APPENDIX. 



ON THE OBSERVATIONS AND CALCULATIONS 

 REQUIRED TO FIND THE TIDAL RETARDA- 

 TION OF THE EARTH'S ROTATION.* 



THE first publication of any definite estimate 

 of the possible amount of the diminution of ro- 

 tatory velocity experienced by the earth through 

 tidal friction is due, I believe, to Kant. It is 

 founded on calculating the moment round the 

 earth's centre of the attraction of the moon, on a 

 regular spheroidal shell of water symmetrical 

 about its longest axis, this being (through the 

 influence of fluid friction) kept in a position in- 

 clined backwards at an acute angle to the line 

 from the earth's centre to the moon. One of the 

 simplest ways of seeing the result is this : First, 

 by the known conclusions as to the attractions of 

 ellipsoids, or still more easily by the consideration 

 of the proper " spherical harmonic " 2 (or Laplace's 

 coefficient) of the second degree, we see that an 

 iquipotential surface lying close to the bounding 



1 From the Rede Lecture, Cambridge, May 23, 1866, "On the 

 'issipation of Energy." 



2 Thomson and Tait's Natural Philosophy, 536 (4). 



F 



