Jan. 15, [885] 



NA TURE 



239 



and at considerable length, is two papers read before 

 the Royal Society in 1796 and 1798. He laid down the 

 fundamental formula by which the length of the arm of 

 the righting or upsetting couple may be determined for 

 any angle of inclination of a ship ; and he showed how the 

 several terms contained in it may be calculated. Two of 

 these terms, viz. the volumes of the wedges of immersion 

 and emersion, and the positions of their centres of gravity, 

 involved very lengthy and complicated calculations. 

 The tediousness and complexity of stability investigations 

 have been chiefly caused by the difficulties connected 

 with finding by actual measurement and calculation the 

 solid contents of these wedges and the positions of their 

 centre of gravity. 



Let Fig. 1 represent the transverse section of a ship, of 

 which w l is the line in which the plane of flotation, when 

 the ship is upright, is cut by the plane of the paper ; the 

 centre of gravity of the whole ship being at c. Let k 

 similarly represent the centre of gravity of the volume of 

 the ship's displacement, or centre of buoyancy, as it is 

 commonly called. Now, suppose the ship to be inclined 

 a few degrees by some external force that acts horizontally, 

 and therefore does not alter the displacement ; and let 



W l' represent the new water-line. The effect of the in- 

 clination has obviously been to lift out of the water a 

 wedge-shaped body, of which w s w' is the section, and 

 to submerge on the opposite side of the ship another 

 somewhat similar wedge-shaped body, of which the sec- 

 tion is L s l'. These wedges are known as the wedges of 

 immersion and emersion respectively. They are each 

 bounded on the outside by the outside form of the ship, 

 and will therefore usually differ in external form ; but they 

 must be precisely equal in volume, or otherwise the whole 

 displacement of the ship could not remain unaltered. 



The inclination of the ship through the angle W S w' 

 has changed the position of the centre of buoyancy B to 

 b' ; and G z is the length of the perpendicular let fall 

 from G, the centre of gravity, upon the vertical b' m, 

 through ii'. G z is the arm of the couple at the ends ot 

 which the weight of the ship and the upward pressure of 

 the water act ; and it is commonly called the righting 

 arm. Atwood's fundamental formula for determining the 

 length of the righting arm is — 



G Z = v x h h' v-BG sin 6, 

 v being the volume of either of the wedges W S W, V S L ; 

 /* h' the distance, measured parallel to \v' 1.', between g and 



g\ the centres of gravity of these wedges ; v the volume 

 of the ship's displacement ; and 6 the angle of inclination 

 w s w'. 



It is obvious that the labour of calculating the volumes 

 and positions of centres of gravity of such irregularly 

 shaped bodies as the wedges of immersion and emersion 

 must be very great. The labour and difficulty are fur- 

 ther increased by the necessity of drawing the inclined 

 water lines, such as w' L', in positions which give equal 

 volumes for these wedges. The point s, where the inclined 

 water-line intersects the upright water-line, thus requires 

 to be determined separately for each angle of inclination- 

 Atwood's manner of approximating to the volumes and 

 moments of these wedges was simplified by Mr. S. Read. 

 The method which has commonly been adopted in 

 recent years is, however, one brought forward at the 

 Institution of Naval Architects, by Mr. F. K. Barnes, in 

 1 861. 



The old systems of stability calculation, even as modi- 

 fied by Mr. Barnes, were so excessively laborious and 

 complex, that very few attempts were ever made to apply 

 them to ships. The initial stiffness, as determined by 

 the metacentric height, was practically the only element 

 of stability that was investigated. It appears that, prior 

 to 1867, no calculations were made which showed how 

 the stability of a ship became affected by inclining her 

 till the water-line came up over the deck, or at what 

 angle the stability vanished. This was done for the first 

 time at the Admiralty in 1867 by Mr. William John, 

 under the direction of the author of the present work. 

 The results of these investigations were published by 

 Sir E. J. Reed in an interesting and instructive paper 

 upon " The Stability of Monitors under Canvas," read 

 before the Institution of Naval Architects in 1868. Curves 

 are appended to this paper which show how the righting 

 moments vary at successive angles of inclination, and the 

 point at which they vanish. This paper proved conclu- 

 sively how great are the dangers that have to be 

 guarded against in ships of low freeboard and with 

 high centres of gravity.J 



The extended application of stability calculations to 

 cases involving greater irregularities in the volumes of 

 the wedges of immersion and emersion than are con- 

 templated by Atwood — such, for instance, as are caused 

 by deck edges becoming immersed, or portions of deck 

 erections becoming included in the volumes of the im- 

 mersed wedges — created a demand for still more syste- 

 matic and simple modes of calculation. This was 

 supplied by Messrs. White and John in a paper read 

 before the Institution of Naval Architects in 1871. 



Down to the time of the Daphne disaster, which oc- 

 curred in July, 18S3, stability calculations made no further 

 progress of importance in this country. At the Ad- 

 miralty, and in some of our mercantile shipyards, the 

 processes above described were gone through in cases 

 where full knowledge of a ship's stability was considered 

 requisite. Such calculations often took about a month to 

 complete ; and the results obtained were usually limited 

 to a knowledge of how a ship's righting moment varied 

 with angle of inclination at one or more chosen draughts 

 of water. Even this was not considered essential when 

 very light draughts of water were being dealt with. 



The evidence given at the Daphne inquiry, and the 



