is only 3,262 atmospheres, or 72 per cent. of the resistance of a homogeneous cylinder.  By increasing the number of layers or rows of hoops shrunk on, while the total thickness of metal and the caliber of the gun remains the same, we also increase the number of layers participating equally in the total resistance to the pressure in the bore, and taking up strains which are not only equal throughout, but are also the greatest possible.  We see an endeavor to realize this idea in the systems advocated by Longridge, Schultz, and others, either by enveloping the inner tubes in numerous coils of wire, or, as in the later imitations of this system, by constructing guns with a greater number of thin hoops shrunk on in the customary manner.  But in wire guns, as well as in those with a larger number of hoops—­from four to six rows and more—­the increase in strength anticipated is acknowledged to be obtained in spite of a departure from one of the fundamental principles of the theory of hooping, since in the majority of guns of this type the initial compression of the metal at the surface of the bore exceeds its elastic limit.[3] We have these examples of departure from first principles, coupled with the assumption that initial stresses do not exist in any form in the metal of the inner tube previous to the hoops having been shrunk on; but if the tube happen to be under the influence of the most advantageous initial stresses, and we proceed either to hoop it or to envelope it with wire, according to the principles at present in vogue, then, without doubt, we shall injure the metal of the tube; its powers of resistance will be diminished instead of increased, because the metal at the surface of the bore would be compressed to an amount exceeding twice its elastic limit.  An example of injury inflicted in this way is to be found in the method adopted for hooping cast iron tubes cast by Rodman’s process.  If we take into consideration the undoubted fact of the existence to a considerable extent of useful initial stresses in these tubes, then the hoops should be put on them either with very little shrinkage or none at all, whereas ordnance authorities everywhere have applied to this case methods which are only correct for tubes which are free from initial stresses.

[Footnote 3:  In certain cases this, of course, may be an advantage, as, for instance, when the inner tube is under injurious initial stresses; but then, in order to be able to apply the necessary shrinkage, we must know the magnitude of these stresses.]

[Illustration:  Fig. 2]

During the process of hooping guns it is very important to know how to take into account the value and mode of distribution of the prejudicial stresses in the inner tube, should such exist.  Knowing these stresses, it is possible, by regulating the tension of the hoops, to reduce the compression of the metal at the surface of the bore to the proper extent, thus doing away with the previously existing tension, and by that