Penny Blood: Serial Sensation and Working-Class Entertainment — page 53: what you’re looking at

Machine-transcribed from the original scan — historical spelling and the odd misread are preserved.

36 LATERAL PRESSURE, [TS AMOUNT, _— [cu. tv. PQ and ST be the curves of greatest and least curvature on its surface. ‘These are by a theorem in geometry necessarily ortho- gonal, Let RO, RO’, the corresponding radii of curvature, be called r, r’. Let T be the pressure on unit of area of the section of the crust in the directions of the tangents at P and @ which is produced by the lateral thrust. Similarly let 7” be the pres- sure in the direction of the tangents at S and 7. The weight of the element is gp PQ x ST xr, and acts in the normal ROO’. Let the angles POQ = 8, SOT = ¢. If then we suppose this element supported by a pressure R on unit of area from beneath, resolving the forces vertically we have for the equation of equilibrium 2Tr'dr sin : + 2T’r@r sin £ = gpr0r' hr — RrOr'd. In the limit, dividing by r@r’¢ this gives T T (= + )T=gpr— BR. r If we regard the surface as spherical and of radius a, 7' and 7” become equal, and we have 2-7 = gor — B. If the support beneath is withdrawn altogether R becomes nothing and then L'= $ gpa, which gives the maximum thrust which would be produced by the shrinking away of the underlying mass. The meaning of this result is that the horizontal force of compression thrown into a stratum at the earth’s surface by the shrinking away of the underlying parts would be equal to the weight of a piece of the same stratum of the same section as the stratum and two thousand miles long—enough to crumple up and distort any rocks. It would be about 830200 tons upon the square foot’. 1 Calculated from a cube of granite weighing 178-339 Ibs, COMIC OOOKS.EO