NATURE 



285 



THURSDAY, JANUARY 29, 1885 



THE STABILITY OF SHIPS " 

 A Treatise on the Stability of Ships. By Sir E. J. Reed, 

 K.C.B., F.R.S., M.P. (London: C. Griffin and Co., 

 1SS5.) 



II. 



IN simplifying the mode of presentation of the scien- 

 tific principles which govern the stability of ships, 

 Sir E. J. Reed touches upon a very important point — 

 the defects of nomenclature. The technical nomenclature 

 of naval architecture has gradually been formed in an un- 

 systematic and often heedless and unintelligent manner ; 

 and it contains many inconsistencies and inaccuracies. 

 Attention has previously been called by ourselves and 

 others to the subject. Sir Edward Reed refers to the 

 confusion that is sometimes caused by giving the name 

 "metacentre" to points upon two curves which are quite 

 distinct from each other. One of these curves indicates 

 the variation in the height of the metacentre with draught 

 of water when the ship is upright ; and the other is that 

 formed by the intersections of consecutive normals to the 

 curve of buoyancy as a ship becomes inclined from the 

 upright. These two curves are entirely different in cha- 

 racter, and have only one point in common — viz. the 

 metacentre for the upright position corresponding to the 

 draught of water for which the curve of intersections of 

 consecutive normals is constructed. The latter curve is, 

 of course, the evolute of the curve of buoyancy. Sir 

 Edward Reed proposes to call the intersections of con- 

 secutive normals to the curve of buoyancy at all angles 

 of inclination from the upright " pro-metacentres," and 

 to restrict the use of the term " metacentre " to inde- 

 finitely small inclinations from positions of equilibrium. 



The points described as " pro-metacentres " are centres 

 of curvature of the curve of buoyancy. They are but of 

 little importance to practical naval architects, and are 

 probably never regarded by them. To persons who may 

 be pursuing investigations in which such points require 

 to be dealt with, such a term as " pro-metacentre " may- 

 be of use. Sir Edward Reed truly says that the points in 

 question " are not ' meta-centres,' except in a very 

 strained, misleading, and wholly exceptional sense." 

 They do not enter into any of the considerations by 

 which the stability of a ship is judged of or calculated ; 

 and their positions are not determined, nor even known, 

 in practice. 



If Fig. 2 represents the section of a ship, E b 3 the 

 curve of centres of buoyancy, and M M 3 the curve of 

 intersections of consecutive normals to b b 3 , or the evo- 

 lute of B h 3 , then the points M,, M 2 , and m, will be the 

 " pro-metacentres " corresponding to those angles of in- 

 clination at which M t Bj, M 2 B.,, and M 3 B 3 are respectively 

 vertical. M is the point corresponding to the position of 

 equilibrium when the vessel is upright, and is the meta- 

 centre proper. Such points as M 1} M 2I and M 3 have some- 

 times been miscalled metacentres, and the curve M M 3 the 

 metacentric evolute. Sir E. J. Reed proposes to call 

 these points " pro-metacentres," and the curve M M 3 the 



1 Continued from p. 240. 



Vol. xxxi. — No. 796 



" curve of pro-metacentres." M,, M a , and M 3 are centres 

 of curvature of bb 3 at the points B,, B 2 , and B 3 ; and the 

 curve M M 3 is the evolute of B B 3 . 



Sir Edward reminds us that the points where the lines 

 Mi B], M., B 2 , and M 3 B 3 intersect the vertical axis of equi- 

 librium through B, have sometimes, in this country, been 

 called "shifting metacentres"; and he considers that 

 although this term has a "measure of justification, its 

 use is not very desirable, and is, indeed, likely, unless 

 great care is taken, to introduce misconceptions into the 

 subject." It is true that the term " shifting metacentre" 

 was suggested for application to these points, even by so 

 eminent an authority as the late Prof. Macquorne 

 Rankine ; but it has failed of its purpose, and passed so 

 completely into oblivion that if Sir Edward had not re- 

 ferred to the circumstance few of his readers would have 

 remembered it. There is little probability of the term 

 " shifting metacentre " now coming into use. 



The most natural mode of treating these points is 

 doubtless to class them all in the category of " meta- 

 centres," without any qualifying adjective of a general 

 character, such as "shifting." In France the term meta- 

 centre includes the point M — which we regard as being 

 the metacentre proper— and Prof. Rankine's shifting meta- 

 centres. It is natural to regard the intersection of M 2 b 2 



with the vertical axis of equilibrium as the metacentre for 

 the particular angle of inclination to which M 2 b, relates. 

 This is quite consistent with Bouguer's original definition 

 of the metacentre, viz. " la terme que la hauteur du centre 

 de gravite" G, ne doit pas passer, et ne doit pas meme 

 attendre." This point constitutes the limit above which 

 the centre of gravity cannot be raised without causing 

 the ship to move farther away from the upright, whether 

 the angle of inclination be great or small. It is convenient, 

 and need not be ambiguous, to call these points meta- 

 centres for the particular angles of heel to which they 

 relate. Thus the intersection of Mi B, with the vertical 

 axis of equilibrium through b is the metacentre at io° of 

 inclination, if 10° be the angle at which Mi Bi is vertical ; 

 and the same for any other angle. 



These points are really of importance to the naval 

 designer, as the distance from such a point to the centre 

 of gravity at any angle of inclination, say 30 , is equal to 

 the length of the ship's righting lever divided by the sine 

 of the angle of inclination. If this distance be zero the 

 righting lever vanishes, and there will be no resistance to 

 further inclination. If the metacentre at 30° fall below 

 the centre of gravity the ship will tend to incline still 



