OF THE STABILITY OF STEAM SHIPS. 399 



several circumstances by which the floatation is regulated, and on 

 which the mode of action depends. 



The late Thomas Tredgold has considered this subject in his work 

 on the STEAM ENGINE, and his views in this case, as in all others 

 where the powers of his comprehensive and refined mind have been 

 called into action, are concise, elegant, and original ; and we cannot 

 close this chapter to greater advantage than by adopting his theory, 

 which however we shall modify to suit the plan and arrangement of 

 the present work. 



486. In order to simplify the investigation of stability, Tredgold 

 considers the vessel to be a solid homogeneous body of the same 

 density as water, with vertical or circular surfaces at the water lines 

 when the vessel is in a state of quiescence. Now, it is obvious, that 

 with regard to a ship which is designed to carry burdens at sea, the 

 first of these conditions cannot obtain ; this however is of no conse- 

 quence as respects the result of the inquiry, for in reality it refers to 

 a mass of water equal in bulk to the immersed portion of the floating 

 body. As another means of simplification, he supposes the transverse 

 sections of the ship at right angles to the axis of motion to be in the 

 form of a parabola, of which the equation is px=iy n , and for the 

 purpose of contrasting the extremes of form, he branches the subject 

 into the two following varieties, viz. 



1 . When the ordinates are parallel to the depth, and 



2. When the ordinates are parallel to the breadth. 



For each of these cases a general equation is deduced, involving 

 the sine of the angle of inclination, the breadth and depth of the 

 vessel, and the index or exponent by which the order of the parabola 

 is expressed. 



487. Having already investigated an expression by which the 

 stability of a floating body is indicated, we do not consider it neces- 

 sary to trace the steps of inquiry in the present instance, for the 

 intelligent reader will at once perceive, that although the form of the 

 equation is somewhat different, by reason of its involving different 

 parts and different data, yet the principles upon which the investiga- 

 tion proceeds, are, and necessarily must be, the same, or nearly the 

 same as before. 



488. When the ordinates of the parabola are parallel to the depth, 

 the general equation by which the stability is indicated, becomes 



(290). 



