128 BRUSH— DISCUSSION OF " [April 24, 



velocity of light, then the displacement of the earth's center from E 

 to E' will be about 52 feet, and the tangential force M'P will be 

 about one twenty-four-millionth of gravity at the distance of the 

 moon. 



Obviously, this very small tangential force will tend to make the 

 moon's orbit an expanding spiral of very small pitch ; but the vastly 

 greater force of gravity will resist this tendency and nearly, but not 

 quite, counteract it ; the net effect being an extremely slow lengthen- 

 ing of the radius vector, and a very slight retardation of real as well 

 as angular velocity. This paradoxical effect, of an accelerating force 

 producing an orbital retardation, is explained by Sir George H. Dar- 

 win in his chapter on tidal friction and the genesis of the moon.* 



I have made only a very rough estimate of the secular retarda- 

 tion of the moon's mean motion which this minute accelerating force 

 will bring about, with gravitational transmission taken equal to the 

 velocity of light, but have satisfied myself that it will amount to a 

 very few seconds of arc only, in a century; and I do not claim that 

 the velocity of light is the velocity of gravitational propagation un- 

 less the postulated ether waves are ultimately found to be transverse 

 like those of radiation. I think it probable that they are longitu- 

 dinal, or otherwise different from those of radiation. If this be true, 

 the velocity of propagation may be several times greater than that 

 of Hght, and the secular retardation of the moon correspondingly 

 less. 



I realize that any uncompensated retardation of the moon's 



motion will add to the present outstanding observed acceleration, if 



any; but am hopeful that the slight departure from Newton's law 



of inverse squares already suggested may, in connection with other 



motions of the moon, supply some of the necessary compensation. 



There is also a minute source of compensation, due to motion 



through the ether, which I intend to consider in another discussion. 



Cleveland, 



April, 1914, 



4 « The Tides," Chap. XVI. 



