

ISOPERIMETRICAL PROBLEMS. 579 



In the modern engineering of railways an 

 isoperimetrical problem of continual recurrence 

 is the laying out of a line between two towns 

 along which a railway may be made at the 

 smallest prime cost. If this were to be done 

 irrespectively of all other considerations, the 

 requisite datum for its solution would be simply 

 the cost per yard of making the railway in any 

 part of the country between the two towns. 

 Practically the solution would be found in the 

 engineers' drawing office by laying down two or 

 three trial lines to begin with, and calculating the 

 cost of each, and choosing the one of which the 

 cost is least. In practice various other con- 

 siderations than very slight differences in the 

 cost of construction will decide the ultimate 

 choice of the exact line to be taken, but if the 

 problem were put before a capable engineer 

 to find very exactly the line of minimum total 

 cost, with an absolutely definite statement of 

 the cost per yard in every part of the country, 

 he or his draughtsmen would know perfectly 

 how to find the solution. Having found some- 



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