Equations of Condition in Naval Architecture. 295 



Line, their right size and form" that he actually made some 

 progress in carrying out this beautiful idea into much genera- 

 lity and fulness. 



During a recent review of some of Chapman's tables, it has 

 appeared to me, that the point to which naval architecture 

 ought to continually approximate as a limit, should be the 

 perfecting of the elements contained in them, or of such others 

 as a more extended experience may at this time possibly sug- 

 gest ; obtaining for them more correct or appropriate coeffi- 

 cients, establishing more completely their necessary relations, 

 and giving to the whole train of inquiry a more extended and 

 philosophical form. Such a method of procedure would be 

 most consistent with the legitimate objects of philosophical in- 

 quiry. In the language of the modern analysis, it would be 

 regarding every element of a ship as a function of some primi- 

 tive element ; and which, by means of properly prepared coef- 

 ficients, would admit of every other element being deduced 

 from it. There must, for example, be in every ship some re- 

 lation between its length, breadth, depth, and displacement ; 

 and some process, more accurate than that of a rude approxi- 

 mation, ought to exist by which any one of these elements can 

 be immediately deduced from the others. Between the length 

 and the breadth, and between each of these elements and the 

 depth, there must, in a ship of acknowledged good qualities, be 

 some relations worthy of investigation. The breadth must be 

 a function of the length, and the depth must be connected to 

 each of these by some relation capable of being exhibited in 

 an equation of condition. The area of the main section also 

 may be so connected with the breadth as to be resolvable at 

 first into terms of the length, and ultimately into that of the 

 displacement itself. In like manner may the area of the plane 

 of flotation, the moment of stability, the place of the metacen- 

 tre, the position of the centre of gravity, and indeed the value 

 of every other element be ultimately traced to the displace- 

 ment. If the whole length of the water line be denoted by X, 

 the entire length of the same line between the rabbits must be 

 some function of the same dimensions ; and as the former may 

 be shown to be a function of the displacement, so also may the 

 latter. Hence the displacement, or some other appropriate 



