( 387.) 
XVI.—The Eliminant of a Set of General Ternary Quadrics.—(Part III.) 
By Thomas Muir, LL.D. 
(MS. received December 12, 1904. Read|January 23, 1905. Issued separately April 15, 1905.) 
(41) The invariance of the equations 
a + by? + e277 + fyye + gy + hyry = 
Ae? + boy? + coz? + foye + gee + hay = 
Ut? + bay? + C422 + foye + gee + Agxy = 
} tl 
oorS 
——_—’ 
with regard to the group of cyclical substitutions, 
and the consequent invariance of the eliminant with regard to the reduced group con- 
sisting of the last two substitutions, has been already referred to. When the eliminant 
is expressed in terms of the three-line determinants formable from the array of 
coethicients, the invariance in question is self-evident, as each of the twenty-eight parts 
composing the expression is invariant by itself. For convenience this form may be 
repeated from § 31 with a slightly improved notation. It is 
0v00 4+ 21'4'8'9 
+ DS007r7. + 34457’ 
— 220016 + 1/558" 
+ 207'8'9’ — 21688’ 
2 SO UAT: — >44'99’ 
+ 0456 => Likes’ 
+ 220159 — >1'6’88 
+ 0123 aT 
+ 30125’ pS # 
+ 304'5'6’ — >4468 
+ 0'7'8'9' — >1'448 
— 0'456 + 21166 
+ >45'7'9' — 21489 
ae STB Mey — 21149 
TRANS. ROY. SOC. EDIN., VOL. XLI. PART II. (NO. 16). 57 
