Gases under High Pressures. 



185 



may denote the general thickness of the two-dimensional jet 

 by b, and take b + rj to represent the actual thickness at the 

 place (z) where the retardation is to be determined. The 

 retardation is then sufficiently represented by A? where 



A=\ {p-Pi)d<J=\ pd?j-i Pl (b + v), • (2o> 



Jo Jo 



p being the density in the jet and p x that of the surrounding 



gas. The total stream 



= \ p(\V + 8w)dy = W\ pdy+p\ 



Jo Jo Jo 



and this is constant along the jet. Thus 



8 w dy ; 



A = V-ipiV 



(26} 



being a constant, and squares of small quantities being 

 omitted. 



In analogy with (9), we may here take 



8w; = Hcos^.cos{ ) % x /(W 2 /a 2 -l)}, . . (27) 



and for the principal vibration the argument of the cosine is 

 to become ^ir when y = ±b. Hence 



f*« , H cos jSz 



Jo s ^ = /v{vv> 2 -ir 



• • (28) 



Also 



<^=j% t ;^ = Wc + /3- 1 Hsin^.cos{^ v /(W 2 /a 2 -l)}, 



Thus 



i _ 1 G*$\ , _ Hcogj88. •{ W Va?-l} 



Accordingly 



A = C- H |^f [„ •{ W/a»-lf + s iyi !p_ 1} ) ; (29) 



so that the retardation is greatest at the places where 77 is 

 least, that is where the jet is narrowest. This is in agreement 



