112 



Tlie Bight Hon. Lord Kelvin 



[May 12 



be laid down in a circle. It shows also that if the sea is to be part 

 of the boundary, starting, let us say, southward from any given 

 point A of the coast, the inland bounding line must at its far 

 end cut the coast line perpendicularly. Here, then, to complete 

 our solution, we have a very curious and interesting, but not at all 

 easy, geometrical question to 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 per- 

 pendicularly 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 plough the furrow in all parts of the area offered 

 for enclosure, and if the value of the land per acre was equal 

 throughout, Codes would certainly have ploughed as nearly in a 



