254 Mr Sang oh the Construction of Circular Towers. 



since the augmentation of the resisting surface, from the 



gi'eater spread of the circle, may be sufficient to compensate 



for the increased strain. 



In the circular tower, there is a new element, the strain c 



on each square foot of the end of the stone. Observing 



that, in the equation (K.) a is constant, we find 



iftdl= d(nrt sin i) (N.) 



whence, it is evident, that in an equilibrated tower, 



d (r t sin i) 

 <rdl = n — ^i ^, or 



(fdl = {sin i dr + r cos i di -I- - sin idt] 



(O.) 



so that the strain a must increase with the radius of the tower, 

 the outline of the wall remaining the same ; and thus the end 

 strain upon the stones of a curved wall is greater with the 

 greater radius of curvature. In practice, it is important to 

 provide that the end tension c do not exceed the bed tension 

 n : were it to do so, the stones would need to be set up edge- 

 ways. 



Having now given the general theory of circular towers 

 formed of a single shell, I may now proceed to apply that 

 theory to a few special cases. 



Hollow Conical Tower. 



In this case we have i constant, 



and counting t = AD from the 



apex of the cone, we have ;• = / 



sin i, and thus in the equilibrated 



building, 



n . nep log w = I sec i + c, or 



, sec i , Ic 



nep log w = I + '- and 



n n 



thus 



c + seci7 



= e 



where the arbitrary constant c 

 must be determined in reference 

 to some starting point of the sys- 



