288 



Mr. Mallet on the Physical Conditions 



cedinc ones within it, with a force inversely proportionate, to that with which it 

 will be afterwards extended, we should have attained, at a certain pressure, a 

 perfectly equal extension for all the successive cylinders, so that their united 

 resistances might be considered as centered in the middle point e or d, and hence 

 that the whole section of metal due to the gun's thickness from gio a would be 

 equally effective, in resisting the internal pressure, as though its resolved forces, 

 produced a straight pull on the tangent at e, perpendicular to a, d, and that the 

 metal of the gun were a straight bar, of the breadth a, ^, and unit of depth, 

 resisting in the opposite direction, but in the same line. That this should be 

 perfectly true theoretically, the number of successive cylinders must be 

 infinite, or the thickness of each infinitely small, in which case it may be shown 

 that for a given total thickness of gun, the strength of that divided into suc- 

 cessive annular laminas will be increased, over that whose thickness is in one 

 solid annulus, in the ratio of 



B'-D" D'^'-D'"' 

 D" ■' D^+W 

 jy being the external and D" the internal diameter of the gun. For any prac- 

 tical purpose, however, it is sufficient to divide the total thickness, into six or 

 eight parts ; and the requisite compressions of the internal cylinders by the ex- 

 tension of the external ones, may be practically and readily produced, by shrink- 

 ing them on upon each other, at high temperatures, in the way that wheel tyres 

 are shrunk-on ; to effect tliis in practice the length of the external cylinders must 

 be not very great. 



281. Lastly, combining all that we have said of 

 Fig. 1 and Fig. 2, — if as in Fig. 3, g, d be as before 

 the caliber of the gun ; that we interpose a certain 

 annular thickness g, h, of merely hard inert ma- 

 terial, such as a number of longitudinal prismatic 

 bars of metal, parallel to the axis of the gun, and 

 forming a cylinder of equal voussoirs, and grasp 

 these externally, by a set of successive closely 

 fitting cylinders, whose total thickness is A, b, and 

 of which the inner half of their total number (3 

 and 4) is in a state of compression, while the outer half (1 and 2) is in a state 



