ISOPERIMETRICAL PROBLEMS. 587 



drawing-board below it, so as to enclose as much 

 value as you can, judging first roughly by eye 

 and then correcting according to the sum of the 

 values of complete squares and proportional values 

 of parts of squares enclosed by it. In a very 

 short time you will find with practical accuracy 

 the proper shape of the wall to enclose the 

 greatest value of the land that can be enclosed 

 by forty miles of wall. When you have done this 

 you will understand exactly the subject of the 

 calculus of variations, and those of you who arc 

 mathematical students may be inclined to read 

 Lagrange, Woodhouse, and other modern writers 

 on the subject. The problem of Horatius Codes, 

 when not only the different values of the land in 

 different places but also the different speed of the 

 plough according to the nature of the ground 

 through which the furrow is cut are taken into 

 consideration, though more complex and difficult, 

 is still quite practicable by the ordinary graphic 

 method of trial and error. The analytical method 

 of the calculus of variations, of which I have told 

 you the result, gives simply the proper curvature 



