80 
MACFARLANE. 
and therefore 
As dp and p are at right angles, can be shifted in front of 
dp without any change of sign, or rather there are two 
changes of sign, resulting in no change; hence 
p 2 d (44 — — 2 p -4 dp = — 2 — dp, 
\p ) P p 
and 
d (-7) = - 2 7 d '- 
In this case the formula is precisely similar to that for a 
scalar quantity, and from the above it is evident generally 
that 
when n is odd, and 
n 
.U + 
- dp 
when n is even. Here we have differentiated internally. 
We can now show that it is not a matter of indifference 
whether we write yr = -i- or yr — p . According to the former 
principle, 
2 2 r q 
yr = — and 
P 
22 2 . „ 1 2, 0 12 6 
pV 2 =: — pr-f 2 rp — = -f- 2 r — — = — T . 
P P P P r p 1 
According to the latter principle, 
pr 2 = 2 rp) hence 
pV 2 — 2 yr . + 2 ryp = 2 (^> 2 + 2). 
