CONTINUANTS RESOLVABLE INTO LINEAR FACTORS. 355 
and thence in the form 
a 2°4b : 
5(b +c) a— 2c 3(b -<) * 
6(6 + 2c) a— 8c 2(b — 2c) 
— 35(b-3c) 56(b-3c) -21(b-5ce) a+8b-42c 
Similarly the operation 
row, — 6row, + 15 row, — 10 row, 
now enables us to remove the factor a—4b—18c; and the operations 
row, ~ 4row, + 3row,, 
row, — | row, 
the remaining factors. The set of column-multipliers 
Apc elem eae 
Lt 4 poe alg 
Tete 20 
1 8 
1 
is thus equivalent to the set of row-multipliers 
eS 28.5 = 56% S3D 
eG) el Vk) 
lee, ee 
ce 
i 
(17) The general result is that the table of row-multiphers swtable for the 
resolution of the continuant of § 2 is 
1 a) are Co) 1) Coro, B59 Cea, LG Steet &O ? ( oy ya 1 Oa n—1 
1 Seas Conant, 1 ? Cons, 2 Fis WORSE DEAD: NS OO SCO Se : (XVI) 
Similarly it is found after a little investigation that the table of row-multipliers 
suitable for the resolution of the continuant of § 3 is 
2 
2 2 
1 i e > ay DCT acc ’ (n a 2) Conan, = "3 (m ar 3)Con—112 Srna enim “my nial =e 
2 . 
1 » — (= 2)Cons, 0); = (n tO) Comey ae 
the general form of the multiplier being 2°Co,41, ». 
Lastly, the table of row-multipliers suitable for the resolution of the continuant of 
§ 13 ws 
(XVIII) 
1 eink Cran 1) Czy ig) atin Chart fp Ont oh Oh OS 
1 De oe Ce. nt) Ce. Dre is) ge wish ie sre 
—that is to say, may be got by a rearrangement of the column-multipliers: for 
