Note on Palmstr0m's Generalisation of Lame's Equation. 
325 
1-11-11 
1-2 3-4 
1-3 6 
1 -4, 
and equally readily by means of the column- multipliers 
1 4 6 4 1 
13 3 1 
1 2 
1 1 . 
That is to say, the operations 
row^ — rowg + rowg — row^ -f-roWg, 
rowj — 2 rowg + 3 rowg — 4 row^, 
bring to light the factors 
- 4y -H 12c 12d, ; 
and the operations 
C0I5 + 4 col^ H- 6 C0I3 + 4 C0I2 4- colj, 
C0I4 + 3 C0I3 + 3 C0I2 + colj, 
the same factors in reverse order. 
(4) In showing how Palmstr0m's case is included in this there is an 
advantage in taking two steps to bring about the specialisation required, 
namely, first putting 
y = /? + 6c and b = — 3c, 
which gives 
X P 4c . . 
4(/5 + 3c) X 2(/3 + 3c) 12c 
3(/5 + 4c) X 3(/? + 6c) 24c 
2(/5 + 5c) X 4(y8+9c) 
/5 -f 6c X 
= (x-4^l3- 12c) (x - 2/3 - 12c) (x - 6c) (x 2fS + 6c) (x + 4,3 + 24c) 
and then putting c = 1. 
(5) Of the many other interesting special cases the one to which one 
naturally turns is that where the determinant degenerates into a continuant, 
and where therefore there is a probability of establishing a contact with 
previous results. Putting then 
c =■ h and d = 
we find the outcome to be 
x . . . 
4(7-36) x + l3-y-^6h 2(/3-b) 3(^-26) 
3(7-26) x-^2f3-2y ^Sb 
2(7-/3) a; i- 3/3-37 + 66 4(/3-36) 
7 4- 4/3 — 47 
