...variables is an expression of which the right-hand member is zero, and the left-hand member consists of a series of terms each of which is the product of n factors, each factor having a different suffix, and the number of the terms is 1x2 x3x ... x(» —...

...is eliminated by the method of Art. 257 ; the first member of the final equation in y then consists of a series of terms, each of which is the product of m factors, and is of the form qra"~rx qb"~' xq/f~ix ... And as we know that the series of terms forms...

...eliminated by the method of Art. 257 ; the \ first member of the final equation in y then consists of a series of! terms, each of which is the product of m factors, and is of the I form qra"~rx ?.6"~' * q,c"~' x ••• And as we know that the series...

...is eliminated by the method of Art. 257; the first member of the final equation in y then consists of a series of terms, each of which is the product of m factors, and is of the form gra"~rx <?.6"~1 x yf"~3 x ••• And as we know that the series of...

...n+2, . . ., 2n whose coaxial minor 1 2 3 ... 2n 1 2 3 ... 2n it skew, we have ') 1 2 3 . . n - 1 148 (7) Both the general identity, however, and the special...framelines intersect are zeros. Thus the Pfaffian which is of the 3rd order, and has a zero at the place (12) where two of the frame-lines intersect,...

...coaxial minor 2n 2n skew, we have 123. .n-1 1899-1900 i i Dr Muir o 2<-r » 2 3...nl,/t /iy o> 148 (7) Both the general identity, however, and the special...that the elements in the places where n — 1 of the '-/> framelines intersect are zeros. Thus the Pfaffian a, a, aa which is of the 3rd order, and has...