224. Mr EARNSHAW, ON FLUID MOTION. 



that y, X, and / are indeterminate, unless the forms of F' and Fl be the 

 same: hence we may write 

 /. F' (fc +gy + h% - at) = -/'. F' \f (e - a) +^' (y - ^) + K (» - 7) - at\ ; 



and fc+gy + h'x. — at=f' {c-a) +g' (y — fi) +//(s: — 7) - at; 



••• g'=g 

 K = h 



C" = — (c - a) or a = 2c 



7 = 0. 

 .-. = F{fx +gy + hz - at) + F\/(2c- .r) +gy + kz - at\ . 



This expression represents two plane-waves : the latter of which is the 

 effect of the screen, and is that which is usually called the reflected- 

 wave. It is evident that tlie angles of incidence and reflection are equal. 



25. When _/= 0, there is no reflected-wave. Now when y= 0, the 

 wave and the screen are at right angles to each other. Hence, a wave- 

 surface may be cut into any number of parts by fixed normal screens, 

 without affecting the motion. Consequently a plane-M'ave may be trans- 

 mitted as perfectly through a prismatic tube, as through an infinite 

 medium. 



If the boundaries of the medium are not normals to the wave there 

 will of necessity be reflection. This circumstance produces nodes and 

 loops, and probably affects the timbre of the notes, and the tone of 

 musical instruments. 



26. I come now to consider the second case of Art. 22, viz. ^^'^here 

 f, g, h in the value of 0, vary continuously in passing from one function 



to another. 



In this case, that ^ may be complete, f, g, h must have all values 

 from -1 to +1, and therefore in assigning to Jig, h, all possible values 

 in the function 



F{f{x -a)+g(y- li) + k(z-y)- at}. 



