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December, 1909 be expressed by a similar formula, dependent on the ,horizontal coeffi- cient. The formula for that would be quite similar. (Capt. Hovgaard here presented: another formula on the blackboard.) It would be that the resistance would be equal to some constant, plus another constant, (additional formulae), the resistance was found, with a horizon- fal coeficient, to' bé 053. Now, "it seems to,'be Mr. McEntee's conctu- sion that the wave making disturb- ances will likewise decrease to a min- imum. It would be interesting if Mr. McEnteé would give us the value of the coefficient of the third line at that momentum. I do not think that is stated in the paper. Influence of Beam. As regards the influence of beam, the transverse dimension Mr. McEn- tee states that the maximum pressure head is approximately proportioned to the beam. If the maximum pres- sure head is proportioned. to. the beam, that would mean that the wave height would also be proportioned to the beam, and as the residuary resist- ance is proportioned to the wave height square, that would make the residuary resistance approximately, at least, proportional: to the © beam square. That again corresponds with the result which I arrived at in same analysis of resistances, where I found by a change of dimensions only, that is, keeping the coefficient of fineness the same and expanding along the depth scale, that the residuary re- sistance would ibe as the beam square. That would also correspond with Mr. McEntee's conclusions here. Velocity and Pressure. D.. W. 'Taylor: This' paper by Mr. McEntee carries further some inves- tigations which I made a good many years ago, and I should like to say a word or two in connection with it, particularly as I believe the subject is likely to be carried very much further in the near future. The ques- tion of the velocity and pressure dis- tribution in two dimension motion, a motion such as that of the strut of a propeller blade through the water, a motion in two dimensions, has been reduced entirely to mathematics. We know theoretically what it would be around an ellipsis of any form, but the trouble is an ellipsis is not a practical form for ship shape form, and the difficulty has been to deter- mine the stream form with the sharp edge. The stream form I worked on many years ago almost necessarily minimum - TAE Marine REvIEW brought out a slightly round in front, might bring it out something like that (sketching on the blackboard) very hollow or round, but they all had a slight round, so that when. the water struck this round the pressure at the extreme point was entirely that due to the velocity head, and the curve of pressure would come to a stop there (illustrating on black board), and drop off rapidly. What Mr. McEntee has done has been by graphical methods to develop a sink and source line, so that he can get a mathematically sharp edge there and that is quite an advance. The difficulty we have, as with all of this work .which has tbeen done scientifically, as far as I know, is that it has to be done graphically, and that involves a great deal of labor. There has been a great deal of labor put on this paper of Mr. McEntee's in doing the graphical work, and in attaining the results which Mr. Mc- Entee gives us. Reducing to Mathematics. Lam 'sorry | Prot.< MeDermott, .ts not here this morning, as he is more familiar with this subject, but I have had some correspondence with Prof. - McMahon, of Cornell University, who has gone into the subject, originally in connection with some. investiga- tions having to do with electricity, but he has developed a method by which he is able to obtain mathe- matical expressions for stream form- ulae,--_the work is not complete yet, 'but practically completed, and I think when his work is completed we will be able to do the work, which has been done graphically hitherto by mathematics, with perhaps one-tenth of the labor, and I think it is quite possible that that will be found to be of great value in dealing with pro- peller blades, for instance. The en- tire edge of the 'propeller blade is now made sharp, instead of round, and I think an investigation of the ? 491 pressures on each side may lead to something well worth while. Prof. H. C. Sadler: Prof. McEntee has dealt with this subject in. two dimensions, but it occurred to me that the general results might apply quite well in case of a shape which, instead of taking the water line, ap- plied it to a series of diagonals, that is, in general the conclusions would probably be about the same. It is interesting to note that the conclu- sions that he has arrived at are prac- tically those we obtain in experi- mental tanks,--as Mr. Taylor has shown in his paper today, that you can get the water line too fine for- ward. I would like to draw Mr. Mc- Entee's attention to some work by Herr Ahlborn, published in the Schiff- baudtechnischen Gessellschaft for 1909 in Germany--I do not know whether Mr. Taylor is familiar with his work also, he has been doing a good deal. 'of work on the flow of water past solids, and he introduces some light seed into the water, so as to enable him to photograph the flow around the adjacent objects. In some of these photographs it is very remark- able the way the eddies form, for instance, a stream line will take some Such" form as that" Gllastrated on blackboard), with quite a marked eddy in the middle of this particular part. They are very instructive photo- graphs, and I think throw: a good deal of light on what happens when water flows around a boat. In some cases it appears as if this eddy had no right to exist there, but a photo- graph shows it up very clearly. These are given in a large volume of the . Schiffbautechrtischen Gesellschaft which shows some work on planes. both moving longitudinally with the water and normal to the spiral, and the form of the eddies is very prettily shown. Adjournment was then taken for luncheon. Application of Electricity to Propulsion of Naval Vessels. RESIDENT Taylor called the af- ternoon session to order promptly at 2 o'clock. The first paper presented was entitled "Application of Electri- city to Propulsion of Naval: Vessels," by W. L. R. Emmet. This paper was an extremely valuable one and further attention will be paid to it by the Review later. The figures and _ state- ments give in the paper for the elec- tric propulsion of battleships are not mere theories, based upon supposed possibilities but in all essentials are accomplished facts. The plans are actual designs worked out in every significant detail which might be and, if opportunity offered, would be, con- tracted for and fully guaranteed. Two plans are outlined--a combina- tion drive of a low pressure turbine and an electric motor upon each pro-