Penny Blood: Serial Sensation and Working-Class Entertainment — page 80: what you’re looking at

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

CH. VI. ] HYPOTHESIS OF SOLIDITY. 63 the depth 2, whose area is 4r(r— zz)’, will have contracted by . a Eten (r— 2)'de x Pn; where Pn =V—2 [e"Sde, Consequently 0 the whole contraction from that depth downwards will be Ean f(r — x)" Pndz: where the integral ought to be taken from @ to the value z has at the depth at which contraction ceases to be felt. It is evident from the diagram that this is almost the case at the depth 2a, where the temperature differs but little (by V x 000468’) from the melting temperature V. 1 Generally gt 4 fe -% pera) ce 0 =7-5)(p-3+ra(3) -p (5) +- (=I (a) te} ae 1 12 aah -5a+is a5 a a 1 3 gt*tl +(- 1)" o on+1 a™ * : The general term of the series is 1 /a\mtl (1) bT [n Qn+1 (= =) ° Suppose the superior limit of the integral to be 2a. Then this becomes 1 Q2+ (- 1)" rst And the next term to this will be » 2 1 QuXatiy+l ~(- Pd @siti 1 «= gant =-(-1) ”Tn+i 12n+3° And the sum of the two terms (-1)" npor m+1. Q? ) = |n + +1\Qn4+1 2n+3 -1p giantl = 9n?—3n-1 =(—1)" [n+1 (2n+1) (2n+3) © GONG oOo SS (CO)