OF AIR OBSERVED IN KUNDT’S TUBIS. 
Whatever may be the actual values of u and r, we may write 
15 
in which 
From (56), (57), 
dx'dy’ dy dx 
„ . du , dv „ , du dv 
V^ = y-+ W’ ^' X P = T~T 
dx dy dy dx 
(58) , 
(59) . 
, ,d\da du _ dw du , d ( da , da\ 
l+V dt)Zv^-Yt +V ^ U - U I- V di l - V \Vt l dx + V iy) ■ 
n ,d\da dv „ dv dv ,d[ da da 
a ~ +V dtUj=~dt +l ’ V ' V ~ U di~ V dy~ 1 ' dy\ U di + % 
■ m, 
( 61 ). 
Again from (60), (61), 
o , d ,d\ „ dxa d( da da\ . 0 / der da 
a+v d l +v 7tr*-w=iA u ^ + %r (v+, ' w 'v^ + % 
dv 
d ( du du\ d ( dv 
— — w—+v— — — \u—+ V j 
dx\ dx dy] dy\ dx dy 
( 62 ). 
For the first approximation the terms of the second order in u, v, and a are to 
be omitted. If we assume that as functions of t, all the periodic quantities are 
proportional to e rnt , and write q for o?-\-inv-\-inv, (62) becomes 
Now by (57), (59), 
so that 
and 
q^ 2 or-\-n z a=0 . 
V 3 </>= — incr—i - V 3 cr, 
n 
, -2 4-, 
<p—l -cr, 
I m ' 
iq da d\]r iq da ddy 
n dx dy’ n dy dx 
(63). 
(64). 
Substituting in (60), (61), with omission of terms of the second order, we get in 
view of (63), 
(t>V 3 — inyy- — 0 , 
dy 
* It is unnecessary to add a complementary function 0', satisfying v 2 0’ —0, as the motion corre¬ 
sponding thereto may be regarded as covered by 0. 
