58o POPULAR LECTURES AND ADDRESSES. 



thing near the true line by a few rough trials 

 they would try small deviations from the rough 

 approximation, and calculate differences of cost 

 for different lines differing very little from one 

 another. From their drawings and calculations 

 they would judge by eye which way they must 

 deviate from the best line already found, to find 

 one still better. At last they would find two 

 lines for which their calculation shows no 

 difference of cost. Either of these might be 

 chosen ; or, according to judgment, a line mid- 

 way between them, or somewhere between them, 

 or even not between them but near to one of 

 them, might be chosen, as the best approxima- 

 tion to the exact solution of the mathematical 

 problem which they care to take the labour of 

 trying for. But it is clear that if the price per 

 yard of the line were accurately given (how- 

 ever determined or assumed) there would be an 

 absolutely definite solution of the problem, and 

 we can easily understand that the skill available 

 in a good engineer's drawing-office would suffice 

 to find the solution with any degree of accuracy 



