22 The Contrast of Practice and Theory. 



be thrown away, inasmuch as the result of the calculations is 

 known in advance by experience, and if any theoretical investi- 

 gation brought out a different result, that could only be due to 

 a defect in the theory, or an error in the process of reasoning 

 from it. 



When, however, advances in other branches of mechanical 

 art, and especially in the manufacture of iron, had introduced 

 new kinds of beams, built up of plates and bars riveted to- 

 gether, the questions that could be solved, in connection with 

 such structures, by theoretical mechanics, increased both in 

 number and importance. 



X, Y, and Z, who would make a very poor show if they tried 

 to deal with so complicated a structure as the vaulting and the 

 flying buttresses of Westminster Abbey, found themselves com- 

 paratively quite at their ease in a railway lattice girder ; and 

 the necessity, on the one hand, of making such bridges safe, and, 

 on the other, of not wasting expensive material, made it worth 

 while to seek their aid, so far as it could be given. It must, of 

 course, be well understood that, in the details of mechanical 

 theory even in extremely simple things, there is a multitude of 

 questions which the theory of framework, as ordinarily applied, 

 does not touch, or profess to solve in any way. 



The preliminary " if " of that theory begins by assuming, in 

 the first instance, that, to all intents and purposes, the girder 

 does not bend, and that no bar or plate in it stretches or 

 squeezes in any way, and that all joints of braces and flanges 

 are points of no sensible size, pinned with microscopically thin 

 pins in perfectly true round frictionless holes. This preliminary 

 "if" then assumes a state of affairs which is, in some ways, 

 most flatly at variance with the real state of matters ; for every 

 real girder does bend, and its joints are not put together with 

 pins or rivets at all comparable in size and accuracy to the 

 pivots a watchmaker puts on the axles of the wheels in a watch. 

 The theory then begins by wilfully assuming a known falsehood 

 to be true. 



This sort of false assumption is invariably made whenever 



