Mr Sang oti the Construction of Circular Towers, 257 



, w r'-irY 



n . nep log -— = « + — —^ — 



(rY / 2mz ^ \ . 

 = ^ + ^(^ -1)' 



2m ^ ' 



hence the logarithm of the ratio of the weight at D to the 

 weight at C consists of two parts, one proportional to the 

 depth A d, the other proportional to the excess of the area of 

 the horizontal section at D above the area of the horizontal 

 section at C. 



Differentiating the above equation, we have 



dw f , (rY /o 2w^x ) - 

 w V 2m ^ ' i 



whence 



1 [z + llziWl 

 d?v = (^w)e'^ ^"^ ^ (1 + 7^)dz', 



so that, taking the weight all round, we have dw^2 icrtdl— 

 2ncrt^{r^m^ + 1) . </.-, or 



3. Parabolic Towers. 

 In the first place, I shall consider the case of a conoid 

 formed by causing a parabola to revolve upon its axis ; the 

 tower will then present a convex appearance. 

 In this case, we have 



2fr = -s', or 

 2fdr — zdz 



whence 





n nep log w =J ^ 1 + ^ j dz 



