Penny Blood: Serial Sensation and Working-Class Entertainment — page 46: what you’re looking at

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

cu. 11.) INTERNAL DENSITIES AND PRESSURES. 29 where p is the surface density, and P the density at the centre. The radius of the earth is here taken as unity. In order to render the equation homogeneous we may write it, a being a earth’s radius, (P —p’) a'=(P—p)r’, or ol P—p a Now Laplace’s equation, which leads to the law of density already referred to’, is ag Mgr p r 3 where @ and q are constants to be determined. Consequently the central density will be given when r=0Q, =Qingr = or P=Q or q whenr=0, = Q¢. Also the surface density will be given by putting T=A; — . .. n8in ga. - p= Q a?’ _ sin gr qr —sin gr P—p ? 7p P—p om singa a'qa—singa’ This is the correct expression for the ratio = . And consequently Waltershausen'’s value of that ratio (viz, 7) 18 strictly true only when the relation is satisfied, qr—singr gqa—singa When the constants Q and qg are determined in accordance with the mean values above given of the density of the whole 1 p. 20. GONG oOo SS (CO)