574 POPULAR LECTURES AND ADDRESSES. 



answer : What must be the radius of a circular 

 arc, A D C, of given length, and in what direction 

 must it leave the point A, in order that it may 

 cut a given curve, ABC, perpendicularly at some 

 unknown point, C ? I don't believe Dido could 

 have passed an examination on the subject, but 

 no doubt she gave a very good practical solution, 

 and better than she would have found if she 

 had just mathematics enough to make her fancy 

 the boundary ought to be a circle. No doubt 

 she gave it different curvature in different parts 

 to bring in as much as possible of the more 

 valuable parts of the land offered to her, even 

 though difference of curvature in different parts 

 would cause the total area enclosed to be less than 

 it would be with a circular boundary of the same 

 length. 



The Roman reward to Horatius Codes brings 

 in quite a new idea, now well known in the 

 general subject of isoperimetrics : the greater or 

 less speed attainable according to the nature of 

 the country through which the line travelled 

 over passes. If it had been equally easy to 



