384 OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



procedure, if in the first place, we take a brief survey of the principles 

 of construction; for this purpose, let act represent any transverse 



section of the vessel, at right angles to the principal longitudinal axis 

 passing through the centre of effort ; then is ef the breadth of this 

 section at the water line when the .ship is loaded and the plane of the 

 masts vertical, and hi becomes the water line, coincident with the 

 surface of the fluid, when the vessel is deflected from the upright 

 position through the given angle fki. 



It is however manifest from the ordinates in the foregoing table, 

 that in this case, the vertical sections are all different, both in form 

 and in magnitude, and consequently, the primary and secondary 

 water lines do not intersect one another in the point k which bisects 

 ef\ let p be the point of intersection, and through the point/?, draw 

 the straight line mn parallel to hi, and making with e/the angle fpn 

 equal to the given angle of inclination. 



Now, by considering the conditions of the problem, it will readily 

 appear, that the position of the point p in any of the sections 

 parallel to acz, cannot be determined on the same principles by 

 which the place of that point was fixed according to the foregoing 

 solutions, viz. by equating the areas of the triangular spaces mpe and 

 fpn; for it is evident, that the volume which becomes immersed 

 below the fluid's surface in consequence of the inclination, and that 

 which emerges above by the same cause, will not now be proportional 

 to those areas, in the same manner as they are, on the supposition of 

 all the vertical sections being equal and similar figures. 



