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I might further say that we do not countenance in our practice, in the larger docks, the placing of any gates that open in the center wall. That has been done in 'the dock Dewey. The matter of stability is maintained en- tirely by the relative volume of the wings or walls to the total lifting power of the dock, in felation: of course, to their distances to the cen- tral axis, the function being such that if pumping is stopped at any time, for any cause, the water settling will leave the dock with a large maximum of safety, so far as transverse stability is concerned. The matter of the pumping power 'exceeding the flow through the passages when locked to- gether, gives added function to the control of the dock. If there is any tendency of the vessel to roll the pump on that side can be increased, and the weight of water thrown out will be taken from the end of 'the beam, and will become a real factor in effecting the control of the dock. In the matter of the division of the dock, that is more a matter of the di- viding of the pumping, as commercial docks are ordinarily handled, more a matter of multiplying the pumping ap- pliances than of centralizing the pump- ing power, and connecting the valves, the idea being to have water-tight divisions without the necessity of valve connections, with the possibility of their being left open. Of course, the subject of floating dry docks is a vety large one, and I only care to call particular attention to these points at the present time. There are many problems that will have to be worked out more definitely as the science in connection with these docks pro- gresses. Capt. W. Hovgaard: I am glad that I have some little share in the appear- ance of this paper. Last spring I had the pleasure of seeing Mr. Roberts, who showed me the great amount of. work he had done in this line, and I advised him strongly to publish it in the form of a paper. I am glad that he has now donc _ s0, for I feel con- vinced that the paper will be of great practical value not only to the build- ers and users of floating docks, but also to teachers. As far as I am aware there exists no connected, com- plete treatment of this subject in point. I have only one thing to crit- icize, and that is in itself unessential, since it deals, not with the treatment of the problem, but only with the use of certain symbols. Still I believe it is worth while to explain at length why I make this criticism, because the explanation may be helpful to those who are not familiar with the sub- "TAE Marine REVIEW. jects of the stability of ships contain- ing free internal water, and it may thus form a supplement to the paper which it is hoped may be useful. _Let Wand Urefer tothe ship in empty condition, in which case (see Fig. 1) the moment of stability is M=WXGM sin.6.. Now suppose bilging to take place, and that the quantity of water of weight, w, and volume, vy; i6 ad- mitted into the ships. We may. deai with the problems in three different ways: First, the water in the bilge is considered as belonging to the ships and as concentrated in w, the meta- center..of. the, free yates (see Bic. 2). Let G be the common center of gravity of the ship and the water so placed. Then the moment::of sta- bility is = (W plus w) G, M, sin. 6, where W is determined by I : B, W= ; V plus v © Second, the volume of. the ships occupied by free water is considered as belonging to the sea. The center of gravity of the ship remains at G, but the center of buoyancy goes up to B: (see-Fig. 3), There. are now two free-bounding surfaces, that of the ship's water line and the surface of the water in the bilge. We have I--i Be We and the moment of W stability is Ms=W--G M. 'Fhird,. the- free water. 1s: at nest considered solidified and the common center of gravity of this water and the ship is at G (see Fig, 4). When the ship heels over, the water in the bilge actually shifts Dy moving to b, and thus the amount of stability (W plus w) GM will have to be reduced by a couple w, bb=w, bu. Now, it will be found that all three methods give the same result, in other words M:=M.--=Ms3. Mr. Roberts has used the third method, and he has used it perfectly correctly, but now consider formula. (1) and (2) in' his. paper. Formula (1) refers to the empty ships, formu- la (2) to the ship after bilging, but the same symbols, W, V, etc. are used. A comparison between his form- ula (2) and my formuta (4) will show that W plus w and V plus v should be used instead of W and V and that both G and U are different in the two cases. As will be seen from the pa- per, however, Mr. Roberts in his sub- sequent treatment attaches the correct meaning to the symbols, so that my criticism concerns only his choice of symbols, which I think is likely to be misleading to beginners. The Vice President: Is there any oe: further discussion? 3 Mr, Leonard M, Cox: To any one who has suddenly been called upon to assemble for himself the "theories scattered about within the science of - naval architecture," to glean the essentials and eliminate the non-essen- tials, and apply the results to' the ~ various conditions of loading and. flo-. tation to which a floating dock is sub-. jected, this very excellent paper will - appear in the light of 4 timely contri- bution to dock literature; of primary interest to the dock operator in that it sets forth in proper order simple methods for determining that knowl- edge of his tool which every operator should possess; it is of equal interest | to the designer in giving him a general view, so to speak, of what he has hitherto seen in such a mass of detail as to endanger his sense of perspec -- tive, Although stability and strength de- terminations for floating docks are based upon nothing more complex than the most elementary principles of floating bodies and resistance of ~ materials, the problem of making such determinations for every position and -- every condition of an actual structure . --when carrying ship load, operating free, _ self- docking, and. at sea--and : interpreting results ° as affecting the" dock as a whole and each separate element is one of greater complexity than would appear at first glance. It has been well said that theoretical calculations for docks, like those for ships, are of great value as guides in fixing general dimensions and type, | but in actual work so much depends _ upon structural considerations, local conditions, education and skill of op- erators, and, last but not least, the judgment and experience of the de- signer, that it is impossible to formu- late a set of rules strictly applicable to every situation and condition. The effective. limits to. the increase in number of compartments in a transverse section are clearly shown in the table giving value of GM-- -- . eet n for varying values of --, but these theoretical results can have but little value in the case of large floating docks, since for reasons affecting strength and general design, there can rarely be less than six. This is seen from the fact that it is neces- sary to provide a heavy longitudinal girder under keel 'blocks; that inter- mediate longitudinal bulkheads be- tween keel blocks and side-walls are desirable for stiffness, if for no other | reason; and that side-walls are sep-