Penny Blood: Serial Sensation and Working-Class Entertainment — page 84: what you’re looking at

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

CH. VI.] HYPOTHESIS OF SOLIDITY. 67 As yet no definite values have been assigned to any of the constants. Taking the observed rate of cooling at »th of a degree F. per foot in descending, the time since the supposed solidification The integral has to be taken from z=0 at the surface to that value of « which expresses the thickness of the rigid crust beyond which corrugations will not have been formed. Now the melting temperature V is reached within an extremely small error at the depth 2a. We may therefore take 2a as the superior limit, and the above quantity becomes | " ( | "Pndz ) d= V (4a*— 2a%) — 1-278820 x 20% 0 & bfl 1 1 (2a)§ 1 11 1(2a) : ate 8P ea Bat ts 67 at ~ 1 (2a)s™+8 +H{~ 1) a +1) (Qn4+3) Qn+8) a™ +t iz of which series the general term after — becomes 1 (~1)"a oe [n+1 (2n +1) (2n + 3) and the next to it Qtwte 1 (a eed Gn+8) Gn t8)' and their sum, after reduction, a (—1)"a% 2 gant 2n? +n +6 [n+2 (2n+1) (2n+8) (3n+5) This is the sum of the two corresponding terms in the former series (A) multiplied by the factor 2 {1+ 2 {n+ 2) —— : 2n +5 2n* — (n — 2) Giving to n the values 0, 2, 4, 6,... 14, we obtain for the sum of the terms of the series to the 16% inclusive, a®b x 0°993840, Hence a | "" ( | Pn de) dz = V2a* — a*b x 2°546640 + a*d x 0°998840. 0 % Or f° Qdx = V2a? — ab x 1°552800, The calculations for obtaining R and | (302 -2R) dx are of a similar character. The numerical results of these series have in every instance been verified independently from the general terms by friends. COLA @ NOO (CO)