420 



NATURE 



[August 30, i88j 



and as they are equal and opposite in direction, it follows 

 that, whatever the inclination, the force acting will always 

 be the same, but the leverage, marked G z, will vary as 

 the centre of buoyancy moves. At 30 degrees inclina- 

 tion, for example, G z is much greater than it is in Fig. 1 

 at 15 degrees. In Fig. 2 these lengths are set up as 



FIG.l. 



ordinates of a curve, and similar lengths for inclinations 

 of 45 and of 60 degrees are similarly set up ; the curve 

 drawn through their upper extremities is this vessel's 

 " curve of stability,' ' observing that the base line is divided 

 into equal lengths for equal angle intervals on [any con- 

 venient scale. 

 As regards the " metacentre," I must explain here, as 



fig. 2. 



I did in my Report, that in former times, when " initial 

 stability" alone was calculated, the word "metacentre" 

 had a much more limited meaning than it possesses now. 

 It formerly had relation to the upright position of the 

 vessel, in which case the buoyancy acts upwards through 

 the centre line of the ship's section — along g m, for 

 example, in Fig. 1. After receiving a slight inclination, 



FIG. 3. 



the vessel has, as we have said, a new centre of buoyancy, 

 and the buoyancy itself will act upwards along a fresh 

 line slightly inclined to what was previously the upright 

 line, and will intersect it at some point, M. This point 

 was called the " metacentre," and if we suppose the 

 angle in Fig. 1 to be very small (very much less than 15 

 degrees), then the M shown there approximately marks the 



" metacentre." When a ship is much more inclined, the 

 point at which two consecutive lines of the buoyancy's 

 upward action will intersect may not be, and often will 

 not be, in the middle line of the ship at all, but this point 

 is nevertheless called the "metacentre," and the use of 

 the word in t is extended sense has recently become 

 general. In Fig. 3 is shown a floating body of square 

 section, inclined in the water at an angle of about 30 

 degrees. W'L is the water line or line of flotation ; 

 its centre of buoyancy. By giving it a " slight " inclina- 

 tion from the position, it will of course have a new centre 

 of buoyancy given to it. If we incline it one way l> will 

 show this, if we incline it the other way b' will show it, 

 and for each of these positions there will be a new line of 

 action or buoyancy. But these lines of action, together 

 with that through B, will all meet or intersect in one 

 point, and this point (M) will be the metacentre at 30 

 degrees of inclination. In Fig. 4 I have shown curves 

 of stability for a prismatic body, with the centre of gravity 

 in the centre of form, and also with that centre in some 

 cases raised and in others placed below the centre of 

 form. In this figure the draught of water is taken at 

 3/25ths of the total depth of the prism. In Fig. 5 I have 

 given curves of stability for the prismatic body with the 

 centre of gravity and the centre of form taken as coin- 

 cident, but with different draughts of water. In Fig. 6 I 

 have given the curve of stability of a similar prismatic 

 body, immersed 2/5ths of its depth, and having its centre 

 of gravity situated 6 inches below its metacentre. These 

 figures serve to illustrate very clearly the error involved 

 in the assumption that with stability at the upright posi- 

 tion and stability at 90 degrees — or but little instability 

 at the latter, which is what some authors have instructed 

 the profession to be content with — there need be no ap- 

 prehension of any deficiency of stability at intermediate 

 angles of inclination. They show that with square sec- 

 tions and prismatic forms there may be various disposi- 

 tions of centre of gravity and draughts of water, with 

 which stability in the upright position and again at 90 

 degrees are not proofs of safety, but indications of the 

 gravest danger. 



With these figures before us, we now have both the 

 Hammonia case and the Daphne case amply illustrated, 

 and can carefully distinguish between the two. The 

 Hammonia case — as put forward by Mr. Biles, who con- 

 ducted her calculations — is that of a high-sided vessel 

 with her stability reaching a maximum soon after she had 

 inclined 30 degrees ; and she therefore finds her ana- 

 logy in one or other of the cases shown in Fi:\ 5. In 

 the latter figure it will be seen that with the centre of 

 gravity in the centre of form all positive stability vanishes 

 at an inclination of 45 degrees in the two cases A 

 and B ; but the growth and decline of the stability are 

 very different indeed at the different immersions. When 

 the immersion is smallest the stability rises in a steep 

 curve (a), attaining a comparatively large maximum 

 something under 20 degrees, and then declines, more 

 gradually than it rose, as the inclination goes on. By 

 increasing the immersion from 3/25ths to 5/25ths the 

 curve B is produced, and here we see a vast change of 

 stability, the curve, which rises very slowly from the base 

 line, never reaching one-fourth the maximum ordinate of 

 curve A ; only attaining its maximum beyond 30 degrees 

 of inclination, and then declining less slowly than it rose, 

 until it vanishes. Immerse the body to double the last 

 immersion, and we find in curve c that now, instead of 

 vanishing at 45 degrees, the stability only there begins, 

 rising to a small maximum a little beyond 60 degrees 

 and vanishing at 90 degrees. It is in curve B that we 

 find a state of things very closely analogous to that dis- 

 closed by the Hammonia curve, which 1 now give in Fig. 

 7. In both cases the stability increases but slowly ; in 

 both it reaches early a maximum ; and in both it disappears 

 altogether before the vessel is more, or much more, than 



