OF EOUTLIBKIUM OF A KOTATINO MASS OF LIQUID. 
3U7 
. . 1 — . 
Then substituting for y8, we find 
X “j“ K"" 
and for both cases 
Hence 
K' = q 
•") 0.0 
2 2 — oy- 
1 — 22^" 
t — 2" 
Slid 
13. (/^) and 1 ^. 2 ^ (/x) = - ( 1 - sin- 6 
Co {(j>) and C/ {(ji) = 1 — g/j cos- (f> 
O 0 
Avliere - ' •' 
5 I 
K- = 1 /- -, and f/- — ^[1 + K- d- (1 — with ujiper 
( 
tirst and the lower sign for the second. 
It appears from (19) and § 7, of “ Harmonics” that 
' p 1 / \ ^ 
(") - ’ 
(/x) = sin ^ (1 — k' sin- 6 )\ 
Cd {(f)) = cos (1 — cos- (f)f 
and from (2i) and (22) that 
I3d (.) = 
(1 — /C” Slid 
Sild ylr 
(g) = sin 6 cos 6, 
So^ {(f)) = sin (f){l — K~ cos-f/))" 
Lastly, from (25) and (2G) 
P/W 
P/ (ia) 
{4>) 
cos )Jr(l — K" sild i/r 
sild -yfr ’ 
cos d (1 — K~ sild d)t 
: sin (f) cos (f) 
Turning to the harmonics of the third degree, we found that in the two 
the ty})e is UEC, 
^3;j {d) and {u) = v{v' - ^ “f J 
2 i; 2 
(10), 
dgn for the 
■ (11). 
• (in)- 
. (13). 
cases where 
