Proceeding now to the hoop (modulus of elasticity, E,); the elongation or extension of any radius r in its thickness is, by (13), Meigs-Ingersoll's Elastic Strength of Guns,

Ar=

==

r [P'R'-P"R" 4RR (P-p")

3E RR2 + (R''-R') r

The extension or elongation of the interior radius of the hoop (substituting R' for r) then is,

The extension of the interior diameter of the hoop caused by the pressures P' and P" then is,

The various simultaneous pressures that may occur in the bore, at the surface of contact, and outside the hoop simply move the surface of contact in or out. An increase in the compression of the exterior diameter of the inner body is accompanied therefore by an equal decrease in the extension of the inner diameter of the hoop (neglecting the very small, secondary, quantities caused by varying pressures upon the thin ring of metal whose thickness is half the shrinkage).

The shrinkage is the sum of the compression of the exterior diameter of the inner body and the extension of the interior diameter of the hoop (or jacket) and is (adding (b) and (d) and denoting the relative shrinkage or shrinkage per inch of diameter by ),

This formula is true for any simultaneous pressures that may occur at the points indicated.

The shrinkage is most readily calculated by supposing the pressure in the bore to be the greatest the gun of given dimen

sions and metal can stand, namely, the elastic strength of the gun. In calculating this, it is necessary to find the pressures at the various surfaces of contact. That is, using the book notation (Meigs-Ingersoll's Elastic Strength of Guns), in finding P., which acts at radius R. of the bore, we have had to find the pressures P1, P1, Ps.... P, which occur simultaneously at the respective radii R,, R., R..... R.

3

Using these pressures and radii in (e), we have for the first shrinkage (assuming the modulus of elasticity constant throughout),

In calculating any shrinkage, say the nth, if P, is (P). (that is, if this elastic strength is determined by the amount the inner circumference can stretch), the last term of the shrinkage is 2R,; that is, the nth shrinkage is

If P is (P)p (that is, if this elastic strength is determined by the amount that the inner radius can be compressed), it is necessary to make the substitution in (f).

[COPYRIGHTED.]

U. S. NAVAL INSTITUTE, ANNAPOLIS, MD.

THE DUDLEY POWDER-PNEUMATIC GUN.

By HOWARD P. ELWELL, Associate Member U. S. Naval
Institute.

Since the introduction of shell fire from the old smooth-bore guns the attention of ordnance officers and experts of every country has been constantly applied to the development of its effectiveness. Gunpowder was naturally first employed, but as the higher explosives were developed and became better known, unremitting efforts have been, and are now being made, toward obtaining some method by which they could be safely used in projectiles in order to obtain the object sought-destructive shell fire.

To obtain such results almost every conceivable scheme has been brought forward, involving either one or the other of two methods: first, of stowing the explosive by various means in specially contrived projectiles, the idea being to neutralize the effects of shock of discharge of the gun; or, second, by using some force other than ordinary gunpowder in the gun, which of itself would act gently instead of creating a shock on the projectile, thus insuring a safe discharge. An example of the first method would be the "Judson shell" and the means by which both the Army and Navy are able to load small quantities of guncotton and other explosives in projectiles fired from ordinary guns. A prominent example of the second method is the pneumatic gun, or "Zalinski dynamite gun," as it is more popularly known, where compressed air is used instead of powder.

In the first method the results obtained are much more effective than they would be with shells loaded simply with powder, but the weight of explosive used is necessarily, on account of the

shock to the projectile, but a very small proportion of the total weight of the shell.

The second method is by far the most effective, as in this case very large masses of the highest explosive may be safely fired. The ability to project these quantities of explosives with perfect safety and fair accuracy, together with the certainty of explosion at will, either on contact or with slight delayed action, is unquestionably of the highest importance. Favorable testimony to this effect from accepted authorities is so abundant and cumulative as to need no additional weight. So important indeed were the results obtainable by this method that a number of these pneumatic guns have not only been constructed and installed as a part of the defensive scheme for several important harbors-New York and San Francisco among them-but a special vessel, the Vesuvius, was designed and built as a “dynamite cruiser," carrying three such guns.

Some years ago the successes of these guns seemed to warrant the belief that they would become an important adjunct to coast defenses, as well as fill an important though distinct office afloat. For the past year or two, however, less and less has been heard of dynamite guns, and while to those not having knowledge of the facts the cause is unknown, it is really easily explained.

Without doubt the results obtained from this gun are as desirable as ever, and this being so, why has not the type been further developed and utilized? There is but one true answer to this-on account of complication in the system. Ordinarily in thinking of the question one simply has in mind the term-pneumatic gun. If the gun were complete in itself, matters would be comparatively simple, and in absence of complication would prove an effective and valuable weapon. As a fact, however, the gun itself, in this case, is but a detail of the whole necessary accompanying system. Without a steam boiler it is inoperative, yet the very mention of a boiler in connection with a gun brings immediately to mind the above-mentioned complications, for between it and the gun itself there must be necessarily a complex arrangement of air compressors, accumulators, pipes, valves and accessories, all of which require expert knowledge not only to assemble, but to keep in order and to operate.

In spite of all this complication the resultant value of the scheme is so desirable that this government encouraged the plan