ON THE MOVEMENTS OF" THE EAlMTl's CRUST. 337 



Darwin's investigations that the lunar tides in v^ery distant periods 

 must have been much greater tlian now. I disregard 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 tlie depend- 

 ence of the tidal wave upon tlie eccentricity might be of geological im- 

 portance, I applied to the observer, EI. Geelmnyden, who with his usual 

 kindness has given me the following answer : 



"The action of the eccentrictity 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 



C 



^ — 73' 



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



In the course of the vear r varies ; but the mean value of ., is found by 



a simple integration to be ^s— — ;r-r^i where « is the unchangeable mean 



^ a\i—e^yd/2 



distance. Consequently, the annual mean value of the sun's tidal force 

 becomes 



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

 force also increases ; if the former increases Je and the latter JP, then 



P l—e^ 



as 1— e^in the denominator is of no siguiflcance. If past times h(i3e=J^, 

 and Je=—0.(X)04:3 per thousand years, then 3e.Je= — 0.00002, or the sun's 

 tidal force decreases every for thousand years by rroooo ^f its value. 

 When the eccentricity has its greatest possible value, 0.0(507 according to 



Leverrier, 6''=0.004t5, 3/2 e2=0.00G07, then P = 1.00007^: or the difter- 



((' 



ence between maximum and miniuuim is , i„ of the value. 



"The monthly mean value of the moon's tidal force will of course, in 

 the same way, be dependent upon the eccentricity of the moon's orbit; 

 but as this is not subject to any noticeable secular variation, it does not 

 come under consideration. On the other hand, the moan's mean dis- 

 tance is dependent, although only to an extremely small extent, upon 

 the eccentricity of the earth's orbit, namely so that the moon's tidal 

 force becomes 



V'=-.^''a-(l.3/2e'). 

 iv' 



H. Mis. 224 22 



