576 POPULAR LECTURES AND ADDRESSES. 



sider the different value of the land in different 

 parts, and thus he had a very complex problem 

 to practically solve. He had to be guided both 

 by the value of the land to be enclosed and 

 the speed at which he could plough according 

 to the path chosen ; and he had a very brain- 

 trying task to judge what line he must follow to 

 get the largest value of land enclosed before night. 



These two very ancient stones, whether severe 

 critics will call them mythical or allow them to 

 be historic, are nevertheless full of scientific 

 interest. Each of them expresses a perfectly 

 definite case of the great isoperimetrical problem 

 to which the whole of dynamics is reduced by 

 the modern mathematical methods of Euler, 

 Lagrange, Hamilton, and Liouville (Liouville's 

 Journal, 1840-1850). In Dido's and Horatius 

 Codes' problems, we find perfect illustrations 

 of all the fundamental principles and details 

 of the generalised treatment of dynamics which 

 we have learned from these great mathematicians 

 of the eighteenth and nineteenth centuries. 



Nine hundred years after the time of Horatius 



