252 Mr Sang on the Construction of Circular Towers. 



^= - sec / ; or, dw=z- wdl sec i ; 

 n n 



hence niv — l dw = dl sec /, and thus n . Nap. log w= Idl sec /. 



On the other hand, when the retaining pressure is perpen- 

 dicular to the surface of the wall, equations (E.) and (F.) be- 

 come 



tdl—dq sin i^rnd {t cos . . (G,) 

 =c?y cos/+w^ (/ sinO . . (H.) 

 by help of which equations the laws of thicknessing in any 

 particular case may be discovered. 



To return now to our origi- 

 nal subject, that of circular hol- 

 low towers : — ^let AB be the 

 axis of the tower CDEF, the 

 outline of the thin wall which 

 forms it; D5sE one of the 

 stones having its beds D 5 and 

 E g perpendicular to the curve 

 of the wall. Since the tower 

 is supposed to consist of a mere 

 shell, there is no substance to 

 oppose a resistance on the sur- 

 face DE : yet, without some out- 

 ward pressure, the building *"r" 

 cannot possibly be stable ; how | 



is that resistance to be obtain- | 



ed? 



The tower being conoid, the | 



stone may be conceived to be bI 

 included between two vertical planes passing along the axis 

 AB, and inclined to each other by some angle 3a. The stone 

 will thus be wedge-shaped, and the pressure on its ends, one 

 of which is D^sE, will prevent it'from advancing to de. 



In the case of the straight wall, we considered the action 

 of a portion of it one foot long, that is, included between two 

 parallel vertical planes one foot apart ; but in the case of a 

 circular tower, we cannot have recourse to the same expe- 

 dient, and must take, instead, a portion included between two 



