16 Professor Ranktnis on the StahUity 



chimney leans, and let q denote the ratio which the deviation of that 

 centre from the middle of the diameter D E bears to the length t of that 

 diameter. 



Then the least moment of stability is denoted by 



W-BT= iq — q) Wt, (3.) 



The value of the co-efBcient q is determined hj considering the 

 manner in which chimneys are observed to give way to the pressure of 

 the wind. This is generally observed to commence by the opening of 

 one of the bed-joints, such as D E, at the windward side of the chimney. 

 A crack thus begins, which extends itself in a zig-zag form diagonally 

 downwards along both sides of the chimney, tending to separate it into 

 two parts, an upper leeward part, and a lower windward part, divided 

 from each other by a fissure extending obliquely downwards from wind- 

 ward to leeward. The final destruction of the chimney takes place, 

 either by the horizontal shifting of the upper division until it loses its 

 support from below, or by the crushing of a portion of the brickwork 

 at the leeward side, from the too great concentration of pressure on it, 

 or by both those causes combined ; and in either case the upper portion 

 of the structure falls in a shower of fragments, partly into the 

 interior of the portion left standing, and partly on the ground beside 

 its base. 



It is obvious that in order that the stability of a chimney may be 

 secure, no bed-joint ought to tend to open at its windward edge ; that 

 is to say, there ought to be some pressure at every point of each bed- 

 joint, except the extreme windward edge, where the intensity may 

 diminish to nothing ; and this condition is fulfilled with sufiicient 

 accuracy for practical purposes, by assuming the pressure to be an 

 uniformly varying pressure, and so limiting the position of the centre 

 of pressure F, that the intensity at the leeward edge E shall be double 

 of the mean intensity. 



Chimneys in general consist of a hollow shell of brickwork, whose 

 thickness is small as compared with its diameter ; and in that case it is 

 sufficiently accm'ate for practical purposes to give to q the following 

 values : — 



For square chimneys, ^ ^ ^ ; | 



For round chimneys, 5' = i- / 



The following general equation, between the moment of stability 

 and the moment of the external pressure, expresses the condition of 

 stability of a chimney : — 



HP= (?-?') W<, (5.) 



