THE STEAM-ENGINE. 161 



got a balance of .10 at his "banker's he is insolvent for 

 certain periods, and therefore he must have a 10 balance. 

 Supposing he gets his income paid every hundred days, he 

 must have 100 balance. Therefore, similarly as we get 

 more or less irregularity in the tangential force, so must we 

 have a larger or smaller fly-wheel, which we may look upon 

 as analogous to a banker's balance. I will take an instance, 

 and ask you to consider that we have a non-expansive engine 

 developing 240 gross indicated horse-power at 60 revolutions 

 a minute; that will be two horse-power for every half 

 revolution, equal in round numbers to 30 foot tons. Now 

 you will find if you calculate out that tangential diagram for 

 a non-expansive engine, that the variation above and below 

 the mean is about 30 per cent., and 30 per cent, of 30 foot 

 tons is 9 foot tons. This 9 foot tons, therefore, has to be 

 stored up in the fly-wheel during the time when we have the 

 excess of pressure, in order to be given out during the time 

 when we have the deficiency. Now if we have a fly-wheel 

 on this engine of such a size (about 13 feet diameter) that its 

 rim is going at 40 feet a second, and if we allow the weight of 

 the rim to be 9 tons, and assume the whole weight of the wheel 

 to be accumulated there, the value of that wheel will be 225 

 foot tons in round numbers. Now we want to store up 9 

 foot tons. It is a 9-ton wheel. We want, therefore, to pub 

 in that wheel a velocity equal to what it would derive in 

 falling from an extra foot in height. The velocity of 40 feet 

 a second is that which it would derive in falling from a height 

 of 25 feet, and we want to be able to put into it a velocity 

 which would equal that derived from falling from 26 feet, 

 which would be a velocity of 40*8 feet per second ; '8 is one- 

 fiftieth of forty, and therefore under the circumstances of 

 which I have spoken, we have a variation above and below 

 the mean speed of the engine of one-fiftieth of that mean 

 speed, a variation not inconsistent with very many purposes 

 to which engines are applied. If we were to use an 18-ton 

 wheel going at the same circumferential velocity, the variation 

 would be half of this fiftieth, and if we were * to use a 9-ton 

 wheel of double diameter we should get only one-fourth of 

 the variation, but if we were to use a fly-wheel of double 

 weight and double diameter we should get only one-eighth 

 of the fiftieth or one four-hundredth variation. 



Keferring to the diagram of the expansive engine, cutting 



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