This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1900 edition. Excerpt: ...the emerged wedge. A specimen table is given on p. 174 for 300. The lengths of the ordinates of each radial plane are set down in the ordinary way, and operated on by Simpson's multipliers, giving us a function of the area on the immersed side of 550-1, and on the emerged side of 477-4We then put down ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1900 edition. Excerpt: ...the emerged wedge. A specimen table is given on p. 174 for 300. The lengths of the ordinates of each radial plane are set down in the ordinary way, and operated on by Simpson's multipliers, giving us a function of the area on the immersed side of 550-1, and on the emerged side of 477-4We then put down the squares of the ordinates, and put them through the Simpson's multipliers, giving us a result for the immersed side of 17,888, and for the emerged side 14,250. The remainder of the work on the preliminary table will be described later. We now proceed to the combination table for 30 (see p. 175), there being one table for each angle. The functions of squares of ordinates are put down opposite their respective angles, both for the immersed wedge and the emerged wedge, up to and including 300, and these are put through Simpson's multipliers. In this case the immersed wedge is in excess, and so we find the volume of the layer to be taken off to be 7836 cubic feet, obtaining this by using the proper multipliers. At the bottom is placed the work necessary for finding the thickness of the layer. We have the area of the whole plane 20,540 square feet, and this divided into the excess volume of the immersed wedge, 7836 cubic feet, gives the thickness of the layer to take off, viz. o-382 foot, to get the true water-line. We now have to find the moment of transference of the 1 The area of the section S/L is given by J Jy. d0, as on p. 15, and the volume of the wedge is found by integrating these areas right fore and aft, or--lffy.d8.dx which can be written--/Ja.dx.de or /(Jjy. dx)de i.e. Jjj/'. dx is found for each radial plane, and integrated with respect to the angular interval. wedges, v X Mi in Atwood's formula, and this is done by using...
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