j^gg " Mr. Mallet on the Physical Conditions 



these centres of effort will be distant about one caliber fromeacli other. The 

 H.eal expansion of cast-iron for 150= of heat is = -000893, and that of gun- 

 metal probably = -001541, the length originally being 1-000000 (Darnell) 



The total elongation, therefore, for a gun of nine feet in length of chase, due 

 to a rise of temperature of 300^ would, if of gun-metal, be = -0332856 inches, 



say -034 inches. 



99. We may readily approximate to the 

 curvature that will be produced in any case. 

 For let ab = the length of the colder and 

 shorter side of the gun ; 

 gh = that of the hotter and longer 

 side, both taken at the as- 

 sumed centres of effort ; 

 OS - the distance between these 

 perpendicular to the axis 

 of the gun ; , z ^ • 



and assume the gun to bend into a segment of a circle, of which gvh = A is an 



arc, k the centre, and kg a radius; then, calling |^ = h and half the difference 

 between ab and ,/. = half the elongation = . ; and let .. = c, then we can find 

 nk and gl -i^R, the radius, and vo = the versed sine of curvature ; for, call- 

 'ing the side ga of the small right-angled triangle gna = t, we have 



i = y(c- + e') 



but 



:: R + i: e + I, 



B + i = 



yc- + 6' X (e + l) 



Again, in the triangle gko, 



and 



y{ir+lf^+ef=-ok, 



(R + i) - ok - ver-sin A. 



(8) 



