THE EIFFEL TOWER. 151 



Thus the resultant wind pressure on the highest section EF, 

 (marked 1), acts through the meeting-point of GF and CB, 

 and so the section GFBC is in equilibrium under a push 

 along BC and a pull along GF. Next, including GFBC and 

 FEAB as one section, the pressure on it (marked 2) acts 

 through the meeting-point of HG and DC, so that the 

 section HGCD is in equilibrium. Thus, since each portion of 

 the tower is in equilibrium, so also is the whole tower, and 

 that without the help of cross pieces HC, GD, FC, BG, which 

 are therefore omitted as being unnecessary. 



While discussing the stability of the tower, we may 

 inquire whether a system of uniform freely jointed rods, as 

 AB, BC, CD, is stable for small displacements when the 



W 



a. 



Fig. 7. 



link BC is weighted at its middle point {Fig. 7). This is 

 essentially the case of the lowest stage of the tower, and, 

 indeed, of every stage. 



The system is unstable. This can be shown in an 

 elementary way as follows : Invert the whole frame so that 

 it swings from AD. Clearly now it is stable for small dis- 

 placements, for one cannot conceive of its being otherwise. 

 This shows that for a symmetrical position of the rods x 

 is a maximum. But restoring the system to its previous 

 position, this is precisely the condition for instability. It 

 is hardly necessary to point out that this is not a pressing 

 element of danger in the tower, because the overturning 

 forces for small displacements are infinitely small and amply 

 counteracted by the virtual rigidity of the joints. 



