account for Glacial Submergence. 

 Table of Cooling in degrees Fahr. 



341 



Time, in years . . . 



1000. 



5000. 



10,000. 



15,000. 



( 







200 



20O 



200 



200 





1000 



4-5 



124 



145 



15-5 





2000 



03 



8-4 



96 



11-5 



.a ^ 



3000 



01 



2-7 



67 



8-0 



5" 



4000 





10 



4-0 



51 





5000 





0-3 



1-5 



3-0 





6000 







0-6 



1-7 



I 



7000 









09 



In order to estimate what amount of depression of the 

 surface may be expected to have been caused by the cooling 

 of the rocks, we observe that the whole contraction will be 

 exhibited in the vertical direction, and that accordingly we 

 must make use of E, the coefficient of voluminal contraction* 

 If, then, F be the cooling at os, the depression of the surface 

 due to the contraction to that depth will be correctly given by 



E I F dx. But owing to the form of the function this cannot 



be directly integrated. We may, however, approximate suffi- 

 ciently closely by means of the above table, taking the depths 

 at increments of 1000 feet. 



Let us assume, for instance, the duration of the ice-sheet at 

 15,000 years. Then the contraction down to 7000 feet, where 

 the fall of temperature becomes less than one degree, will be 



E{ *° + 2 15 - g 10004- 15 ' 6 + 10<5 1000 + &c.} 

 = E(10 + 46-2) 1000. 



Now E, according to Mallet's experiments, is about 

 0*0000215*. Adie's t and Keade'sJ estimates are rather less. 

 Using this value, we get the contraction and resulting de- 

 pression of the surface, 1*2 feet. 



One further example may suffice. We will take the dura- 

 tion of the ice-sheet at 100,000 years, and, as before, calculate 

 the cooling at intervals of 1000 feet down to the depth of 



* Phil. Trans. Roy. Soc. vol. clxiii. p. 201. 

 t Trans. Roy. Soc. Edinb. vol. xiii. p. 370. 



X ' Origin of Mountain Ranges/ p. 112. See also the author's • Physics 

 of the Earth's Crust/ 2nd edit. p. 102. 



Phil. Mag. S. 5. Vol. 34. No. 209. Oct. 1892. 2 B 



