1883, ] 95 [Hagen. 
Hence we have the second condition 
sy m 
ea ee We a (2) 
r=0 Aaa) 
3. Case. Oay + lay + Pag t+. bey =* 
" This equation admits of the combinations : 
ado On ay as 4 r do ay a a3 a4 | r 
a SOO OE ed Cee OS Ue 
| 1 0 ul 0 0 2 1 2 0 0 0 eet 
I 2 0 i 0 0 3 2 2 0 0 0 4 
| 
Hence the third condition is 
Sala 5 Bi Bi 
Ale 0 ; 0 | Ski 8 
0) [Seay ay + aw acl =O sf 
4 Case. Oa + lay + Pa. +++ >be ay 
The combinations of this case are the following : 
j Dy Oh Og Oe Cis | r Oy Ong Oy Cy Ga |i MD Gy 1 Ag A, Oy as] Y 
Ce Ooo Os LO OURS wie OO ee” te 
Loree" 1-0". 0) 2 i ee Me lta 8 1) /8'70):0 4 
By Ose O eae OO 8 ee O00) 4 Ro) Og | 5 
Oa os eR dite 
| Hence the fourth condition 
r=m [ Bj" B, Bt? B,B, By? B? 
“ mt sy) é = Q, | 
2 Arn@ Le@—1 xGy! G8) aU) 7 ne x@—8) 7@)J—% 
| 5. Case. Oa + lay + 2a + - py = 4, 
Here we have the following possible combinations : 
| Hy Ay Ag Ay Aq Ms | I Gy O% % S| L Gy A, Ug A | r 
| ee 08 18 be reo the: OR. 10 1 e 
N WTC Oude a i a hs) Net U ka at ‘ My 98 ode 4 
; RO OMOR 0 108 Body CO aL slid, Pais tree) 5 
Oy Oy as | I ie. Ce Oy Cela 
0 4 0 4 LUNG OP a a 2 
leer: a0) 5 hed Oe! eel 3 
Bik Bh pd asl 0 8 ON. ei Ol 4 hee 
Wee \ 
Hence the fifth condition : 
tet 
1B, Bu ( BB, . B,? By BY By 
kin A 060) tee wl) txt —B) (<a a) tx(2))+ a8) w(8)xC1) 
