90 
MACFARLANE. 
We shall next find p and p 2 for any function, scalar or 
vector, expressed in terms of the cylindrical coordinates 
r, 0, z. * 
In this case R = rp + zk where k is constant, and p = cos 0 A 
-f sin 0 . j . Hence 
?R = pr . p + r y e + V* • 
and as yR = 3 absolutely, it follows that 
1,1 1 
V T = —, V 0 =-—, yz = -J -, 
P „ d P k 
and 
Hence 
do 
F _ H_) 1 + «(_J _J_ + H_) 1. 
<5r p dO dp dz k 
r do 
+ 
+ 
+ 
( d 
i + 
S 1 
V Sr 
— j 
0 
dO dp 
7 ~d0 
S*( 
) i 
dr 2 
p‘ 
S>( 
) i 
& 2 
F 
3 / 
'<?( 
) 1\ 1 
(Sc \ 
^ dz 
1 
** 1 
A f 
H 
) i\ i 
00 V 
dz 
k ) dp 
r ~M 
f d 
1 \ 1 
J *( 
~d0 
r 'V ) ir 
so J 
a l 
_l \ /_*__l , J_i_ , JU 
k) \ <?r /O dd dp dz k) 
. ( 9 ) 
p d0 dp_ 
dO 
CD + A/*L_)J_\_k 
dO [ dO dp 
■^r (2) 
(3) + 
(Sc 
ii-J 1 \A (4) 
< 5 > +MI j) 
do 
1 
dp 
+ 
dz \ dr' p ) k 
( 6 ) 
( 8 ) 
) 
