A. Ritchie-Scott 
109 
Comparing this with the generalized equation (61) for enneachoric r previously 
found in which all the frequency volumes were weighted, we have 
a>i, = — , 
■ Xl2 
and since oj^^ = w,t - m^s+i, t - ^s, «+i + ^'^s+i, «+i , 
it can be easily shown* if there are p rows and q columns that 
Ws< = OJst + (^s,M + ^i^s, (+2 + ••• + "^s+l, « + <^s+l, M-1 + 
+ '^J)-!, i + <^3)-2, i+1 + ••• <^2),<? ('''8), 
that is the sum of all the weights having the same suffixes as the points contained 
within the d quadrant of which n^i occupies the corner. 
* Consider a two-fold extension ruled and named in a manner similar to the jsolyclioric scheme on 
page 94. 
Then = 
m,, = »7i,, +7/?,, 
Ws< = WlI + «12+Wl3 
+ ^21 + ^22 + ''^S + ™2 
+ «,i + n.f^ + «,3 + 
Hence Wj^wtu + w-^^m-^^ + . 
= 11 + Wj, ( /i, 1 + );.i2) + Wi3 ( «ii + ?ti2 + ftj.,) 
+ 
+ "s« («11 + "12 + «1( 
+ «21 + "22 + «3( 
+ 
+ 71,1 + ?l,2 + 
If we rearrange this in terms of iiu, n-^^. we shall have 
Wii ((On + cji2 + a>s() 
+ Mi2 (Wi2-|-tOi3 + £0,j) 
= **'ll'»Il+Wl2"l8+ W^itl^i^ WpqUprj. 
It is clear that iv^t will be the sum of the w's belonging to all the m's of which n^f is a constituent, 
that is, from the figure, all the w's whose boundary lines lie beyond the lines h=s - I, k = t - ], i.e. 
s t 
= - -"si- 
1 1 
The relation n^t = m,t - '«s-i • ( - • «-i + • <-i 
may be compared to the partial finite difference in two variables 
^x'^v Ux, II = U^+i, ,/+! - C/j.^.1, 11 - {7 J., v+i + ?7j., „ , 
which may help to make the above relation clearer. 
