420 A. Blytt 071 the probable Cause of 



as 1 — ^ in the denominator is of no significance. If past 

 times be 3e=^(^, and Ae= — 0*00043 per thousand years, then 

 Se .Ae= — 0"00002, or the sun's tidal force decreases for every 

 thousand years by q-^Jq-^ of its vakie. When the eccentricity 

 has its greatest possible value, 0*0667 according to Leverrior, 



^2^ 0-00445, 3/2^2 = 0-00667, then P = 1-00667-3; or the dif- 

 ference between maximum and minimum is -^Iq 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 notice- 

 able secular variation, it does not come under consideration. 

 On the other hand, the moon's mean distance is dependent, 

 although only to an extremely small extent, upon the eccen- 

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

 force becomes 



F=^(l-g. 3/2.2). 



" Here, therefore, the eccentricity acts in the opposite 

 direction, namely so that the force diminishes as the eccen- 

 tricity increases ; but as the factor q, by which 3/2 e^ is 

 multiplied, is only about 3/400, Mdiile the magnitude outside 



the brackets —^ = 5/2 . -3 (the lunar tides being in propor- 

 tion to the solar tides most nearly as 5 : 2), its action upon 

 the whole tidal wave is ^§g . ^ = ^L of the former." 



Thus we see that the tidal force rises and sinks with the 

 eccentricity of the earth's orbit. It varies by about gig of 

 its value from the highest to the lowest eccentricity. This 

 force is the most important force for the alteration of the day, 

 and it makes it longer. The most important force for short- 

 ening the day, according to Thomson, will be the refrigeration 

 of the earth, but he has calculated its value at only go^oo ^^ 

 the tidal force (and he has only taken into account the marine 

 tidal wave). If, therefore, the tidal force diminishes and 

 increases by 5^5 of its value, this periodical variation cannot 

 compete with forces which act in the opposite direction ; and 

 we may therefore conclude that the sidereal day is constantly 

 becoming longer, but that its increase is periodically stronger 

 and weaker. It increases in length more and more rapidly 

 so long as the eccentricity of the earth's orbit increases, more 

 and more slowly so long as the eccentricity diminishes. In 

 other words : the centrifugal force diminishes and the equa- 

 torial regions increase in weight more and more rapidly 



