270 On the relation which subsists between a 



the second including that part of the friction on the gudgeons which 

 arises from the pressure of the 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 fric- 

 tion being thus 300 lb. or about l-13th 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 diameter, and the pressure on the 

 piston 1,600,000 lb. The friction of the first species would amount 

 to 2000, that of the second to 40,000, and that of the third to 

 800,0001b., so that the sum total of the friction, no less than 

 842,0001b., would be fully more than half of the inciting pressure. 



It is then clear that such an enormous engine would be highly 

 disadvantageous as a mechanical agent, and that, if the enlargement 

 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 cylin- 

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

 the steam upon the piston would only be 10 lb. ; the three kinds of 

 . friction would amount respectively to 51b. lqr. and 1-S0th 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 steam. 



From this it is apparent that, for each shape of the 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 develop- 

 ment of the powers of the instrument. A skilful arrangement of 

 the parts may, indeed, extend the limits both ways, and may thus 

 change considerably the most advantageous size, yet, even with that 



assistance, 



of 



force, in proportion to the quantity of coal they cousume, than mod- 

 erately-sized ones are ; and, in many instances, it would have been 

 better to have employed two or three middle-sized engines than a 

 single one possesed of two or three times the nominal power. 



