The Contrast of Practice and Theory. 27 



Now, pay attention to the fact that a theoretical rule is apt 

 to mean exactly what it says explicitly and no more. Listen 

 again to one part of it : — 



" You must supply no less than a hundred pounds worth." 



Therefore, the rule says nothing whatever about how much 

 more than a hundred pounds worth you may perhaps find it 

 necessary to supply. And, moreover, it so happens that it gives 

 practically no assistance in estimating whether, in any actual 

 engine, the excess will be great or small. We can indeed 

 specify the conditions under which there will be no excess ; but 

 then they, like all exact theoretical conditions, are unattainable 

 in practice, and we have seen in the case of the pillars that an 

 extremely small deviation from exact theoretical conditions 

 may lead to very large consequences, having no very direct 

 relation to the largeness or smallness of the deviation itself. 



I shall endeavour to illustrate by an example the sort of leap 

 in the dark that is taken when an attempt is made to explain 

 the losses of heat beyond a certain point, in a heat engine, by 

 seeking assistance from the laws of Joule and Carnot. Suppose 

 we had a tank on the top of a hill with a pipe leading to a small 

 water motor, which drove the brushes in a hairdresser's shop 

 for instance. Suppose moreover that, instead of a natural 

 supply to the tank, we had to drive the motor by pumping back 

 the water to the top of the hill. Then suppose we got a man 

 to work the pump, and told him that he had to pump up at 

 least twenty gallons, which is about six or seven bucketfuls, tor 

 every customer's hair brushed, and explained to him how this 

 was the exact quantity necessary, after making due allowance 

 for the efficiency of the water engine, to give the power required 

 to drive the brush. Then suppose, when he came to do the 

 pumping, he found it necessary to pump a hundred and fifty 

 gallons or so instead of twenty, or else the tank would run dry, 

 he would naturally be disappointed, and probably would infer 

 that the rules for calculating the power of a fall by the height 

 and discharge were fundamentally wrong. It would be no 

 comfort to him if we, with our heads full of the beauty of the 



