662 Transactions. — Miscellaneous. 



"range of stability." You may remember a sentence which' 

 occurred early in the paper, as follows : " The form of the 

 bottom, it is true, has its influence on stability, but flatness 

 of bottom in a sea-going vessel tends to reduce it." It is' 

 "initial stabihty " which is thus affected. The "range of 

 stability " is determined only by the form of the vessel in the 

 neighbourhood of the water-level section. 



As the finding of the metacentre is necessary before we can 

 determine either of these phases of stability, I will now ex- 

 plain what that point is. In order to avoid this technical name 

 as long as possible, I have alluded to it as the "culminating 

 point of the upper pressure of the water." It is a point which 

 is always in a vertical line above the centre of buoyancy, but 

 its distance from the latter usually varies at different angles of 

 heel. A reference to fig. 1, Plate L., will serve to indicate the 

 metacentre. First consider the section in its upright position 

 with the centre of buoyancy at B. Then incline it, and as- 

 sume that the centre of buoyancy in the new position is at b. 

 Eemember that the buoyancy acts vertically upwards through 

 this point._ Now, if a line is drawn upwards in this direction 

 from h it is clear that it will intersect the centre-line. The 

 point M, at which it intersects, is called the metacentre ; and 

 its height above the centre of buoyancy can be readily calcu- 

 lated, for an infinitely small angle 'of heel, by means of a 

 well-known formula. If it was so calculated for a number of 

 vessels, of which the centres of gravity have been ascertained 

 under similar conditions of loading, it would afford us the data 

 for a very fair comparison of their merits as far as the one test 

 of initial stability is concerned. 



The last paragraph brings before you for the first time, in 

 conjunction with each other, the two points which must be 

 determhied before the measure of any vessel's stability can be 

 ascertained. These points are the centre of gravity of the' 

 vessel and her metacentre. The distance betw^een the two in 

 a vertical direction is known as the metacentric height. When 

 the metacentre is found to be above the centre of gravity the 

 vessel is known to be stable ; when their positions are re- 

 versed she is unstable; and when they coincide with each 

 other she is indifferent, and will yield, without resistance, to 

 any inclining force. When we know the metacentric height 

 of a vessel we can form a good idea of the amount of resistance 

 which she will, at the outset, offer to an inchning force. 

 It IS not of itself the measure of this first act of resistance, 

 known as initial stability ; but its value — as will be proved 

 directly — is comparative, because it always bears, in dif- 

 ferent vessels, at a minute angle of heel, a certain proportion 

 to another measure in each, known as the " righting-lever." 

 The convenience of its use consists in the fact that the calcu- 



