1879.] On the Secular Effects of Tidal Friction. 17 5 



fig. 1 a strip is marked off and shaded on each side of the vertical 

 axis* within which the figure has no physical meaning. 



Since the moon's diameter is about 2,200 miles, and the earth's 

 about 8,000, therefore the moon's distance cannot be less than 5,100 

 miles ; and in fig. 2, which is intended to apply to the earth and moon 

 and is drawn to scale, the base of the strip is only shaded, so as not to 

 render the figure confused. The strip has been accidentally drawn a 

 very little too broad. 



The point P in fig. 2 indicates the present configuration of the 

 earth and moon. 



The curve of rigidity x 3 y — \ is the same for all values of h, and 

 by moving the line of momentum parallel to itself nearer or further 

 from the origin, we may represent all possible moments of momentum 

 of the whole system. 



The smallest amount of m. of m. with which it is possible to set the 

 system moving as a rigid body, is when the line of momentum touches 

 the curve of rigidity. The condition for this is clearly that the- 

 equation & 4 — lix s + 1 = should have equal roots. If it has equal roots 

 each root must be %h, and therefore 



(fA)*-A(}*) 8 +l=0. 

 whence fc 4 =^ or Ti = ^=V75. 



The actual value of h for the moon and earth is about 3f , and hence 



