Stability of River and Canal Boats. ^yf 



the area of the included rectangle able — 1440 fquare 

 inches, and the altitude of its centre of gravity 13 inches j 

 in like manner the area of the re&angle A Be d will be 

 found = 5184 fquare inches, and the altitude of its centre 

 of gravity 48 inches ; therefore we mall have 



Momentum of the s quadrants = 904-7808 x 13-8177 = 12501-98966015 

 Momentum ofthereftrm. <?£.'> =1440- x iz = 17180* 



.Momentum of the rcfitan.ABf <;'=•; -84- X48 =248851- 



75287S0S z786*3-98y66oi6 



Now the fum of the momenta divided by the fum of the 



... . 278613-98066016 * • -i , , 



areas will o-ive -k~~—k = 37-006 inches, the al- 



& 75287808 °' 



titude of G the centre of gravity of the fe&ion ABCD 



above the bottom. In like manner the altitude of R the 



centre of gravity of the feftion MMCD will be found to 



, 123093-98966016 . , , , 



be equal — •* < ■ / '^ s= 24-934 inches; and confe- 



4936-7^08 T yD ^ 



quently their difference, or the value" of GR = 12*073 



inches, will be found. 



Suppofe the vciTel to heel 15°, and we Avail hare the fol- 

 lowing proportion, namely, As radius : tangent of 15° : : MX 

 = 54 inches : 14-469 inches = ME or MF; and confe- 

 quently the area of either triangle MXE or MXF = 

 390-663 fquare inches. Therefore, by theorem 4th, As 

 4936-7808 : 390-663 : : 73 = nn — f AB : 5*6975 inches 

 -=RT- and again, As radius : fine of 15 : : 12*072 = GR : 

 3-1245 inches = RN ; confequently RT— RN == 5*6975 — 

 3*1245 = 2*573 mc hcs = SW the (lability required. 



Moreover, As the fine of 15 : radius : : 5-6975 = RT: 

 22-013 = RS, to which if we add 24-934, the altitude of 

 the point R, we (hall have 46-947 for the height of the 

 metacentre, which taken from 72, the whole altitude, there 

 remains 25-053; from which and the half width ■= 54 

 inches, the diltance BS is found = 59'529 inches very 

 7 nearly, 



