1879.] 



On the Secular Effects of Tidal Friction. 



179 



x 4 *— h% 5 + 2=0 has equal roots), then the surface may be conceived as 

 an infinitely narrow and deep ravine, opening out at one part of its 

 course into rounded valleys on each side of the ravine. In this case 

 the contours would resemble those of fig. 4, supposing the round closed 

 curves to be absent. The course of the ravine is at 45° to the axes of 

 y and z, and the origin is situated in one of the valleys, which is less 

 steep than the valley facing it on the opposite side of the ravine. The 

 form of a section perpendicular to the ravine is such as the curve of 

 energy in fig. 3, so that everywhere there is a slope towards the 

 ravine. 



Every point on the surface corresponds to one configuration of the 

 system, and, if the system be guided by a point on the energy surface, 



