involved in the Construction of Artillery. 185 



96. The plate No. 4 illustrates this effect on brass guns. Fig. 1 shows a 

 12-pounder gun fit for service. Fig. 2, the same gun " drooped at tlie muzzle," 

 in an exaggerated degree. The gun becomes bent on precisely the same prin- 

 ciple that the length of the " gridiron pendulum" is preserved invariable, or the- 

 bar of zinc and brass in parallel bands of Doctor Ure's "therraostad" is inflected, 

 namely, by the difference of expansion, in these latter cases, of two metals having 

 the same temperature, but different coefficients of expansion, in that of the gun 

 by the bar or portion of the cylinder of the same metal, heated to different tem- 

 peratures at opposite sides of its axis, and, therefore, differently expanded. In 

 a gun whose weight is supported as usual altogether by its trunnions, its own 

 weight acts in favour of the distorting action of this expansion, by the over- 

 hanging mass of the breech and muzzle (a fact which, no doubt, led to the 

 popular view oi drooping at the muzzle) ; but the same effect, and very nearly 

 to the full extent, would take place if the gun were supported at the two ends, 

 a and b, Fig 2, in place of on the trunnions, in which case, in place of drooping, 

 the centre parts of the gun would rise and become arched or hogged, an 

 example that would afford an experimentum crucis as to the views here an- 

 nounced. 



97. If A be the total deflection, and 8 that due to local inequality of tempera- 

 ture, and (j) the experimental flexure of the material for the unit of length and 



12 f TF 

 diameter, then A = o + — — ^ when the gun rests upon the trunnions, and 



5 2PW 

 A — h — - J when the gun is supported at both ends only, assuming the 



general form cylindrical, and neglecting the comparatively small portion re- 

 moved by the bore. 



98. From statements further back, as to the variable temperature of points 

 taken from the inside towards the outside of the tliickness of the gun, it will be 

 seen that we are not able at present to determine at what distance from the axis, 

 in a vertical diameter passing through it, we might consider the whole of the 

 opposing forces tending to bend the gun concentrated ; were we able to fix these 

 centres of effort for any particular gun, the extent of its distortion for a given 

 difference of temperature between the upper and lower sides might be calcu- 

 lated. It is probable that in guns of the usual proportions of heavy bronze guns, 



