involved in the Construction of Artillery. 405 



whence the mean tension 



The total thickness of the tuhe in this example is very great; but it will smtain a pressure 

 more than double of that which would burst the thickest tube that can be constructed in one 

 piece of the same material, provided the calculated distribution of pressure be not alteied 

 by inequalities of temperature when the tube is in use ; for it is evident that if the inner 

 surface be made very much hotter than the outer, the original inequality of pressure will be 

 thereby increased ; and this might be extended so as to split the outer surface without the 

 application of any other force from within." While, on the other hand, any required in- 

 equality of temperature may be allowed for in the first instance in proportioning the succes- 

 sive tensions of the shells or rings, a thing impossible in a tube constructed in one solid 

 piece. 



Again, if an example be taken of a cylinder sustaining a pressure of 6 tons per square 

 inch, and that the maximum strain on the metal shall not exceed 8 tons per square inch, 



3 



the requisite thickness will be i? - r = j ?• ; and let this be divided into four concentric rings, 



3 



each of the thickness tt-v r ; then, before any pressure is applied from within, the tensions 



should be — 



Of the outer ring . . . 1-840 tons per square inch, 



Of the second ring . . . 0-937 ,, „ 



and the compressions of the two other rings — 



Of the third ring, . . . 0-366 tons per square inch, 



Of the inner ring, . . . 2-410 ,, „ 



But for the purposes of construction it is necessary to compute what the strain on the two 

 VOL. XXIII. 3 G 



