The Contrast of Practice and Theory. 31 



The number of practical questions incapable of being all 

 taken into account together in any reasonably simple theory 

 tends therefore to increase continually; but the great difference 

 between the use, as a guide to a fairly accurate preliminary 

 estimate of results, of the theory of electricity, remains in strong 

 contrast to the practical impossibility of attaining any similarly 

 accurate results by any equally simple and direct methods in the 

 case of the heat engines in ordinary use. 



It has been pointed out that Theory is no guide in regard 

 to a great many of the practical consequences which follow 

 either from a correct or incorrect application of it. Conse- 

 quently it cannot be held to be true as a universal principle, that 

 to be able to deduce correctly ^the direct consequences of any 

 theory, no matter how true, is a sure way of avoiding errors. It 

 has been pointed out that theory in the case of the mechanics of 

 framework, of beams, and of girders is directly useful in so far 

 as it enables us to dispense with experiment, more especially 

 with experiments on a large and expensive scale. In addition, 

 as in the case of struts and ties in framework, the theory of the 

 design of the framework as a whole may be obscured by the 

 necessity for taking account, in designing one part, of the small 

 practical deviations from the exact theoretical data, when 

 similar deviations may be left out of account in other parts. It 

 is therefore necessary, in order to understand the results, to 

 know when minute deviations from assumed conditions are of 

 great importance, and when they are not. 



It has been pointed out that sometimes theory only sets a 

 limit, as in the case of steam engine work, of such a nature 

 that outside that limit the rules of calculation are totally unlike 

 those by which the limit itself is fixed ; and it is more impor- 

 tant for practical purposes to know what the theory leaves 

 out of account than what it takes into account, in judging of 

 the value of theoretical conclusions. Therefore it is often more 

 necessary to know what the precise data of theory are not, 

 than what they are ; and more important to see clearly what 

 things a certain theoretical principle does not determine, than 



