140 Fisher — Notes to Rival Theories of Cosmogony. 



Art. XIV. — Mathematical Notes to Rival Theories of Cos- 

 mogony / by O. Fisher. 



The following mathematical notes are supplementary to the 

 discussion of "Rival Theories of Cosmogony " in the June 

 number of this Journal (pp. 414-422).* 



Let— 



r = distance of any point from the earth's center. 

 a = the earth's mean radius in feet, 

 log a = 7-3201961. 



qa = 2-4605 in radians = 140° 58' 35". 



s = the density of the surface rock (2*75). > 



gs = the weight of a cubic foot of the same, viz : 171*875 

 pounds. 

 p = the density at any depth. 

 p = the pressure in pounds per square foot at the depth 



where the density is p. 

 c = the coefficient of compressibility at that depth measured 



by atmospheres. 

 J — Joule's equivalent, 772. 

 a = specific heat of rock. 



(1) Laplace's law of density is, p — Q"- — — , 



where Qq is the density at the center, 10*74, 

 and qa = 2-4605 in radians = 140° 58' 35". 



(2) The relation upon which the following calculations 

 depend is one which I have proved in the Appendix to my 

 " Physics of the Earth's Crust " (p. 32), viz : 



ff S a / 2 2\ 



P = — : i — (p — s) : 



r 26 2 1 — qa cot qa ^ ' ' 



= B(p 2 —$ 2 ), suppose, 



which, reduced to numbers, gives for the relation between the 

 pressure measured in pounds per square foot and the density, 



p = 5-8855 X 10 7 { / o 2 -(2-75) 2 (. 



Hence we see what is the value of the constant R, which is 



implied in Laplace's law of density, viz: 5*8855 X 10 7 in the 



above units. 



... p — s \ p — s 

 Also since cp = or c = — , 



P P P 



* Attention is called to the following erratum: On p. 421, for 20 miles read 

 40 miles. 



