Penny Blood: Serial Sensation and Working-Class Entertainment — page 124: what you’re looking at

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

CH. IX. } CRUST NOT FLEXIBLE. 107 The next step is to conceive a long trough, bent lengthwise into a circular form of large radius, and that the crust and liquid are acted upon by a force gravitating towards the centre, and so we approximate to what would be, in the case we have supposed, a section of the earth’s surface, taken along a great circle. In this case we must suppose the curve reentering. No extraneous force acting, the circular festooned form will approximately represent the curve of equilibrium. But for simplicity of conception it will be better to return to the idea of the rectangular trough, and to suppose that the curve is in the phase of an anticlinal where it meets the trough at either end; which condition is necessary for equilibrium if there is no friction there: and that there are m festoons. Having found the form of equilibrium we have now to enquire what relation it holds to the length of the trough. We will consider that the trough was originally of the length Z, and that it 1s compressed until its length becomes IL(1—e). Then since =P is the radius of every circular are which can admit of equilibrium, and that the chords of the m festoons, or arcs, must equal the reduced length of the trough, putting ¢ for the angle subtended by each festoon, we must have 20 7 PL m.2.——k sin 5 = L(1-e), and because the whole length of the crust is that of the trough before compression, 2p sn £ | whence > ao Med SPP PE TTT TTaT Tree Trae Terre (1), y 4 _¢ - and m= 2p kd TTETEUETELTESETECEE TTT ee (2). Any value of ¢ less than unity substituted in (1) will give a corresponding value of ¢, and thence from (2) a value of m. COMMUC NOO SS (CO)