240 



Mr HOPKINS ON AERIAL VIBRATIONS 



or, 



v=-f{aT-x)-f{aT-{^l-x)} , ^ 



r^n ^ it / 



. . . ^nl 



Similarly, we find 

 as = f(fiT-x)+/{aT-{2l-x)}, 



+ 2,., {<t> [« (r + ^) -(.r + c)] + [« (^. 4-^^) -(2/ + C- .r)]}. ^ 



\...(D)(1). 



\.. .(D)(2). 



8. The function /(ar — x), in the expression for v, represents the 

 velocity of any particle produced by the first wave, propagated 

 along the tube from the original disturbance at A, so long as t 



is less than - ; and if this wave were reflected entirely from B, 



a 



the first line of the above expression for v, would give us the velocity 

 of any particle within the sphere of the reflected wave, the time t 



not exceeding — . 



With our supposition as to the original disturbance, the form of f 

 T less than — I will be immediately known from that of (p. The 



