406 Mr. Mallet o?i the Physical Conditions 



inner rings is before the third is put on, and, again, what the strain on the third is before 

 the outer one is put upon it. These are found to be— 



The strain of the second ring upon the first, .... 0-93 tons per square inch, 

 ,, ofthe third ring upon the first and second, . 149 „ ,, 



„ ofthe fourth ring upon the three inner ones, 184 „ „ 



Let it be assumed that a strain of one ton per square inch results from a dlfierence of tem- 

 perature of 16° Fahr. in a thin hoop, placed hot upon a solid cylinder of cold cast-iron, then if 

 the thickness of two superimposed rings be the same, it is obvious that the inner one will 

 be compressed, as much as the outer one is extended. The strain on each, therefore, will 

 only be half a ton per square inch. So that the difference in temperature at the moment 

 of superposition ofthe first and second rings should be 29°- 76 Fahr., and the same diffe- 

 rence of temperature would very nearly answer for each of the other rings, which results 

 in the simple rule, that each ring should be put on at a temperature of 30° above that of 

 the preceding ones. 



The larger the diameter ofthe gun, the less injuriously will it be affected, upon this 

 construction, by the inequality of temperature produced by firing hot shot or by quick 

 firing. If a greater maximum pressure per square inch than that above taken be demanded, 

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

 the increased thickness is readily found. If it be 20 tons pressure per square inch, the 

 thickness must be = 2-5r; if 40 tons, = 5?'; and soforth — the temperatures ofthe successive 

 rings being calculated as before. 



The latter part of the preceding calculations, it will be observed, proceeds upon the 

 conception that the physical conditions of the metal of the cylinder (iron) are such as 

 to give rise to a strain of 1 ton per square inch for every 16° Fahr. difference of tempe- 

 rature, in accordance with the books of physical writers (e. g. Dixon on Heat, sec. 85). 

 The error of this conception has been pointed out in the text, as well as the extreme faci- 

 lities of practically fulfilling all the requisite conditions of theory, in cylinders thus built 

 up, which the actual physical constitution of wrought-iron confers. In fact, its ready power 

 to become stretched, at temperatures above a bright-red heat, at once avoids all difficulty 

 as to the precise temperature at which each ring is to be superimposed, and as to mathe- 

 matical precision in their respective diameters. The process in practice with rings varying 

 from 36 inches up to more than 70 inches diameter, and of various thicknesses, from 2 inches 

 upwards, and of different widths, from 24 inches down to 4 inches, has, in fact, been 

 actually found to be attended with as little difficulty as the shrinking-on ofthe tyre of a 

 railway wheel. 



