148 



THE EIFFEL TOWER. 



happen that P passes through the intersection of AB and 

 DC, it will resolve along AB and CD alone, and there will 

 no longer be any need for the cross pieces BD or AC. 

 Thus a great expense and weight will be saved. 



Hence: the broken line of the toiver must he such that 

 the opposite ascending girders of any section vieet on the 

 line of action of the ivind pressure in that part of the tower 

 which remains above that section* 



* When the sections are indefinitely diminished in height and in- 

 creased in number, the outline becomes a continuous curve. The theory 

 of this curve has been investigated by Mr. A. G. Greenhill in the 

 *' Cambridge Philosophical Society's Proceedings," vol. iv., p. 66, from 

 the above property, observing that the " girders of the section " must be 

 replaced by " the girders tangent to any section at its two opposite 

 highest points." 



A 



Fig. 4. 



Ihus, if the tower (lying sideways, Fig. 4) be represented hj A E B, 

 and we assume that the centre of pressure on the area A E B coincides 

 with its e.g., then if x,y be the co-ordinates of A referred to E as 

 origin, we have — 



^p_ fy^dx 



fydx 



Again, since ^P is tangent .*. £P= a; — -^ 



ay 



dx 



fxiidx y 



Assume v= fjdx and z=fvdx so that i/ = 



dx" 



