ADDITIONS. 



Among the effects of friction, \ve may notice the standing of a stone 

 arch. For each of the vaulting stones of an arch is a truncated wedge ; 

 and though a collection of such stones might be so proportioned in 

 their weights as to balance exactly, yet this balance would be a totter- 

 ing equilibrium, which the slightest shock would throw down, and 

 which would not practically subsist. But the friction of the vaulting 

 stones against one another prevents this instability from being a prac- 

 tical inconvenience; and makes an equilibrated arch to be an arch 

 strong for practical purposes. The Theory of Arches is a portion of 

 Mechanics which has been much cultivated, and which has led to con- 

 clusions of practical use, as well as of theoretical beauty. 



I have already spoken of the invention of the Arch, the Dome, and 

 Groined Vaulting, as marked steps in building. In all these cases the 

 invention was devised by practical builders ; and mechanical theory, 

 though it can afterwards justify these structures, did not originally 

 suggest them. They are not part of the result, nor even of the appli- 

 cation of theory, but only of its exemplification. The authors of all 

 these inventions are unknown ; and the inventions themselves may be 

 regarded as a part of the Prelude of the science of mechanics, because 

 they indicate that the ideas of mechanical pressure and support, in 

 various forms, are acquiring clearness and fixity. 



In this point of view, I spoke (Book iv. chap. v. sect. 5) of the Arch- 

 itecture of the Middle Ages as indicating a progress of thought which 

 led men towards the formation of Statics as a science. 



As particular instances of the operation of such ideas, we have the 

 Flying Buttr esses which support stone vaults; and especially, as al- 

 ready noted, the various contrivances by which stone vaults are made 

 to intersect one another, so as to cover a complex pillared space below 

 with Groined Vaulting. This invention, executed as it was by the 

 builders of the twelfth and succeeding centuries, is the most remark- 

 able advance in the mechanics of building, after the invention of the 

 Arch itself. 



It is curious that it has been the fortune of our times, among its 

 many inventions, to have produced one in this department, of which 

 we may say that it is the most remarkable step in the mechanics of 

 arches which has been made since the introduction of pointed groined 

 vaults. I speak of what are called Skew Arches, in which the courses 

 of stone or brick of which the bridge is built run obliquely to the 

 walls of the bridge. Such bridges have become very common in the 

 works of railroads; for they save space and material, and the inven- 



