ISOPERIMETRICAL PROBLEMS. 585 



to the cusped and looped orbits of G. F. 

 Hill 1 and Poincare 2 can be obtained without 

 disproportionately great labour. 



In the dynamical problem, the angular velocity 

 of the revolving line of reference is numerically 

 equal to half the value of the land per square 

 yard ; and the relative velocity of the moving 

 particle is numerically equal to the cost of the 

 wall per lineal yard in the land question. 



But now as to the proper theorem of curvature 

 for each case ; both Dido and Horatius Codes no 

 doubt felt it instinctively and were guided by it, 

 though they could not put it into words, still less 

 prove it by the " calculus of variations." It was 

 useless knowledge to the bees, and, therefore, they 

 did not know it ; because they had only to do 

 with straight lines. But as you are not bees I 

 advise you all, even though you have no interest 

 in acquiring as much property as you can enclose 

 by a wall of given length, to try Dido's problem 



1 Hill, Researches in the Lunar Theory, Part 3. National 

 Academy of Sciences, 1887. 



2 Methodes Noiivelles de la Mecanique Celeste, p. 109 (1892). 



