Penny Blood: Serial Sensation and Working-Class Entertainment — page 49: what you’re looking at

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

32 INTERNAL DENSITIES AND PRESSURES. [cu. 111. Since the attraction of the portion of the sphere exterior to the shell, whose radius is 7, upon a particle within it is nothing, the value of g’, due to the remaining portion, will be, | "4err?drp’ J =—-—_,—. Substituting for p’ its value gen gr and integrating, we have — j= = (sin gr — gr cos gr); and therefore, | gp = a (sin"gr — gr sin gr Cos qr). Hence, g and p being the values of g and p’ at the surface, g gp 5 sin® sin gr — qr sin gr cos qr gp =a sin’ ga — ga sin gacos ga’ _A sin* gr — gr sin gr cos gr =A—+_4 5 Substituting for gp’ from (1), and integrating by parts, when r=a, p=0; ns _ gpA (a qr sin’ a2 a a? If we write na for r, and restore the value of A, this may be put in the form, gpa (= qna sin 2ga (tan ga — qa) qn'a’ qa’ — sin "aa). P — This gives the pressure at any depth, the only variable quantity in the expression being sin” ai gna gna 3 COMiCOOokxS.conn