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.

In 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.

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

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

The binomial theorem may, for instance, be stated for (x+a)n alone; the formula for (x-a)" being obtained by writing it as {x+(-)a} n or Ix+(- a) } n, so that (x-a) n =x"- 1)**xn-laF**...+(-)rn(r)**xn-rar**+..., where + (-) r means - or + according as r is odd or even.

This is expressed by saying that the sequence converges to (x+h)" as its limit; it may be stated concisely in any of the three ways, (x+h) n =lim(x"+n(1)**xn-lh**+....+ n(T)**xn-rhr**+ï¿½ï¿½.),(x+h)n =lim Sr, Sr. (x+h)n.

Then {(x+h)n - S T } /h r + l lies between n (r+1>x n-r-1 and n(r+1}**xn-r-**1(i +O)n; and the difference between these can be made as small as we please by taking h small enough.

Thus 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.)).

At 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.

Since, 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."

=0, a'**xn**+ (b'y+c'z)**xn-**1+...