INTRODUCTION. XXXV 



quiry, cannot be represented by lines ; but having once obtained 

 by computation, the dimensions of the extant and immersed 

 portions of the body, the sides of which are always given in the 

 question, we can easily exhibit the geometrical construction. 

 The method of proof, by calculation, which we have applied to 

 this part of our work, seems to leave nothing to be added to an 

 elegant branch of the Mechanics of Fluids, so highly important 

 in the practice of naval architecture. 



In the Thirteenth Chapter, we have considered the stability 

 of floating bodies and of ships. The subject of stability is the 

 same to whatever form of floating body it may be referred, 

 whether the body be a ship driven by wind or steam, logs of 

 wood, or masses of ice, and it consists entirely in resolving the 



equation x = S sin. d>. The determination of the se- 

 ra 



veral quantities of which this equation consists, depends entirely 

 upon calculations drawn from the particular circumstances of 

 the individual case under consideration ; and these circum- 

 stances as referred to a ship, it is impossible to assign by esti- 

 mation ; they must be obtained by actual measurement, and when 

 they have been obtained in this manner, they are to be inserted 

 in the above equation, to obtain the measure of stability. The 

 investigation of this subject is both laborious and intricate, but 

 from what we have done in Problems LXI. and LXIL, with 

 their subordinate examples, it may become intelligible to the 

 general reader. The mathematician who has consulted the 

 writings of the Swedish Admiral CHAPMAN, and the scientific 

 investigations of ATT WOOD, knows well that in considering the 

 properties of a vessel, the orderly arrangement requires that we 

 should treat, First of stability, or the power a vessel has of 

 resisting any change of position when afloat. Secondly, the 

 forms having stability which have the least resistance, and are 

 therefore best adapted for speed. Thirdly, the different methods 

 of propelling ships ; and Fourthly, the construction for strength. 

 But our inquiries are much more limited in this Treatise, and 

 might conveniently end with the exposition of the equation of 

 stability. We have, however, carried the subject a little farther, 

 and considered it in reference to steam navigation, in order to 

 point out that the stability of a ship is greatly increased, byaug- 



