DE. W. J. MACQUOEN EANKINE ON PLANE WATEE-LINES. 
391 
Art. (15.) Graphic Construction of those Trajectories. 
(16.) Properties of the Trajectory of Swiftest and Slowest Gliding. 
(17.) Water-Lines of Smoothest Gliding, or Lissoneoids. 
(18.) Orbits of the Particles of Water. 
(19.) Trajectory of Transverse Displacement. — Of Speed of Gliding equal to Speed 
of Ship. — Orthogonal Trajectories. 
(20.) Disturbances of Pressure and Level. 
(21.) Integral on which the Friction depends. 
(22.) Statement of the General Problem of the Water-Line of least Friction. 
(22 a.) Another Class of Plane Water-Line Equations. 
Section III . — Remarks on the Practical Use of Oogenous Water-Lines. 
(23.) Previous Systems of Water-Lines. 
(24.) Variety of Forms of Oogenous Neoids, and their likeness to good known 
Forms of Water-Line. 
(25.) Discontinuity at the Bow and Stern. — Best limits of Water-Lines. 
(26.) Preferable Figures of Water-Lines. 
(27.) Approximate Buies for Construction and Calculation. 
(28.) Lissoneoids compared with Trochoids. 
(29.) Combinations of Bow and Stern. 
(30.) Provisional Formula for Kesistance. 
3 G 
MDCCCLXIV. 
