OF GUN-METAU IZ7

84. This being premised ; let a gun (PI. 1, Fig. 4)A B C D be calt of the same metal, calibre, and length asthose of which the thicknesses are sought, and its dimensionsdetermined by a right line C D drawn obliquely to A B, sothat the thickness A C of the breech may resist the pressureof the fluid ; the thickness B D at the muzzle will be muchless. Suppose this gun (83 ) burst at the first round in anypoint between A and B, as at G ; should it burst in severalplaces at once, most attention should be paid to the openingnext the breech. Let F G where the metal yields to thepressure of the fluid be thickened in the proportion of thetenacity of the bronze, heated by siring as much as it can beon service (35) to its tenacity when cold, and call it = m ;then 711 expresses the proper thickness of metal at the pointG of the length A B. It is essential to remark, that thefracture in G was occasioned solely by the pressure of thefluid, and not by the percussion of the shot against the sidesof the gun, nor by any defect in the metal; as may beknown by examination.

85. Let H E represent the bore of a gun, whose thick-nesses of metal are fought; (PI. 2, Fig. 5) draw the scaleLOQ_R (83) of the pressures of the fluid deducedfrom the rectangular ordinates; make EP equal AG (PI. 1,Fig- 4) and PT equal to m ; then if O P be the greatestordinate of the scale L O Q_R, from the point T draw T Yparallel to P E for the thickness of metal from P to E ; inorder to find them from P to H make the following propor-tions; PO:NQ.::PT:NV, and PO : H R :: PT : HX,draw a line through the points T V X; then YTVX willbe the scale of thicknesses sought. But if KI be the greatestordinate, find K S a fourth proportional to P O, T P, K L;and from the point S draw S Z parallel to KE, in order tohave the thicknesses from K to E ; then Z S T V X will bethe scale of thicknesses in the whole length E H of the gun.

86. To apply this theory to a particular cafe; (Pi. 2,Fig. 5 ) let a 32 pr. be charged with 13 Ib. 2 oz. offine war powder, and the wads rammed so as not to dimi-nish the volume of the powder. Let the proportion of tinin the gun-metal be 4 and the gun be so heated as to firepowder; its greatest thickness in 2 state of equilibrium willbe K S. If the gun be fired under the most favourable cir-cumstances to the inflammation of the powder, that is, «=j 200 (33) the greatest thickness K S ought to be of the

diameter

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