

ISOPERIMETRICAL PROBLEMS. 583 



The problem of Horatius Codes combines the 

 railway problem with that of Dido. In it the 

 curvature of the boundary is the sum of two 

 parts ; one, as in the railway, equal to the rate 

 of variation perpendicular to the line, of the 

 Neperian logarithm of the cost in time per yard 

 of the furrow (instead of cost in money per yard 

 of the railway) ; the other varying proportionally 

 to the value of the land as in Dido's problem, 

 but now divided by the cost per yard of the line 

 which is constant in Dido's case. The first of 

 these parts, added to the ratio of the money-value 

 per square yard of the land to the money-cost per 

 lineal yard of the boundary (a wall, suppose), is 

 the curvature of the boundary when the problem 

 is simply to make the most you can of a grant 

 of as much land as you please to take provided 

 you build a proper and sufficient stone wall round 

 it at your own expense. This problem, unless 

 wall-building is so costly that no part of the 

 offered land will pay for the wall round it, has 

 clearly a determinate finite solution if the offered 

 land is an oasis surrounded by valueless desert. 



