62
d UdA^ :c?U
dA w.* ‘
■ ‘ dM ni , ' dA ti ,dTJ dTJdA t $
dXJ
dTJ
■ ■■
dTJdA K , s
d\J
■ 1 dM K , \ -
_
n(Zm —1)independ-ent equa-tions.
r
«!U
dTJ -tfU
dTJ
dTJ
dTJ ~
no new
un-
dK,a ’
"dM ni „' dA"„
' dA *,«"
"rfM.,.-
knowns.
Pa,„ ■
■ -Pm,„ ■ Pa„
* Pal, t
Pa, k' '
: - Pm, K
Pa, „ + Pa
P«,*+ Pm,
[
e = Pm, a
m equations.
no new unknowns.
No. equations : 2w* -\-(n— l)-\-Zmn+n(Zm— \)-\-m=.Q>mn-\-Zm — 1.No. unknowns: Zmn-\-Zm -\-Zmn-\-0 -)-() =6mn-j-3m.
The second set apparently contains n equations instead of n— 1as above recorded. But, by multiplication of the first line of thefirst set, we have :
( A w ,i+ • • • + A TT,n) Pa, n ( A «,> + • • • + A K ,n) Pa.rr
( A «,l + • ' ’ + A e,») Pa,a ~ l A *,l + ' • • +A K ,n)Pa, t
adding and remembering that p„ iK = Pa,„+Pa„ we get :
A „, 1 • Pa, v + • • • ■+■ A tt, n • Pa, „ 4" A e, 1 ■ f’a, e + • • • + A e , n • Pa, e =
A (t. 1 • Pa, *+ • • • + A k,« • Pa, k
Writing the similar equations from the second, third, etc. lines of thefirst set and adding we get (rearranging terms):
A t, 1 • Pa,„ + • • + I . p m ,„ 4- A e ,, . />„, r + . . + , . p m< c -j-
+ A :r, 2- Pa, * + • • + !•/>»,„+ .-.-. _ _
+ A t,« • Pa,„ +..+ ■ Pm, t
A „1 • Pa, K + ■ ■ • + M.,, . p miK ++ A «, » • Pa, K +.
k "4" A «, » ‘ Pa, k “I" • ' • “H n • Pm, K
If from this equation the 'sum of all but one of the second set besubtracted the result will evidently be the remaining one.
We are therefore at liberty to write
Pa, K = 1
to determine a standard of value.