582 POPULAR LECTURES AND ADDRESSES. 



length of the line varies. This statement would 

 give the radius of curvature in fraction of a mile. 

 If we wish to have it in yards we must take the 

 rate per yard at which the Neperian logarithm 

 of the price per unit length of the line varies. I 

 commend the Neperian logarithm of price in 

 pounds, shillings and pence, to our Honorary 

 Secretary, to whom no doubt it will present a 

 perfectly clear idea ; but less powerful men would 

 prefer to reckon the price in pence, or in pounds 

 and decimals of a pound. In every possible case 

 of its subject the " calculus of variations " gives 

 a theorem of curvature less simple in all other 

 cases than in that very simple case of the railway 

 line of minimum first cost, but always interpretable 

 and intelligible according to the same principles. 



Thus in Dido's problem we find by the calculus 

 of variations that the curvature of the enclosing 

 line varies in simple proportion to the value of 

 the land at the places through which it passes ; 

 and the curvature at any one place is determined 

 by the condition that the whole length of the 

 ox-hide just completes the enclosure. 



