Now a11A11= alla22a33...ann, wherein all is not to be changed, but the second suffixes in the product a 22 a 33 ...a nn assume all permutations, the number of transpositions necessary determining the sign to be affixed to the member.
From the theorem given above for the expansion of a determinant as a sum of products of pairs of corresponding determinants it will be plain that the product of A= (a ll, a22, ï¿½ï¿½ï¿½ ann) and D = (b21, b 22, b nn) may be written as a determinant of order 2n, viz.
Anibll +an2b12+ï¿½ ï¿½ï¿½ +annbin a11b21+a12b22+ï¿½ï¿½ï¿½ +alnb2n, a21b21+a22b22+ï¿½ï¿½ï¿½ +a2nb2n, ï¿½ ï¿½ ï¿½ ani b21 + a n2 b 22 + ï¿½ ï¿½ ï¿½ +annb2n alib31+a12b32+ï¿½ï¿½ï¿½+ainb3n, a21b31+a22b32+ï¿½ï¿½ï¿½+a2nb3n, .ï¿½.a n lb 31 + a n2 b 32+ ï¿½ï¿½ï¿½ +annb2n a ll b nl + a 12 b n2+ ï¿½ï¿½ï¿½ + a ln b nn, a21bn1+a22bn2+ï¿½-ï¿½+a2nbnn, ï¿½ ï¿½ ï¿½ ani b nl + a n2 b n2 +ï¿½ ï¿½ ï¿½ +annbnn and all the elements of D become zero.
In particular the square of a determinant is a deter minant of the same order (b 11 b 22 b 33 ...b nn) such that bik = b ki; it is for this reason termed symmetrical.
The Adjoint or Reciprocal Determinant arises from A = (a11a22a33 ...a nn) by substituting for each element A ik the corresponding minor Aik so as to form D = (A 11 A 22 A 33 ï¿½ï¿½ï¿½ A nn).
If al, a2, ...a, n be the roots of f=o, (1, R2, -Ai the roots of 0=o, the condition that some root of 0 =o may qq cause f to vanish is clearly R s, 5 =f (01)f (N2) ï¿½ ï¿½;f (Nn) = 0; so that Rf,q5 is the resultant of f and and expressed as a function of the roots, it is of degree m in each root 13, and of degree n in each root a, and also a symmetric function alike of the roots a and of the roots 1 3; hence, expressed in terms of the coefficients, it is homogeneous and of degree n in the coefficients of f, and homogeneous and of degree m in the coefficients of 4..
Draw NR the same multiple of Nn and upwards.
Schoma.nn and of G.
With urea it gives " /CH NN quinazolone I, and with mandelic nitrile and its H /C0 homologues it forms oxazole derivatives (S.
Meyer, A nn., 1870, 156, p. 274).
The diagonal telescope nn is provided with cross hairs, and is used fcr the final centring of the instrument over an object.
A set of stirring blades carried in the frame (b b), and driven by gearing, NN,, ï¿½,, .
Some phonetic characteristics of the dialect may be regarded as quite certain; (I) the change of the original short o to a (as in the last syllable of the genitive kalatoras); (2) of final -m to -n (as in g ran); (3) of -ni- -ti- -si- respectively to -nn- -to- and -ss- as in dazohonnes " Dasonius," dazohonnihi " Dasonii"; dazetOes, gen.
One important fact should m nn 23yz FIG.
Nllp p .m?mammlRUn1 !11 uu1p111MimmmMlumnuunn lluum11u?nlNnul?I I Imm11FUUUMMmIIlmmumNll1111m1m1111-1111tI111u11 c Nm Ih.nfl111111411?,q1mt1 n?It1?1111111111n111111U1 11111111111111111?IU 1?11111II OII?IIIIIIIII i IIIIII I 11U 4 I?I III I IIIIBIIIIII i I IInIIIIIIIIII I [[Iiiiiii?Iii Ii Iiiiiiiiiiiiiiii I Iiiiiiiiii I Iiiiiiiiiiiiiiiiiii Ii]] ' 'uml?ul?111?nn?11nnu.luuiui?.411?nllunnflunulrinnlm?nnunnl (p ?
1111111r11n1Ut11111Nn1n1111111U11n111hm1U1111-1111t4Nzm11111 11111rtlllu'mlla11?111h g 11P111111111NL111 'IIIIIO III IIIII' 11111 'N11111111111111J1?111'IIIIIIIIIIIIIIIIIIIIIt1111111111111N?mllllll111ro ' 'M11m111u11 11 Mmhm,ml1Nul?man?mhnnll?nN,r,ni??
N 'n i nn eii n u ?;e?.?oow nci?,rn;' ??
W a q anza s E 0_ nn JJ Po h oon ?'?.??,??e i I i L AY 122 D Longitude West of Greenwich A B;., :.
Nn, Nemacaulus or virgular tube.