with a View to the Saving of Fuel. 357 



scending from its bottom will be heated at least twice 

 as soon as a cylindrical boiler of the same diameter with 

 a flat bottom. 



In order that a cylindrical boiler with flat bottom, 

 surrounded by flame on alj sides, might have the same 

 extent of surface exposed to the fire as a boiler with 

 tubes, it would be necessary to give it a diameter greater 

 than that of the boiler with tubes in the proportion of 

 the square root of 1160.44 to tne square root of 566.68, 

 that is, of 17.171 to 12. 



Therefore, in order that a cylindrical boiler with a 

 flat bottom might have the same extent of surface ex- 

 posed to the fire as our boiler with tubes of 12 inches 

 in diameter, it would be necessary to give it a diameter 

 of 17.171 inches. 



But if the diameter of a boiler intended for pro- 

 ducing steam be increased, it is necessary, at the same 

 time, to increase its thickness, in order to increase its 

 strength. 



The necessary increase of thickness, and the expense 

 that it will occasion, can be easily calculated. 



The effort that an elastic fluid exerts against the sides 

 of the containing vessel is in proportion to the surface 

 of a longitudinal and central section of the vessel, and 

 consequently in proportion to the square of its diameter, 

 the form remaining the same. Hence we may conclude, 

 that a steam-boiler of a cylindrical form with a flat bot- 

 tom, which has the same extent of surface exposed to 

 the fire as a boiler of 12 inches in diameter with tubes, 

 should be at least twice as thick as this last, in order 

 to have an equal degree of strength for resisting the 

 expansive power of the steam. 



The boiler which I have the honour of presenting to 



