A treatise on gyrostatics and rotational motion . ineering, II, 1911]. By means of balances thecomponents of the force due to air pressure, and the moment of the coupleon the model were measured, and so the directions of the resultant forceswere laid down in the diagram, for different amounts of obliquity of theaxis of the ship to the air current. The direction of motion is from left to right. E is at the intersectionof the direction of the resultantforce and the axis of the ship,and is farther out the smaller theobliquity. By means of vanes in the rearpart of the model stabilisingforces could
A treatise on gyrostatics and rotational motion . ineering, II, 1911]. By means of balances thecomponents of the force due to air pressure, and the moment of the coupleon the model were measured, and so the directions of the resultant forceswere laid down in the diagram, for different amounts of obliquity of theaxis of the ship to the air current. The direction of motion is from left to right. E is at the intersectionof the direction of the resultantforce and the axis of the ship,and is farther out the smaller theobliquity. By means of vanes in the rearpart of the model stabilisingforces could be applied. Whenthese were in action the positionof E was behind the centre ofgravity, and the couple, whichwithout them tended to turn theship broadside on to the stream,gave, when compounded withthe forces on the vanes, a couple bringing the ship back to the direction ofthe wind. The diagram in such a case is shown in Fig. 71. It will be seenthat in this ease the greater the inclination of the air current to the axis thefarther is K from ( Fui. 71. .- 11. Motion oja perforated so/id in a perfect fluid. Use of Lagranges equations. We do not discuss the general motion of a solid in an infiniteliquid ; for this the reader may refer to Lambs treatise on Hydrodynam ics,to Halphen, Fonctions Elliptiques, t. II, chap. IV, or to Greenhill, , chap. VI11, $27. But the problem of the motion of a perforated solid withcirculation through it is of importance from the point of view of gyrostatic action, and therefore we give here an account of its solution, under certainrestrictions as to the form of the solid. xiii MOTION OF A RING IN A PERFECT FLUID 27!» We shall suppose thai the solid is a circular ring, and refer the motion toaxes of coordinates, 0(x, //. z), taken along and at right angles to the axisof figure. The choice of the position of the origin on the axis of figure isof importance as regards the form of the terms included in the expressionfor the kinetic energy, as
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