586 POPULAR LECTURES AND ADDRESSES. 



for yourselves, simplifying it, however, by doing 

 away with the rugged coast line for part of your 

 boundary, and completing the enclosure by the 

 wall itself. Take forty inches of thin soft black 

 thread with its ends knotted together and let it 

 represent the wall ; lay it down on a large sheet 

 of white paper and try to enclose the greatest 

 area with it you can. You will feel that you must 

 stretch it in a circle to do this, and then, perhaps, 

 you will like to read Pappus (Liber V. Theorema 

 II. Propositio II.) to find mathematical demon- 

 stration that you have judged rightly for the case 

 of all equal areas of the enclosed land equally 

 valuable. Next try a case in which the land is 

 of different value in different parts. Take a 

 square foot of white paper and divide it into 144 

 square inches to represent square miles, your forty 

 inches of endless thread representing a forty miles 

 wall to enclose the area you are to acquire. 

 Write on each square the value of that particular 

 square mile of land, and place your endless thread 

 upon the paper, stretched round a large number 

 of smooth pins stuck through the paper into a 



