SECT, vii.] STEAM ENGINES. 247 



270 a 



h= 7- ,. 



the increase which would strain the metal as far as it would bear without per- 

 manent derangement. 



519. Here we suppose the heat to be confined to a single point; but generally, 

 or rather in all cases, a considerable portion of surface is directly affected by the 

 heat : in this case a near approximation will be to double the effect of expansion, 

 or make, 



In the case of pipes and cylinders, the greatest difference of temperature will 



never exceed 300 ; and then, 



300 t 2'2 t 

 the force of cohesion the cylinder loses by unequal expansion = j^g-^ = -^ . 



If this be added to the former, we derive, 



2-54 a P 2-2 1 _ 



' ' " 



/ a \ 

 \a-2-2j ' 



_ 

 15000 a ' "6000 



The effect of irregular expansion is sensible only in small cylinders : in the case 

 of a cylinder of 60 inches diameter we found its thickness -305 inches, and it became 

 only '315 when corrected for expansion. 



For pipes of less than 5 inches diameter, 



t __ ! _ _. 

 - 6000 (1 - 0-116 a) 



For working cylinders both wear and other causes of pressure exist ; the latter 

 will require at least that the thickness should be double, and for wear half an inch 

 may be added, as about the proper quantity of allowance. 



520. RULE. For the thickness of a working cylinder. Multiply four times 

 the elastic force of the steam in Ibs. per circular inch by the diameter in inches, 

 and divide by 6000. The result multiplied by the quotient arising from dividing 

 the diameter by the diameter less 2'2, is the thickness for strength, to which half 

 an inch may be added for wear. 



Example 1 . A cylinder 24 inches in diameter is to be made of cast iron, for 

 steam not exceeding 3^ Ibs. per circular inch on the safety valve, or ITS + 3'5 = 15 

 elastice force, required its thickness. 



We have = '24 ; and l- x -24 = -264 ; 



which, added to half an inch, is '764 inches, the thickness required. 



Example 2. A cast iron cylinder for a high pressure engine being 9 inches 

 in diameter, and for steam 50 Ibs. per circular inch elastic force, required the 

 thickness. 



