1889] 



„The effect of the eccentricity (e) of the Earth's orbit 

 upon the force that produces flood and ebb and which for short- 

 ness' sake I will call tidal-force, is as follows: If r is the Sun's 

 distance, then the solar tidal-force P = ^, in which equation C 

 contains the Sun's mass and the terrestrial radius. In the 

 course of the year r varies, but the mean value of ^ is found 

 by an easy integration to be 3 where a is the con- 



stant mean distance. Consequently, the annual , mean value of 

 the solar tidal-force is: 



p = — i + 3 / 2 « 2 + • 



a*(l- e *f 



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

 the tidal-force also increases. If the increase in the first-named 

 is A e, and in the last-named A P, then 

 AP_ 3e.Ae 

 P ~ 1 _ e2 -3e.Ae, 



as 1— e 2 in the denominator is of no consequence. 



At present 3e = 1 / 2 o and A e = — 0.00043 per thousand 

 years, consequently 3 e . A e = — 0.00002; or the solar tidal-force 

 loses mfajf of its value in every thousand years. When the 

 eccentricity has attained it's greatest possible value, according 

 to Leverrier 0.0667, then e 2 = 0.00445, 3 / 2 e 2 = 0.00667, conse- 

 quently P = 1.00667 — v or the difference between maximum and 

 minimum is ^ of the value. 



The monthly mean value of the lunar tidal-force will, of 

 course, in the same manner, be dependent on the eccentricity of 

 the lunar orbit, but as this is subject to no particular secular 

 variation it need not be taken into consideration. On the other 

 hand the mean lunar distance is, in an extremely slight degree, 

 it is true, dependent on the eccentricity of the Earth's orbit, in 

 such manner that the lunar tidal-force becomes 



