A Treatise On The Principles And Practice Of Harbour Engineering

2 l6 HARBOUR ENGINEERING. extreme right, and that the adjoining compartnients of each have likewise experienced a similar transfer of area. The most obvions way, therefore, of determining the new position of the centroid of buoyancy is to sum up the products of the individual areas transferred, into the distances of their respective transferences, and divide by the whole buoyancy area. This will give us the proportionate trans- ference of the centroid of buoyancy of the original rectangle. Also, it will be well to proceed by means of the horizontal and vertical components, as before, which yield the co-ordinates of the locus. Let D (fig. 191) be the depth of buoyancy as originally immersed, and A the extent of emergence or submergence of either side under an angular displacement 0. The emergence or submergence in any compartment of N compartments we will call 8. If d be the original depth of water inside the pontoon, then D+d equal the depth of the pontoon. We have A =— tan Ø- 2 Also from similar triangles, 2N Therefore 8— N The area of buoyant section transferred from the extreme lefthand to the extreme right-hand compartment (Ist to 5th) is (a-A^, \ N/N’ and the horizontal distance between the centres of gravity of the two compartments is N L The product of these two is fA-Ak A.^k, \ N/ N \N/’ which, for the purpose of forming a series for summation, may be written The similar product in the case of the 2nd and 4th compartments is . A.PLAk, \ N / N \ N / ’ and, in the event of there being additional compartments, we could write as the next term, \ N / N \ N / i