the Weight of Continents and Mountains. 265 



is open to much uncertainty.* When the sea is solidified into 

 rock the 5,000 meters of depth is reduced to 3,200 meters 

 below the actual sea-level. Thus the average effective depres- 

 sion of sea-bed is about nine times as great as the average 

 height of the land. I shall take it as exactly nine times as 

 great, and put the depth as 3,150 meters ; but it is of course to 

 be admitted that perhaps eight and perhaps ten might be more 

 correct factors. 



In the analytical investigation of this paper the outlines of 

 the vertical section of the continents and depressions are 

 always sweeping curves of the harmonic type, and the magni- 

 tude of the elevations and depressions are estimated by the 

 greatest heights and depths, measured from a mean surface 

 which equally divides the two. 



We have already supposed the outlines of continents and 

 sea-beds to have been smoothed down into sweeping curves, 

 which we may take as being, roughly speaking, of the har- 

 monic type. The smoothing will have left the averages 

 unaffected. 



Thes 



3 questions now 1 

 proper greatest 

 spheroid, which will bring out the above averages i 



proper greatest heigh 

 ' >id, which will 1 

 mated from present sea-level, and what is the position of the 



vith reference to the sea-level. 

 From the solution of the problem considered in the note 

 elow,f ^ appears that, if the continents and sea-beds have sec- 

 ons which are harmonic curves, then if we take, — 



* In a previous paper, "Geological Changes, etc.," Phil. Trans., vol. 167, Part 



thorities will be found there. 



t Conceive a series of lations corrugating a mean hori- 



ntal surface, and suppose them to be flooded with water. This will represent 



the sea-level. 



■■■;.■■ ■ . , 1 : ■ . , . '. ■ ■.,,.,...,,■. 



The average height of the dry parts is clearly — f + " yi 

 Similarly the average depth below water is 



