24 The Contrast of Practice and Theory. 



point far below its crushing limit, get into an unstable state in 

 respect of bending over and doubling up, even when firmly 

 bolted down to a fixed base, on the smallest provocation. The 

 importance, therefore, of the invariable existence in practice of 

 some small crookedness in every bar, differs greatly for„bars in 

 tension and bars in compression. For most theoretical and 

 practical purposes all, even the minutest, crookednesses are of 

 nearly equal and great importance in pillars, and of unequal, 

 but extremely small, importance in tie rods. 



The principal use of theory in bridge work is, of course, that 

 it enables us to dispense with experiments. It would for 

 instance be impossible by a process of trial and error on full 

 size models to design such a thing as the Forth Bridge, or even 

 much smaller structures. If the theoretical mechanics of frame- 

 work had not been carefully worked out, the construction of 

 many structures of no unusual size would have been impossible, 

 not because it was forbidden by the nature of things, but because 

 nobody could have told the right proportions for important parts. 

 Practice often fails to distinguish clearly between what cannot 

 be made for want of materials and tools, and what must not be 

 attempted because the thing would break down. Theory can 

 generally distinguish between these. 



Coming now to my second instance, the steam engine, we 

 shall find a very different relation between Practice and Theory 

 from that existing in the case of beams and girders. After 

 James Watt's discoveries and inventions, and his reduction of 

 the method of designing the parts to an orderly one in place of 

 the blind, haphazard sort of way previously existing, the prin- 

 cipal improvements came through increased skill in manufacture, 

 and increased accuracy arising from the use of machine tools. 

 Meantime, during the second quarter of the present century 

 especially, a great advance, from a scientific point of view, had 

 been made by the labours of Carnot, Joule, Clausins, and others 

 in the explanation of how heat, supplied by the furnace to the 

 boiler, becomes converted into work in steam and other heat 

 engines. An extension of our powers of dealing with this con- 



