account for Glacial Submergence. 339 



when £ = 0, XT .2b f°° 2 , 



V 7rJ 



. 2b . V^ 

 = mx + -—= x — — , 



V 7T 2 



Hence condition (1) is satisfied. 

 When x = 0, 9A fo 



V 7TJo 



Hence (2) is satisfied. 



When x is infinite and t finite, the result is the same as for 

 condition (1). Hence (3) is satisfied. 



When t is infinite and x finite, 



tt 26 r - 



— f°< 



— mx. 



Hence (4) is satisfied. 



We have now to show that the condition (5), viz. 



is satisfied, 

 i^ince 



where 



dV _ d 2 Y 



dt ~ K dx 2 ' 



Y = mx-\ -= I e'^dfiy 



VttJo 



^ 



V4/e£ 



rf/A 1 



Substituting from this, and differentiating with respect to t } 

 dV 2b =*L * 



eft \/tt 2\/4^p 



Similarly differentiating /* with regard to x y 



dfi_ 1 



d* ~" V4/d' 



dV 26 ^l 1 



.'. — = m + --=e^ — ; 



