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xn

Thus ortho-phenylene diamine yields the following products: N H N ./`N; Xn NZ In some cases oxidation of condensed benzenoid-heterocyclic nuclei results in the rupture of the heterocyclic ring with the formation of a benzene dicarboxylic acid; but if the aromatic nucleus be weakened by the introduction of an amino group, then it is the benzenoid nucleus which is destroyed and a dicarboxylic acid of the heterocyclic ring system obtained.

11In general in space of n dimensions we have n substitutions similar to X l = a11x1 +a12x2 + ï¿½ ï¿½ ï¿½ + ainxn, and we have to express the n 2 coefficients in terms of Zn(n - I)i independent quantities; which must be possible, because X1+X2+..."IL Xn =xi+x2 +x3 +...+4.

00..yn xi, and as a particular case (y1, Y2,...yn) (x1, x2,...xn) = 1.

00are not independent functions of x1, x2,...xn.

00=0, are non-unitary symmetric functions of the roots of a xn-a l xn 1 a2 x n-2 -...

00Thus we arrive at the differential coefficient of f(x) as the limit of the ratio of f (x+8) - f (x) to 0 when 0 is made indefinitely small; and this gives an interpretation of nx n-1 as the derived function of xn (ï¿½ 45)ï¿½ This conception of a limit enables us to deal with algebraical expressions which assume such forms as -° o for particular values of the variable (ï¿½ 39 (iii.)).

00At the Revolution he took up arms in behalf of the king, became commander of the "army of Conde," and fought xn conjunction with the Austrians till the peace of Campo Formio in 1797, being during the last year in the pay of England.

00Came into conflict with the governor Orestes, who formed a (mainly Xn) political faction opposed to Cyril.

00We may take X =6 X I o' 5 cms.,, u - I =0.0003; whence from (21) we obtain as the distance x, equal to I/h, which light must travel in order to undergo alteration in the ratio e : 1, x=4 4XIo 13 Xn (22) The completion of the calculation requires a knowledge of the value of n, the number of molecules in unit volume under standard conditions, which, according to Avogadro's law, is the same for all gases.

00Thus ortho-phenylene diamine yields the following products: N H N ./`N; Xn NZ In some cases oxidation of condensed benzenoid-heterocyclic nuclei results in the rupture of the heterocyclic ring with the formation of a benzene dicarboxylic acid; but if the aromatic nucleus be weakened by the introduction of an amino group, then it is the benzenoid nucleus which is destroyed and a dicarboxylic acid of the heterocyclic ring system obtained.

00In general in space of n dimensions we have n substitutions similar to X l = a11x1 +a12x2 + Ã¯¿½ Ã¯¿½ Ã¯¿½ + ainxn, and we have to express the n 2 coefficients in terms of Zn(n - I)i independent quantities; which must be possible, because X1+X2+..."IL Xn =xi+x2 +x3 +...+4.

00..yn xi, and as a particular case (y1, Y2,...yn) (x1, x2,...xn) = 1.

00are not independent functions of x1, x2,...xn.

00=0, are non-unitary symmetric functions of the roots of a xn-a l xn 1 a2 x n-2 -...

00Thus we arrive at the differential coefficient of f(x) as the limit of the ratio of f (x+8) - f (x) to 0 when 0 is made indefinitely small; and this gives an interpretation of nx n-1 as the derived function of xn (Ã¯¿½ 45)Ã¯¿½ This conception of a limit enables us to deal with algebraical expressions which assume such forms as -Ã‚° o for particular values of the variable (Ã¯¿½ 39 (iii.)).

00At the Revolution he took up arms in behalf of the king, became commander of the "army of Conde," and fought xn conjunction with the Austrians till the peace of Campo Formio in 1797, being during the last year in the pay of England.

00Since, however, we find elsewhere one name appearing as both Sirach and Sira (ch = tt), Aceldamach may be another form of an original Aceldama (xn" t Ypr), the " field of blood."

00

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