EQUILIBRIUM OF THE ARCH. 313 



The existence of the points Q and Q', about which the two upper 

 portions of the arch have a tendency to turn, and about which the 

 material is first observed to yield, has long been known to practical 

 men. The French engineers have named these points the points of 

 rupture of the arch ; and the determination of their position by a 

 tentative method forms an important feature in the very unsatisfactory 

 theory which they have applied to this important branch of Statics. 



13. The theory of the equilibrium of the groin and that of the 

 dome are precisely analogous to the theory of the arch. 



In the former case a mass springs from a small abutment spread- 

 ing itself out symmetrically with regard to' a vertical plane passing 

 through the centre of its abutment. It is in fact nothing more than 

 an arch, whose voussoirs vary as well in breadth as in depth. The 

 centres of gravity of the different elementary voussoirs of this mass 

 lie all in its plane of symmetry. Its line of pressure is therefore in 

 that plane, and its theory is embraced in that which has been already 

 laid down. 



Four groins commonly spring from one abutment ; each opposite 

 pair being addossed, and each adjacent pair uniting their margins. 

 They thus lend one another mutual support, partake in the properties 

 of a dome, and form a continued covering. 



The groined arch is of all arches the most stable ; and could ma- 

 terials be found of sufficient strength to form its abutment and the 

 parts about its springing, it might be safely built of any required 

 degree of flatness, and spaces of enormous dimensions might readily 

 be covered by it. 



It is remarkable that modern builders, whilst they have erected the 

 common arch on a scale of magnitude nearly approaching perhaps the 

 limits to which it can be safely carried, have been remarkably timid 

 in the use of the groin. 



H. MOSELEY. 



King's College, London, 

 Ocl<^er 9, 1833. 



