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to the north-east, was famous in antiquity for its figs and fuller's earth (KL,ucwXia yi), and contained a considerable city, the remains of which cover the cliff of St Andrews.

Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..

origin up to the moving origin 0, so that dy x=y=z=o, but dt U, dt= ' dG _ dyl =l (- yi y3Q x2w+xiv) +m (dY2yP+Yrxu+xw) +n (?

and y = yo, y = Yi, The method of constructing the formulae is explained in § 62.

If yi and y 2 are the two separate displacements and if y =3/1-4-Y2, then w = - E (dye/dx + dye/dx) =0.) i w2.