WHICH SATISFY GIVEN CONDITIONS. 
Ill 
(a, b,c)=(a+l)(b + l)(c+l) 
[rm — a — b — c ] 3 
+ [rm— a— b— c— l~f(a-\-b-{-c )[D]‘ 
+[rm— a— b— c— Z\\ab-\-acbc)[p')* 
+ abc [D] 3 
— [S<?(«+1)(£+1) f \rm—a—b — c — l] 2 
J _|_[rm— a— c_2] 1 («+^)[JD] 1 
[+ ab [D] 2 
-\-\%bc(a-\- 1) j \rm—a—b — c— 2] 1 
1 + aD 
—abc [«] 3 
77. The foregoing examples are sufficient to exhibit the law; but as I shall have to 
consider the cases of four and five contacts, I will also write down the formula for 
(a, b , c, d ), putting therein for shortness 
a-\ -b-{-c-\-d=cc, ab-\- . . -\-cd=f. 3, abc. . -\-bcd—y , abcd=ti, 
a-\-b-\-c=a !, ab-\-ac-\-bc=l 3', abc= f l /, a-\-b=a", ab-\-(3", a=al " ; 
and also the formula for (a, b, c, d, e), putting therein in like manner 
(cc, (3, y, a, .), (*', (3', y', V), (a", (3", y"), (3"% (*'"') 
for the combinations of (a, b , c, d, e ), (a, b, c, d ), (a, b, c), (a, b) and (a) respectively. 
We have 
(a, b, c , d)= 
(a+l)(b+l)(c+l(d+l) 
[rm— a ] 4 
+ [rm— a — lJapD] 1 
-j- [rm — a — 2] 2 |3[D] 2 
+ [rm — a — 3] 1 y [D] 3 
+ *[D] 4 
[^(a+l)(5+l)( C +l) 
[ [rm— a— l] 3 
J -j-[rm— a— 2]V [D] 1 
I +[rm— a — 3]‘/3' [D] 2 
1 + r' [D]’ 
]W 
+pSei.(a+l)(i+l) [ [m-«-2]* l][*] s 
| +[m-a-3]'a" [D]' | 
1+ 0"[D?J 
-pW(«+l)f [m-a-3] 1 ]][*]> 
1 + 
