Withy. — On the Stability of Ships. 661 



water buoying up the ship. It will be necessary here also to 

 make an assumption — namely, that no hole exists in the part 

 brought under water by the act of careening. It will simplify 

 our work at this stage if we deal with one cross-section of a 

 ship — say, the midship one — and assume for the moment that 

 the vessel from end to end is of that form. Fig. 1, Plate L., will 

 serve for this purpose. Please observe that there are two lines 

 drawn across the section — the horizontal one representing the 

 water-line when the vessel is inclined a few degrees, and the 

 other W'hen she is upright. Let us look closely at the changes 

 which have been effected by thus careening the vessel. It at 

 once appears that the wetted surface has been increased on 

 one side and reduced on the other. That implies that the 

 portion of the vessel acted upon in the inclined position by 

 the water-pressure is not identical with that acted upon when 

 she is upright. Does this change make any difference in the 

 stability? Yes, in all cases, with the single exception, which I 

 will deal with by-and-by, of a vessel whose section throughout 

 her length, hke fig. 4, Plate LI., is circular. In considering the 

 nature of these changes please bear in mind two facts already 

 stated — namely, that the act of careening has not added to 

 nor reduced the total weight of the ship, and that the dis- 

 placed water is, under all circumstances, exactly equal to that 

 weight. It follows that the bulk of the vessel under water 

 remains the same, and, as we are dealing with a vessel sup- 

 posed to have the same form of cross section throughout her 

 length, the area of that section must remain the same. As 

 this is so, then it follows that the amount of area gained on 

 one side in the diagram is equal to that lost upon the other. 

 You will see that the pieces added and deducted are triangles. 

 We may therefore define the position by saying that the 

 triangle of immersion in the given example is equal in area 

 to the triangle of emersion. But while this addition and 

 deduction have not altered the total area of the section, it 

 will be seen that they have materially altered its shape, and 

 that, as a consequence, the centre of buoyancy must have 

 been removed from its original position towards the enlarged 

 or lee side of the section. This important change, then, has 

 been effected by transfers of buoyancy, at the level of the 

 water-line, from one side of the vessel to the other. It was 

 this fact, of the only alteration taking place at the water-level, 

 which caused the remark early in the paper that " if there is 

 any part of a ship w^hich may be considered at all analogous 

 to a base it is the water-level section." 



We shall find the present stage a convenient one to draw 

 another distinction — namely, between the two phases of the 

 question of stability. I allude to the fact that every vessel 

 which has any stability at all has an *' initial stability " and a 



