Mr Sang on the Construction of Circular Towers. 249 



depends for its efficacy on the worst quality of stone, and on 

 that quality exhibited in its worst form. The dovetail has, 

 in fact, the advantage of a wedge, and tends to break over a 

 piece of stone at its narrow part ; nor does the dowall appear 

 under a more promising aspect. I question whether the re- 

 sistance to dislocation obtained in this way, be comparable 

 with that which results from the friction of one stone upon 

 another under an enormous pressure, assisted as that friction 

 must be by the consolidation of good mortar. 



The greatest strength and maximum stability of a structure 

 are obtained when the parts are so formed as that a perfect 

 equilibrium would exist although there were no friction be- 

 tween the contiguous surfaces. The friction and the cohe- 

 sion of the mortar are then over and above what is needed 

 for stability ; whereas, by any other arrangement, part of the 

 latter elements must go to give mere stability, the remaining 

 part only serving to resist extraneous influences. 



On the supposition that the whole of the weight is equably 

 distributed over each horizontal section, the form of a tower 

 of solid masonry, which shall have each portion equally press- 

 ed on, has long been known to be that of a logarithmic conoid. 

 But it cannot at once be inferred, that the same form will 

 hold when the internal structure of the parts is taken into 

 account. The same form was given by Professor Robison as 

 that required for a suspended rod, and lately Professor Forbes 

 has again proposed it for the shape of Gothic pendants, for- 

 getting, it would appear, that such pendants do not hang by 

 the cohesion of the stones, but that they are built upon an 

 internal rod. 



The form which would result as the correct one for a solid 

 tower may not be applicable to the situation and purposes of 

 the building. There is no need for restricting ourselves to 

 this or to any other particular form, since, the form being 

 given, we may set ourselves to inquire what ought to be the 

 mode of construction. 



By way of lemma, I shall first consider the law of strain 

 among the parts of a curved wall, regarded as very thin. 



Let CDEF be the end view of a curved wall ; then, in or- 

 der that the pressures may be transmitted along the line 



