasoning exactly analogous to all that is contained 

 in this Art., will apply to the case in which the diaphragm pro- 

 duces rarefaction. 



By what precedes we are informed what will take place, 

 if a partition, which separates a column of condensed or rarefied 

 fluid from fluid of the mean density, be suddenly removed ; for 

 the action of the fluid will be the same as if the partition were 

 suddenly converted into a moveable diaphragm. 



As we have now considered the effects of impact, and of 

 pressure on the fluid, and as every disturbance mu.st be made 

 by the one or the other of these means, or by both together, 

 the foregoing discussion will suftice for determining the eflfect 

 produced by any disturbance, the exact nature of which i.s 

 given. 



