The Contrast of Practice and Theory. 23 



theory deals with practical matters. It may, in fact, be laid 

 down as a general rule for all practical purposes, that a point of 

 contrast between Practice and Theory lies in the fact that 

 Theory always starts with one or more false assumptions about 

 the facts of the case ; its preliminary and very first " if" always 

 precedes an untrue statement ; and there lies, therefore, behind 

 all its conclusions the practical question, how far does the error 

 of the very first step affect the conclusions drawn later on ? 



It would be impossible to make use of a quite complete 

 theory which took account of everything — bending, tempera- 

 ture, motion of load, and so forth — all at once everywhere, 

 on account of its frightful complexity. In theory, therefore, 

 we begin by leaving a great number of things out of account; 

 and we take a limited set of causes, as if they were the only 

 causes in operation ; whereas in practice everything is sure to 

 come into account some way, and every cause sure to produce 

 its effect in due proportion. In theory we treat all the 

 things and causes that we are taking account of as equally 

 important till we have calculated their results ; in practice it 

 is only necessary to be able to attain some particular results, 

 and all others may be neglected, no matter how intimately 

 they may be connected in theory with the rest. A curious 

 case of this sort occurs in questions as to the strength of 

 pillars. It might appear at first sight that, except for the 

 difference between crushing and tearing strength, a straight 

 pillar ought, in theory, to bear compression, by a load on its 

 top, just as well as tension ; and that the theory of frames, 

 such as the lattice girder, should be just as independent of the 

 theory of elastic bending in regard to struts as it is in regard 

 to ties. It is well known, however, that, except for very shore 

 pillars, the load that will break a pillar or strut is less than 

 what will crush the material of the pillar. Consequently the 

 sizes of struts in the lattice girder have to be calculated by a 

 different rule from that used for ties, and designed in a different 

 way. This pecuharity of struts is explained by showing, from 

 the theory of bending, that a tall pillar can, when loaded to a 



