- 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). - It is an old and easily proved theorem that, for a curve of the order m, the number 6+K of nodes and cusps is at most = Ernr) (
**m2**); for a given curve the deficiency of the actual number of nodes and cusps below this maximum number, viz. - 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. - With regard to a parallel line through the centroid are given by Mi=N1 - xNo=o,
**M2**= N 2 - 2xN i -{- x 2 No = N2 - x2No, M Q = N Q - g _ 1 q(q 2, I) x 2 Ns -2 - Then, since Hp, the force at M due to m and - m, is the resultant of d, and -
**m2**, we have (L Hp m d d2 2ml H = d3, the direction being parallel to AB.

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