Mr. Barnaby. the inlet was unstopped, and water allowed to flow in, there would be a momentary unbalanced pressure driving the boat forward, which was immediately balanced by the sternward pressure exerted by the inflowing water as it was deflected upwards by the pipe, and there would be no resultant effect.

4 March, 1884.

SIR J. W. BAZALGETTE, C.B., President,

in the Chair.

The following Associate Members have been transferred to the class of

The following Candidates were balloted for and duly elected as

The discussion upon the Paper on "Hydraulic Propulsion," by Mr. Sydney W. Barnaby, occupied the whole of the Meeting.

11 March, 1884.

SIR J. W. BAZALGETTE, C.B., President,

in the Chair.

The discussion upon the Paper on "Hydraulic Propulsion," by Mr. Sydney W. Barnaby, occupied the whole of the Meeting.

18 March, 1884.

Sir J. W. BAZALGETTE, C.B., President,

in the Chair.

(Paper No. 1958.)

"Wire-Gun Construction."

By JAMES ATKINSON LONGRIDGE, M. Inst. C.E.

In the year 1855 the Author submitted to the Ordnance Department of that day proposals for the construction of guns by steel wire coiled upon an inner tube. These proposals were based upon experiments previously made by him, which were generally described in the Paper read before this Institution in February 1860.1 In the same year, the Author constructed the 3-inch wire-gun, which was first fired at Southport in that year, and which was exhibited in this Institution in 1879, when the Author's second Paper was read and discussed.2 At various times between 1860 and 1879 the Author in vain attempted to obtain an official trial for his wire-gun system. Within the last four or five years other parties, amongst whom the first was probably Captain Schultz, of the École Polytechnique, took the matter up, and Sir William Armstrong soon after did the same. In August 1882 the Author was asked by the Secretary of State for War to give evidence before the Ordnance Committee on the "general question of gun-construction, as to metal, construction, breech-closing arrangements, form and size of chamber, obturation," &c.; but that body has not thought it desirable to do more than put a few general questions in writing which had no very important bearing on the matter.

Before entering on the specific subject of this Paper, it may be well to make a few further remarks upon the present system of hooped-gun construction, as referred to in some papers which have been received by the Institution from the Ordnance Department, U.S.A.3 These papers are mostly translations from Virgile,

1 Minutes of Proceedings Inst. C.E., vol. xix., p. 283. 2 Ibid., vol. lvi. p. 171. 3 Notes on the Construction of Ordnance, Nos. 1-23. Washington, July, 1882-June 1883.

Colonel of the French Marine Artillery, Rosset, Director of the Turin Arsenal, and Clavarino, Captain of the Italian Artillery. The Author has also carefully examined Colonel Virgile's treatise on the Resistance of Metallic Tubes, simple or compound, published in Paris in 1874.

These documents are valuable and interesting, and show the great importance attached to the mathematical treatment of the subject of gun-construction by the French and Italian Governments. Their translation and publication by the Ordnance Department at Washington evinces a like solicitude on the part of the United States Government. The investigations of Virgile and Clavarino, who deal chiefly with the theory of the subject, although conducted in a somewhat different method, bear out exactly the conclusions and formulas in the Author's first Paper.

The fundamental formula, on which everything else depends, was independently arrived at by Dr. Hart,1 of Dublin, and by the late Professor Rankine, and it is in accordance with the principle laid down by the eminent French mathematician and physicist, Lamé; but it differs materially from the formula of Professor Barlow.1

Although, as stated, the fundamental formulas of the various investigators arrive at the same result as was given in the Paper of 1860, there are one or two remarks which it is necessary to make respecting their application. The first is, that some modification must be effected in certain cases, by introducing into the results the effect of what are known as Wertheim's coefficients. This was brought before the Institution by Dr. Hopkinson in the discussion on the Author's Paper of 1879.2 It is also fully dealt with by Virgile in his treatise before mentioned, and upon it the following remarks may be made.

When a bar of metal, length 1, is subjected to the tension of a force ƒ, the extension within the limits of elasticity is l 1 where

k'

k is the modulus of elasticity. Now, if at the same time the bar is subjected to forces f, and f,, laterally, it may be proved, as is done by Virgile, that the extension will be no longer 1, but

k'

assuming that k has the same value for tension as for compression, and this assumption is either absolutely or very approximately true for such metals as are used in gun-construction.

α=

From analytical considerations Poisson arrived at the values 4, B = 2; but Virgile shows that these estimates are incorrect, and arrives at the conclusion that a and B are each equal to 3, and this agrees with the result arrived at by Wertheim after a long series of careful experiments. Consequently, it may be taken as a fact that the actual extension of the bar is

Now, in the case of a hooped gun, taking l as the length of a filament of indefinitely small thickness, f the circumferential strain, f, the normal pressure, or actual compression, and ƒ,, the strain in the direction of the axis of the bore, the actual extension will not be l

1, but

and the question is, what modification does this involve in the general formula for tension?

case.

In guns constructed according to the Author's principle ƒ, would not exist, and in guns as ordinarily constructed it is shown by Virgile that its effect is so insignificant, as affecting the extension, that it may be neglected. It is therefore only necessary to deal with the modifying effect of the radial compression f, and the effect of this upon the general formula is fully shown by Virgile. It is not of serious importance in any Dr. Hopkinson calculated that in the 9-inch gun it would increase the tensile strain of the inner surface of the steel tube from 16.97 to 18.2 tons, and would decrease that of the iron hoop from 14.45 to about 14 tons per square inch. It may, however, be shown that these variations are due entirely to the fact, that the tube and the hoop have not the same modulus of elasticity. When the moduli of elasticity are the same, the normal or radial force has no effect upon the tension. Consequently, in a gun entirely of one material, with the same modulus, the radial force f, may be omitted in the calculation. But in guns built up of hoops having different moduli from the tube, their forces may be taken into account, although their effect is comparatively small.