150 



THE EIFFEL TOWER. 



E. If the string P (which is fastened at the intersection 

 of AB, DC) be pulled, the structure remains firm and upright. 

 But if either Q or R be piTlled, the frame collapses. In the 

 first case, the rods AB and CD turning leftwards about 

 their pivots, and in the second case, rightwards. 



Fig. 6. 



It will be observed, that in the well-known outline of the 

 tower these requirements are approximately fulfilled {Fig. 6). 



dz dy 



dx=^dx .', log 3= log 1/+ constant 

 z y 

 .'. y = kh where k is some constant 



drz 

 dx 



t = kh .' .z = Ae^''+ Be-** 

 d'z 



.•.y=^2=Ce**+De-^* {C=Ak^, D=Bk^). 



This is . • . the equation to the curve. 



If the tower goes off to infinity in the negative direction, we get the 

 logarithmic curve y = Ce'^, which is probably the one in the Eififel 

 Tower. 



If the tower comes to a point at the origin (and is .*. a spire), we get 

 y = CSinh kx, the curve of '• shines." 



Mr. Greenhill also gets the logarithmic curve as the best for a tree, 

 but from independent considerations. 



