the Difplacement of Shore-lines. 419 



of square miles. The Vulcanism of the present day seems 

 feeble in comparison with these gigantic eruptions. 



We will now pass to the inquiry whether these changes in 

 the form of the earth may stand in any relation of dependency 

 to the periodical variations of the eccentricity of the earth's 

 orbit. We start from the fact that Thomson and Tait are 

 right when they say that the tidal wave is the most powerful 

 of the forces which contribute to chano;e the length of the 

 day. But besides the tidal wave of the sea, the interior 

 friction accepted by Darwin, (" the bodily tides ") is also 

 effective. Both, of course, are dependent upon the distance 

 of the sun and moon ; and we may therefore examine whether 

 the tidal action of these bodies upon the earth varies with the 

 eccentricity of the earth's orbit. It appears from Darwin's 

 investigations that the lunar tides in very distant periods must 

 have been much orreater than now. 1 disreoard this, as the 

 time in question is so long ago, and because the profiles, which 

 later on will combine in curves for the eccentricity of the 

 earth's orbit, come down from a past geologically so near. 

 When I perceived that the dependence of the tidal wave upon 

 the eccentricity might be of geological importance, I applied 

 to the observer H. Geelmuyden, who, with his usual kindness, 

 has given me the following answer: — 



" The action of the eccentricity of the earth's orbit, e, upon 

 the force which produces tide and ebb, and which, for the sake 

 of brevity, I will call the tidal force, is as follows : — Let r be 

 the sun's distance, then the sun's tidal force is 



where C represents the sun's mass and the earth's radius. 

 In the course of the year r varies ; but the mean value of -^ 



is found by a simple integration to be -^r^ owttk? v/here a is 



•^ ° a^{l—e)6l2, 



the unchangeable mean distance. Consequently, the annual 



mean value of the sun's tidal force becomes 



P= 3M ^-^0/, = ^(1+3/2^ + . ..)• 

 a\l — e^)dl'2 ar^ ' ^ 



" From this it follows that, when the eccentricity increases, 



the tidal force also increases ; if the former increases Ae and 



the latter AP, then 



AP Ze.C^e ^ ^ 

 ^ = -^-^=3.. A., 



2E 2 



