QUICKEST DESCENT. 



PROBLEM. 



If two weights, m and w, be connected by 

 a string, passing over a pulley, at A, in what 

 curve must the weight n move, that it may 

 descend from A to B, in the least time possible. 



Tftm 



3)' 

 C 



Let A n nVB be the curve required. And, let the 

 time through A n together with the time through 

 n"B be supposed constant : then, the time through 

 the two elements of the curve, nnf and n'n' must 

 be a minimum. 



Let AD, AD', AD'', be the consecutive values 

 of the abscissa. 



b2 



