256 Mr Sang on the Construction of Circular Towers, 



w sin 2 2 P 



and hence / is a minimum when 



, sec i 1 1 , 



/ = 1, or when I =.n qosi', 



* n 



now, it is to be observed, that n is the height of a column of 



stone sufficient to produce the actual strain upon any part of 



the bed, and thus, having laid off this distance w = A w, and 



drawn the perpendicular wN to AF, N is the point at which 



the thickness of the wall is the least. 



2. Logarithmic Conoid. 

 Let (Fig. p. 252.) CDEF be a logarithmic curve, having 



AB for its axis, then putting Ac? = ^r, r = (r) Z*'^, (r) being 

 the radius at the top, and m some arbitrary constant. We 

 have now, equation (M.), 



n . nep log w = fdl-z- 



dz 



now, here, dr — (r) me^^ dz 



— rmdz; 

 whence, d?^ = ?^m^ dz*, and 



fl?/* = (r^rn^ + 1) dz*; whence 



n . nep log w = / dz (r* m^ + 1) 



=fdz{(rye^'^' + 1) 

 , va 1 2mz 



r^ 



■/: 



Putting z — 0,w = (w), we have 

 n . n( 

 whence subtracting, 



n . nep log (w) = + ^ + c; 

 si tn 



