Penny Blood: Serial Sensation and Working-Class Entertainment — page 81: what you’re looking at

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

64 ELEVATIONS ON THE [cH. VI. There will remain the effect of the contraction of the re- mainder of the sphere from the depth 2a to the centre. This we will assume to be as great as at the depth 2a, and then we shall be sure that the whole cubic contraction at and below the depth z is a quantity less than 4cr (r — 2a)’ %0 s 2a) , E+er | (r—2)*Pnda + B=" "9 7 x 00468. #8 e Suppose £’ to be the mean coefficient of contraction for all the matter below the depth 2 Then the whole contraction from z to the centre of the sphere will have been dir (r — 2)? 8 3 < E4er | “(pr — 2)'Pade Kk’ Aer (r — «e)* ia—>s _ 8 +E ——— V x 0:00468. And the coefficient of linear eompression at the depth @ will be the same as the coefficient of linear contraction of the spherical surface at that depth. That is to say, c= = ; (r — 0) Pade + ar (= 7a) x 000468. <eaapl, *(r=a) If we then take 2a as the limit of depth to which compres- sion has reached, which we may do because the cooling below In this expression n=0 will give the first and second terms of the series, m=2 the third and fourth, n=4 the fifth and sixth, &., &c. Making n successively 0, 2, 4,...18 (for which last value the first significant digit will not occur before the 7@ place of decimals), we get for the sum of the first 20 terms =: 0°882083, whence at the depth 2a, Pn= V — b x 0°882083, ( where b= 75)» 0°882083 =V(1- » (s/w=1-77245)) . x= V x 000468. commiclsoolkks (CO) $$