VOL. LXXXVIII.] PHILOSOPHICAL TRANSACTIONS. 319 



other necessary conditions being known, it is required to find, by geometrical con- 

 struction, a line which shall approximate nearly to the measure of the vessel's sta- 

 bility. This is accordingly determined in 2 different ways. 



Case 13. The longer axis of a vessel is supposed to be divided into a given num- 

 ber of equal parts, and vertical sections to pass through the several points of divi- 

 sion, intersecting the axis at right angles : the form and magnitude of each parti- 

 cular section being given, with the common distance between them, the positions 

 of the centres of gravity of the vessel, and of the volume displaced, and the dis- 

 tance of the water-section from the keel, being known, it is required to construct 

 the measure of the vessel's stability, when it is inclined from the upright through 

 a given angle. This is accordingly effected in several instances ; and application is 

 then made to some numeral calculations on cases of certain vessels, of known 

 figures and dimensions. After which are given some practical observations as 

 follow. 



The object of the preceding propositions, and inferences founded on them, has 

 been rather to establish general principles, which may be of use in forming plans 

 of construction, than to investigate what modes of construction are the most ad- 

 vantageous ; a discussion more extensive than would be consistent with the subject 

 here proposed to be considered, which relates to the stability of vessels only. The 

 practice of navigation requires the co-operation of many qualities in vessels, the 

 laws and powers of which, considered as acting either separately or conjointly, it is 

 the employment of theory to investigate. In respect to the construction of ships, 

 it is obvious that no one of the component qualities can be regulated, without pay- 

 ing attention to all the others ; because, by increasing or diminishing any of the 

 powers of action, the others are commonly more or less influenced. It has been 

 shown, by the propositions demonstrated in these pages, that there are many prac- 

 tical methods by which the stability of vessels, at any given angle from the upright, 

 may be augmented ; a circumstance which gives to the constructor great choice of 

 means for regulating this power, according to the particular service for which the 

 ship is designed ; for it is not every mode that will be advantageous. The several 

 varieties of form and adjustment by which stability is increased, may be so unskil- 

 fully combined, that, in consequence of the very means used to obtain that essen- 

 tial quality, either the ship shall not steer well, or shall drift too much to leeward, 

 or shall be liable to sudden and irregular motions in rolling, by which the masts 

 are endangered ; or those angular oscillations of the ship shall be performed round 

 an axis situated so much beneath the water's surface, that the motion of rolling 

 shall be excessive and laborious. It is the proper use of theory, or right principle, 

 whencesoever derived, so to adapt the means to the end proposed, that the required 

 stability shall be imparted, without producing inconveniences of any kind, or such 

 only as are unavoidable, and are the least prejudicial : the same observation applies 

 to the other qualities of vessels. By duly combining the whole, ships are con- 

 structed so as to fulfil the purposes of navigation. 



