CRITICAL AND SUPPLEMENTARY. 



207 



probably about as before. The time-scale of the phenomena can be con- 

 sidered practically the same as before, especially in view of the uncertainty 

 as to the appropriate values of the thermal constants. 



Under the other supposition, that A and ap are constant, the funda- 

 mental functions are again defined by (67), while the primitive tempera- 

 ture is 1 



(88) 



1 



d=d,{i-x'y{\—^x') 



where now 



d =-^ 





SnV"^ ri«7r« j 



or about 58,000°. The coefficients of the series are given by 



A„=2(-l)"-^| 



the first few of which are : 



Aj = 0.80006 ^2 = 0.29146 



^3= —0.14122 



(89) 



(90) 



^8 = 0.03598 



A, = 0.08054 

 ^g= —0.05174 A^= —0.02645 



the alternation in sign and steady decUne in numerical value continuing 

 throughout. 



The time-interval T, during which the first component declines by 1 

 per cent, is the same as with the former density formula, or about 1^ billion 

 years, with the thermal constants assumed. The effect of the conduction 

 in modifying the distribution of temperature is indicated in table 11, for 

 epochs differing by five such intervals. To the order of accuracy for this 

 table the numbers of components of sensible influence range from about 100 

 for the earliest epoch to 4 for the latest given. 



Table 11. 



