SECT, vii.] STEAM ENGINES. 253 



the valve in Ibs. per circular inch, and divide by 240 times the cubic contents of 

 boiler for each horse power for malleable iron, or for copper by 144 times instead 

 of 240. 



Example. A boiler is of a spherical form, 20 feet in diameter, with 20 cubic 

 feet to a horse power, and the load on the valve 7 Ibs. per circular inch, what 

 should be its thickness ? The diameter is 240 inches, therefore 



7 x 240 Q _ . , 

 2401T20 =: >35 inches > 



or a little less than three-eighths of an inch. (See note to art. 523.) 



When cylindric boilers have spherical ends, the radius of curvature may be 

 equal to the diameter of the cylinder, and they will be equally strong with the 

 same thickness of metal : flat segments are more convenient in construction, and 

 occupy less space to get the same effect. 



CAST IRON BOILERS. 



528. The preceding rules apply only to boilers of ductile metals : in forming 

 one for brittle ones, the effect of unequal expansion must be considered. For 

 cylindric boilers, 



2-54 a p 40 an . _ n _ , _~ N 



* = --J-* x - = j5^, (art. 517 and 523.) 



and the mode of allowing for expansion was shown in treating of cylinders, 

 art. 519. 



In boilers composed of solid tubes it is possible that in a tube having a diameter 

 of 8 inches or more, the excess of temperature on one of its sides may be 1000, 



and then - - = the loss of force, indicating that in those circumstances a tube 



would ultimately burst, of whatever strength it were made, if 7 - 4 t were made 

 greater than a ; for whenever the quotient is unity, or more than unity, the unequal 

 expansion alone is beyond the power of the material. 



This explains the known fact, that such tubes break without apparent defect, or 

 the use of steam stronger than usual. 



From these principles we derive the following for cast iron boilers : a being 



the diameter, and p the elastic force of the steam, jg^ = the thickness for 



strength ; which, added to a thickness equivalent to the loss of force it may 

 sustain by unequal expansion, is, for boiler cylinders above 8 inches diameter, 



a p 7-4 t 



+ 5 whence ' 



t= a<t P 



150 n (a - 7-4) ' 



