332 Mr. C. W. Merrifield on a New Method of Calculating [Jan. 24, 



January 24, 1867» 



Lieut.-General SABINE, President, in the Chair. 



The following communications were read : — 



I. " On a New Method of Calculating the Statical Stability of a 

 Ship.^' By C. W. Merrifield, P.R.S., Principal of the Royal 

 School of Naval Architecture. Received January 15, 1867. 



The time required for the calculations of the stability of ships has prac- 

 tically restricted the ordinary draughtsman to the use of the metacentre. 

 This implies that the locus of the centres of buoyancy cuts the transverse 

 midship plane in a curve which may be treated as a circle ; and this is 

 only true, in general, for very small limits of inclination. In some parti- 

 cular cases it has been felt desirable to supplement this by computing the 

 moment of stability at some definite angle of inclination, by means of the 

 "ins and outs," or immersed and emersed wedges. But this has only 

 been applied to one selected inclination, generally of 10° or 14° ; and owing 

 partly to this, and partly to the very scant time left available to the skilled 

 draughtsman or calculator, this has never been a part of the ordinary work 

 of the computation of a ship's quantities. For this reason it becomes of 

 great consequence to find some method of getting at the stability, with an 

 amount of extra work, which should not exceed that of the ordinary sheet 

 known as the " sheer-draught calculation"*. 



A method has occurred to me by which, as I think, this object may be 

 attained. Upon conferring with some of my students f, who have sug- 

 gested and removed certain difficulties of detail, we think we see our way, 

 by an easy calculation, to place the whole account of a ship's statical 

 stability in the hands of any person who understands simple equilibrium, 

 either in an algebraical or geometrical form, as he may prefer. 



It will take some time, with my present occupations, to prepare detailed 

 examples. But as the method is complete in respect of principle, I have 

 thought it best to bring it at once before the Society. 



The fundamental assumption is, that the locus of the centres of buoyancy 

 can be sufficiently represented by a conic. The stability is then measured 

 by the perpendicular, from the centre of actual weight, on the normal due 

 to the inclination. The chief step, therefore, is to find the conic, of which, 

 I may remark, we already know the vertex, and the tangent and curvature 

 at the vertex ; for these are given by the ordinary calculation of the 

 centre of buoyancy and the metacentre. Now I observe that the conic is 

 completely determined if we can find the length of another radius of 

 curvature corresponding to a known inclination. This is obtained by 

 finding the moment of inertia about one of its principal axes (longitudinal) 



* See * Ship-building, Theoretical and Practical/ by Watts, Eankine, Barnes, and 

 Napier, p. 46, for the sheer-draught calculation commonly used in this country, 

 t Messrs. Deadman, Edgar, John, and White. 



