290 OF STEAM NAVIGATION. [SECT. x. 



will be more easy, in proportion as the cross section approaches to that of a solid 

 of revolution. 



599. LATERAL STABILITY. The inequality of the surface of the sea will 

 alone produce considerable lateral motion, if the sides be not sensibly vertical ; 

 hence, in sea vessels lateral stability should not be obtained by form at the surface 

 of the water. The next important point is, that the stability should be equal 

 throughout the length. 



To render it easier to manage the inquiry, we may consider the vessel to be 

 a homogeneous mass of matter, with vertical or circular surfaces at the water 

 lines when at rest ; and that it is of a parabolic form, having the equation p x y", 

 taking the two cases when the ordinate y is the half breadth, and when it is the 

 depth ; for these cases enable us to contrast very opposite forms. 



600. The ordinates being parallel t(^ the depth, we have the difference of the 

 moments of the parabolic parts, when i is the angle the body makes with its 

 position, and B D (Fig. 3. Plate xvi.) coincides with the water line = 





and the difference between this quantity and the moment of twice the area of 

 the triangle B C b is the stability. 



2 / b \ s . b s sin. i ., f ., . . i 



cut, -Q ( -5 J sin - * = TO = the moment of the triangles ; 



hence, 



. * ri- ' (v - J>" g * V the stability. 

 12 \ 2 + /' 



The capacity of the section is f^,. 



601. If the negative quantity be less than b z , the body has no stability; hence 

 we see that a certain relation must hold between the breadth and depth, to render 

 a vessel stable. 



602. If the form be a triangle, then n = 1, and putting A = the area, we 

 have, 



Sb sin. i ,, n , a b 



= j_ (6* 2 o), and A = _^-. 



603. If the form be a common parabola, then n = 2, and 



86 sin. t ,, . 2 a b 



= - (6* - 3 a"-), and A = --. 



