X907.] AND CONTRACTION OF THE EARTH. 197 



applicable to these extreme conditions. Accordingly, with k =■ 

 I 2/3, we have Q/JV= 1/2; and we see that only one half of the 

 heat of condensation has been radiated away, and an equal amount 

 remains stored up in the condensing mass. We must then draw the 

 temperature curve so as to fulfill these two conditions : an elliptical 

 distribution, constructed on an absolute scale such that one half of 

 the primordial heat of condensation is still stored up in the earth. 



If it be urged that the earth's matter was not sufficiently heated 

 to be monatomic throughout its whole history, we may recall that 

 when k = 1.4, as in common air and most gases, the amount of heat 

 stored up is about 81 per cent. (cf. ^. A^., 4053) ; but as this biatomic 

 phase would be of short duration, the extra accumulation during 

 early stages would perhaps about compensate for the loss since sur- 

 face cooling began. Accordingly a secular accumulation of one half 

 of the primordial heat of condensation would seem to be nearly 

 correct. 



In his " Auwendungen der Mechanischen Warmetheorie auf 

 Kosmologische Probleme " (" Baumgartner's Buchhandlung," Leip- 

 zig, 1882), A. Ritter has established the following formula for the 

 condensation of a gaseous sphere : 



Cj,(% — @^) = Arjr (2) 



where Cp is the specific heat under constant pressure, 0.2375, 

 ©1 = 273°, ^ = 1/424, r = 6,370,000 meters, and 



£(Sh 



g being the acceleration of gravity at the surface and g' that at any 

 depth where the radius is p. For uniform density 



and we have 



By means, however, of a more exact investigation, based on 

 Laplace's law of density, Helmert calculated for Ritter the value 

 7} = 0.73, which is no doubt sufficiently near the truth. Accordingly 

 with these values the above equation (2) gives 



