On the Influence of the Tidal Wave on the Earth's Rotation. 285 



It is very likely that they made a third bisection, which would 



3927 

 justify and may even have suggested the change into -. 9 ^ n « 



Certainly if they could have calculated nine bisections of the 

 side of a circumscribed square, they would have actually obtained 

 3*1416025 . . . ; or from nine divisions of the side of a hexagon 

 they would have obtained a value slightly in excess of 3*14159, 



as nearly as I can determine from s(^ — ^ =3' 30"y^j, with 



only seven places of logarithms. But in this latter case at least, 

 if they worked with a decimal diameter of 1*000 . . . , why should 

 they put 3*1416 for 3*14159 ? Why use a vulgar fraction at 

 all ? There are three probabilities thus suggested in favour of 

 the rational right-angled triangle. (1) The fractional form. 

 (2) The difficulty of calculating so many bisections. (3) The 

 probability that they would try to measure the circle experi- 

 mentally by a many-sided polygon ; and I might add that they 

 probably hoped, even if the circumference and radius were 

 incommensurable, to find some rational right-angled triangle one 

 side of which would exactly measure either one circle or a small 

 number of circles. 



7857 

 Unless some historical hint of the fraction -x^r^r could be 



2o01 



found, this must remain a mere conjecture, and pass for what it 



is worth. 



I am, Gentlemen, 



Your obedient Servant, 



Norwich, March 16, 1864. Henry Norton. 



XL1X. On the Influence of the Tidal Wave on the Earth's Rota- 

 tion, and on the Acceleration of the Moon's Mean Motion. By 

 Mr. James Croll*. 



IT has been shown by M. Mayer that the tidal wave tends to 

 diminish the earth's rotation. The rotation of the earth 

 carries the wave a little to the east of the meridian, over which 

 the moon is raising it. And as the attraction of the moon tends 

 continually to pull the wave back to the meridian against the 

 direction of rotation, the wave must act as a drag upon the 

 earth's motion. As the drag acts by friction, the vis viva of 

 rotation is converted into heat. 



There is, however, another way in which the tidal wave tends 

 to diminish the earth's rotation, which does not appear to have 

 been noticed by physicists. But in order fully to comprehend 



; * Communicated by the Author. 



