

ISOPERIMETRICAL PROBLEMS. 575 



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 circle as 

 he could, and would only have deviated from 

 a single circular path if he found that he had 

 misjudged its proper curvature. Thus, he might 

 find that he had begun on too large a circle 

 and, in order to get back to the starting point 

 and complete the enclosure before nightfall, he 

 must deviate from it on the concave side ; or he 

 would deviate from it on the other side if he 

 found that he had begun on too small a circle 

 and that he had still time to spare for a wider 

 sweep. But, in reality, he must also have con- 

 sidered the character of the ground he had to 

 plough through, which cannot but have been 

 very unequal in different parts, and he would 

 naturally vary the curvature of his path to 

 avoid places where his ploughing must be very 

 slow, and to choose those where it would be most 

 rapid. 



He must also have had, as Dido had, to con- 



