152 Mr Sang on tfie relatiQti which subsists 



steam upon the piston, and all other friction proportional to the 

 square of the linear dimension ; and the third including all that 

 friction which arises from the weight of the parts, and which is 

 thus proportional to the cube of the dimension. 



Suppose now, for the sake of an example, that, in an engine 

 whose cylinder is '20 inches across, and whose inciting pressure 

 will thus be 4000 lb., the friction of each kind is 100 lb., the 

 entire friction being thus 300 lb. or about 1-1 3th part of the 

 moving force. And, to make a handsome enlargement at once, 

 let us propose one of which this may be a mere model, on the 

 scale of 20 to 1 ; the new cylinder will be 4000 inches in dia- 

 meter, and the pressure on the piston 1,600,0001b. The fric- 

 tion of the first species would amount to 2000, that of the second 

 to 40,000, and that of the third to 800,000 lb., so that the sum- 

 total of the friction, no less? than 842,000 lb., would be fully 

 more than half of the inciting pressure. 



It is then clear that such an enormous engine would be high- 

 ly disadvantageous as a mechanical agent, and that, if the en- 

 largement were pushed a little farther, the whole of the moving 

 force would be expended in overcoming the friction. There is, 

 then, a greatest size beyond which it is impossible to proceed in 

 the construction of the steam-engine. But there is also a least. 



Let us, in fact, take an engine similar to our first, but with a 

 cylinder of only 1 inch in diameter. In such an engine the 

 pressure of the steam upon the piston would only be 101b.; 

 the three kinds of friction would amount respectively to 5 lb. 

 1 qr. and l-80th part of a lb., the first kind alone being equal 

 to half the inciting force. Were the diminution still farther 

 continued, the friction of the packing of the piston might equal 

 the pressure of the st.aro. 



From this it is apparent that, for each shape of steam-engine, 

 there are two extreme limits as to size, at which the utility of 

 the engine ceases altogether, and between which there is placed 

 a best size, or one which is accompanied by the most complete 

 development of the powers of the instrument. A skilful ar- 

 rangement of the parts may, indeed, extend the limits both ways, 

 and may thus change considerably the most advantageous size, 

 ^t, even with that assistance, very small or very large engines 

 are less productive of force, in proportion to the quantity of coal 



