OF WHICH IS MOVING ROTATIONALLY AND PART IRROTATIONALLY. 369 
Therefore 
dudv 
dx' dy 
d°X dX 
dX 
d 2 X 
dX 
dX 
dxdt 
dy 
1 
dt 
dxdy 
dt 
dy 
d 2 \]r dy\r 
n 
d-yfr 
d~yjr 
dijr 
d\]r 
dxdt 
dy 
dt 
dxdy 
dt 
dy 
d 
aIX 
dX 
dX 
dX 
2 dx 
dx 
dy 
dx 
dy 
d.yjr 
dijr 
d-yjr 
d\fr 
dx 
dy 
dx 
dy 
d~X 
dX 
dX 
d*X 
dX 
dX 
dxdy 
dt 
i 
dx 
dydt 
dx 
dt 
d“->\r 
d\Jr 
i 
dyjr 
d 2 \Jr 
d\[r 
d\jr 
dxdy 
dt 
dx 
dydt 
dx 
dt 
d 
dX 
dX 
dX 
dX 
2 dy 
dx 
dy 
dx 
dy 
d-^r 
dyjr 
d-yjr 
dyfr 
dx 
dy 
dx 
dy 
dX 
dx 
d-yjr 
dx 
dX 
dx 
difr 
dx 
But from the equation of continuity 
Therefore 
du dv 1 (d d d 
&+A, = ~p \dt +u dx +v dy) P 
1 (d , d , d 
' p \j<+ u lZ J r v 
\dt~ r u, dx' TU dy) p 
dX dX 
dx dy 
dyjr d\jr 
dx dy 
d n -X 
dX 
dX 
d-X 
dxdt 
dy 
+ 
dx 
dydt 
d?yjr 
d\]r 
d\Jr 
d~y\r 
dxdt 
dy 
dx 
dydt 
dX dX 
dt dy 
d-yjr dy\r 
dt dy 
dX dX 
dx dy 
d\fr dijr 
dx dy 
d 
2 dx 
dX 
dx 
d\jr 
dx 
dX 
dX 
dx 
dt 
d-yfr 
d\jr 
dx 
dt 
d 
dX 
dx 
2 dy 
dx 
dy 
d\\r 
d~^r 
dx 
dy 
3 B 
dX dX 
dx 
dy 
d\Jr dyjr 
dx dy 
clX 
dy 
dijr 
dy 
dX 
dy 
d-^r 
dy 
dX 
dy 
d-yjr 
dy 
MDCCCLXXXIV. 
