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practical method may be devised of proving their force andjustness.

156. Since the cylindrical bore of fire-arms should be inequilibrio with the action of the fluid generated from fired -powder, the thickness of metal must at every point of theirlength be proportioned to theordinates of the scale of pressure:this may be reduced to the four following cafes;

1 . When the scale is parallel to the cylinder, thethickness of metal should be the same throughout thewhole length of the gun.

2. The scale may diverge from the axis AEG inadvancing from E to G; or after diverging it may runparallel to the. axis; in both these cases there should bethe same thickness of metal from the breech to the muz-zle, since the sides must be in equilibrio with the greatestordinate.

3. It may from the point E diverge from the axis toa certain point, and then converge towards it; in thiscafe, the metal should be of equal thickness to the pointof the greatest ordinate, with which it must be in equi-librio ; thence it may diminish in the ratio of the cor-responding' ordinates.

4. It may from the point E continually convergetowards the cylinder; then the thickness of metal shoulddiminish proportionally from the breech to the muzzle.

157 * The entire scale of pressures can be deduced from thethickness of metal only in the fourth cafe; in the third case,that part of the scale only is known that converges towardsthe cylinder; in the two first, the greatest pressure of thefluid is only pointed out.

158. In musquet scharged with fire-work, fowling, or can-non powder, and the wads well rammed, the scale of pres-sures is found to correspond with actual experiment in thefourth case; and likewise in the third, if the wad be rammedwith less force; since the greater this force, the farther fromE where the charge is lodged, is the greatest ordinate of thescale.

In the following chapter will be pointed out the method ofdetermining experimentally the scale of pressures in fire-armsof all calibres.

Chap.