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F.," in Zeitschrift fiir Philosophie, cx.

00In Iiia, the episternum (a) and cx, Coxa.

00af Expression in Terms of Roots.-Since x+y y =mf, if we take cx any root x 3, y1, ofand substitute in mf we must obtain, y 1 C) zaZ1 ï¿½; hence the resultant of and f is, disregarding numerical factors, y,y2...y,,.

00Other forms are n-1 n-2 2 ax +nbx x +n(n-i)cx x +..., 1121 2 the binomial coefficients C) being replaced by s!(e), and n 1, n-1 1 n-2 2 ax 1 +l i ox l 'x 2 + L ?cx 1 'x2+..., the special convenience of which will appear later.

00may be a simultaneous invariant of a number of different forms az', bx 2, cx 3, ..., where n1, n 2, n3, ...

00From the three equations ax = alxl+ a2x2, b.= blxl+b2x2, cx = clxi+c2x2, we find by eliminating x, and x 2 the relation a x (bc)+b x (ca) +c x (ab) =0.

00-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.

00If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.

00To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.

00Since this last collection includes a psalm (cx.) which can scarcely refer to any one earlier than Simon the Maccabee, and cannot well be later than his time, we are justified in assigning the compilation of this collection to about the year 140 B.C. But by this time a great change had taken place in the aims and aspirations of the Jews.

00as if containing the OH group; this leads to the formula H 3 C C(OH): CX CO 2 C 2 H 5.

00123 and 124) is the following: If points X and x are taken dividing the link BC and the tangential velocity cb, sothat cx: xb=CX:XB, then Ox represents the velocity of the point X in magnitude and direction.

00The Cartesian equation to the caustic produced by reflection at a circle of rays diverging from any point was obtained by Joseph Louis Lagrange; it may be expressed in theform 1(4,2_ a2) (x 2+ y2) - 2a 2 cx - a 2 c 2 1 3 = 2 7 a4c2y2 (x2 + y2 - c2)2, where a is the radius of the reflecting circle, and c the distance of the luminous point from the centre of the circle.

00The language was in all probability Semitic-Hebrew or Aramaic. The paronomasiae in the Greek in verses 54-55 (inrb cX%vov ...

00CX, i.e.

00wind tunnel testing has shown that the RSV 1000 R has a CX of only 0.3.

00F.," in Zeitschrift fiir Philosophie, cx.

00Besides the revolutionists and republicans who promoted con~ spiracy and insurrection whenever possible, and the moderates or Neo-Guelphs, as Giobertis followers were called, we must mention the Italian exiles who were learning the art of war in foreign countriesin Spain, in~ Greece, in aas Poland, in South Americaand those other exiles who, ~rn CX CS Paris or London, eked out a bare subsistence by teaching Italian or by their pen, and laid the foundations of that love of Italy which, especially in England, eventually brought the weight of diplomacy into the scales for Italian freedom.

00In Iiia, the episternum (a) and cx, Coxa.

00af Expression in Terms of Roots.-Since x+y y =mf, if we take cx any root x 3, y1, ofand substitute in mf we must obtain, y 1 C) zaZ1 Ã¯¿½; hence the resultant of and f is, disregarding numerical factors, y,y2...y,,.

00Other forms are n-1 n-2 2 ax +nbx x +n(n-i)cx x +..., 1121 2 the binomial coefficients C) being replaced by s!(e), and n 1, n-1 1 n-2 2 ax 1 +l i ox l 'x 2 + L ?cx 1 'x2+..., the special convenience of which will appear later.

00may be a simultaneous invariant of a number of different forms az', bx 2, cx 3, ..., where n1, n 2, n3, ...

00From the three equations ax = alxl+ a2x2, b.= blxl+b2x2, cx = clxi+c2x2, we find by eliminating x, and x 2 the relation a x (bc)+b x (ca) +c x (ab) =0.

00-2 _ ab 2an-2bn-2Crz z x () x x x, Each term on the right-hand side may be shown by permutation of a, b, c to be the symbolical representation of the same covariant; they are equivalent symbolic products, and we may accordingly write 2(ac) (bc)ai -1 bi -1 cx 2 =(ab)2a:-2b:-2c:, a relation which shows that the form on the left is the product of the two covariants n (ab) ay 2 by 2 and cZ.

00determinant factors (abc), (abd), (bce), etc...., and other factors az, bx, cx,...

00If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.

00To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.

00Mag., 1879) is that of a rectangular aperture, traversed by a cylindrical wave with aberration equal to cx 3 .

00Since this last collection includes a psalm (cx.) which can scarcely refer to any one earlier than Simon the Maccabee, and cannot well be later than his time, we are justified in assigning the compilation of this collection to about the year 140 B.C. But by this time a great change had taken place in the aims and aspirations of the Jews.

00as if containing the OH group; this leads to the formula H 3 C C(OH): CX CO 2 C 2 H 5.

00123 and 124) is the following: If points X and x are taken dividing the link BC and the tangential velocity cb, sothat cx: xb=CX:XB, then Ox represents the velocity of the point X in magnitude and direction.

00The Cartesian equation to the caustic produced by reflection at a circle of rays diverging from any point was obtained by Joseph Louis Lagrange; it may be expressed in theform 1(4,2_ a2) (x 2+ y2) - 2a 2 cx - a 2 c 2 1 3 = 2 7 a4c2y2 (x2 + y2 - c2)2, where a is the radius of the reflecting circle, and c the distance of the luminous point from the centre of the circle.

00The language was in all probability Semitic-Hebrew or Aramaic. The paronomasiae in the Greek in verses 54-55 (inrb cX%vov ...

00CX, i.e.

00Extensive wind tunnel testing has shown that the RSV 1000 R has a CX of only 0.3.

00For example, CX London offers Playboy and La Rocka brands and has a range of products that includes everything from babydolls to suspender belts.

00

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