OF WHICH IS MOVING ROTATIONALLY AND PART IRROTATIONALLY. 389 
therefore 
therefore 
therefore 
dt 
dx' 
dy' 
1 u cos cbt + v sin ait -|- d>y' —u sin <bt + v cos dot — <bx' 0 
dt dx dy' d\fr 
1 u' + doy' v' — <bx' 0 
dt dx' dy' dyjr 
V x 0 
2 4 -vg, 
The integrals are 
** ■ y'* 
(/) 3 + 5 =» 
X 1 lr 
ah . (od 
t — — sin - 
2 / \a 
V i)= n 
therefore 
x =(/)(S+? 
The current function A =\— -|c5r 3 
ab . 
— *—— sm -1 
x 
a 
2 / 
V 
= (/)($+$)-1^ + ^) 
To find^+V 
P 
(d d d \ 
First express \yf^ u (f v ^ v ~yy) a f° rm i n which x, y\ t are independent variables. 
d d\ d dx' d dy' d (dx' d dif d 
/+T17 
dt dx dy] dt dt dx' dt dy' \dx dx' dx dy 
dx' d dy' d 
^ /7)/ ) l ’( ,7,/ 1“ 
dy dx' dy dy‘ 
*i 4 a \ d / # # « # a \ d 
= Y+(<y?y cos <y£-f-v sm cot) (~ox —it sm + v cos &V) 7-7 
CLJj Ct'i10 CL'IJ 
dx' 
_ d | X . X | /\ ^ ./ /\ ^ 
ate' 
2yy ^ 
dt b“ dx a dy 
therefore the equations 
du , du du 
