28 The Contrast of Practice and Theory. 



method for calculating the power of a fall from the height and 

 discharge, entered into elaborate explanations of how it would 

 make no difference if instead of water we used one thirteenth 

 or fourteenth of the same amount of mercury, or twenty per 

 cent, more paraffin oil, to get the same power out of the same 

 tall. He would persist in believing that our rules and calcula- 

 tions about power and fall were all wrong, until he discovered 

 that we had only told him he must pump twenty gallons to 

 support the motor, and forgotten all about six or seven other 

 pipes which led from the tank on the hill down to the sump 

 hole his pump drew from, and were running full bore all the 

 time. Of course it would then be clear that the rules for 

 calculating the twenty gallons might be right enough, but that 

 he had to pump not only them, but all the water that came by 

 the other pipes as well. 



The theory of steam and other heat engines is, as it happens, 

 full of the most harassing and troublesome " ifs " at every turn; 

 and not only that, but when a preliminary statement of facts, 

 allowed to be perhaps not too false or incomplete, has been 

 adopted, there are all sorts of troubles and difficulties in the 

 mere process of evolving the conclusions which follow. Small, 

 or what might at first sight appear small, variations in the list 

 of facts and causes taken account of, lead to considerable varia- 

 tions in the consequences, so that very little advantage can be 

 got from thermodynamical considerations in steam engine 

 design, compared to the advantages, in the way of dispensing 

 with experiment, gained from the theory of stresses in designing 

 girders and beams. 



Passing nOw to the last instance I am taking, which is the 

 application of electricity on a large scale, the relations of 

 Practice and Theory are again different from those in both of 

 the other cases. 



In this case the purely scientific and theoretical side of the 

 question rested on a much more ample and firm foundation, 

 long before dynamos on any commercial scale were introduced, 

 than either thermodynamics or the theory of stresses did when 



