237 



taken from the mean of the experiments, is 2 4 19, or rather higher 

 than the square. 



Combining the above laws into a general expression, we have, as 

 the formula for the strength of tubes subjected to a uniform external 

 force, 



where P is the collapsing pressure, k the thickness of the plates, 

 L the length of the tube, which should not be less than 1-5, or 

 greater than 1 feet ; D the diameter, and C a constant to be deter- 

 mined by the experiments. For tubes of greater length than those 

 above specified, a variable quantity, dependent upon the length, must 

 be introduced ; and the value of this has yet to be determined. For 

 ordinary practical calculations the following formula will probably, 

 however, afford the needful accuracy : 



P=806,300x . 

 LxD 



Thus, for example, take a tube or boiler-flue 10 feet long, 2 feet 

 diameter, and composed of plates inch thick ; and the collapsing 

 pressure will be 



P=806,300x -I?^- = 2101bs. 

 10x24 



per square inch or nearly so. 



Some experiments have also been made upon elliptical tubes ; and 

 the results have been most conclusive as to the weakness of such 

 forms in resisting external pressure. No tubes in use for boilers 

 should ever be made of that form. 



With regard to cylindrical internal flues, the experiments indicate 

 the necessity of an important modification of the ordinary mode of 

 construction, in order to render them secure at the high pressures to 

 which they are now almost constantly subjected. If we take a boiler 

 of the ordinary construction, 30 feet long, 7 feet in diameter, and 

 with one or more flues 3 feet diameter, it will be found that the outer 

 shell or envelope is from three to three and a half times as strong in 

 resisting an internal force as the cylindrical flues which have to resist 

 the same external force. This being the case, it is evident that the 

 excess of strength in those parts of the vessel subjected to tension, is 



