8) may be cited as the two most important types, both as regards geographical and geological range, of this Mesozoic family; these ferns are recorded from England, France, Belgium, Germany, Austria, Portugal, Poland and Italy (Map B, M 1), also from Greenland (Map B, M2), Spitsbergen (Map B, **M3**), and Persia (Map B, M 4).

Or generally, if M 1 M2 **M3** are the moments of the external forces to the left of 0, A, and B respectively, and s, t and c the perpendiculars from 0, A and B on the directions of the forces cut by the section, then Ss=M11 Tt=M2andCc=**M3**.

As the loads move over the girder, the points C, D, E describe the parabolas M1, M2, **M3** i the middle ordinates of which are 4W 1 1, 4W 2 1, and 4W3l.

1 2 3 We have found above that the coefficient of (x 1 1 x 12 x 13...) i n the product XmiXm2X **m3** ...

+o (m l m2 **m3**) +..., Theorem of Expressibility.

The Binary Sextic.-The complete system consists of 26 forms, of which the simplest are x2y2z2 + (1 +8 **m3**) 2 (y3z3 +z3x3 +x3y3).

'?^ the sum being for all separations of 1 A1112 ` / a3 3 ...) which have the specification (m41 m2 2 **m3** 3 ...).

(J1)11(J2)12(J3)j3ï¿½.ï¿½ jj!j2!j3!..ï¿½ where since(m1 1 m2 2 **m3** 3 ...) is the specification of (J1)j1(J2)j2(J3)j3..., ï¿½ l +ï¿½2+/23+ï¿½ï¿½ï¿½ =ii +j2+j3+ï¿½ï¿½ï¿½ï¿½ Comparison of the coefficients of x:14243...