

Stability of River and Canal Boats. 395 



lations become very eafy. Veflels of this kind are generally 

 of the fame tranfverfe fection throughout their whole length, 

 except a fmall part in prow and (tern, formed by feoinents 

 of circles or other Ample curves ; therefore a length may 

 eafily be afligned fuch, that any of the tranfverfe feclions 

 being multiplied thereby, the product will be equal to the 

 whole fohdity of the veffel. The form of the fe&icn 

 AB CD is for the mod part either rectangular as in fig. j. 

 (Plate XIII.), trapezoidal as in fig. 2. or mixtilineal as in 

 fig. 3. in all which MM reprefents the line of floatation 

 when upright, and EF that when inclined at any angle 

 M X E ; alfo G reprefents the centre of gravity of the whole 

 veflel, and R that of the part immerfed. 



If the veflel be loaded quite up to the line AB, and the 

 fpecific gravity of the boat and burden be the fame, then the 

 point G is fimply the centroof gravity of the fe&ion A BCD; 

 but if not, the centres of gravity of the boat and burden 

 muft be found feparately, and reduced to one by the com- 

 mon method, namely, by dividing the fum of the momenta 

 by the fum of weights, or areas, which in this cafe are as 

 the weights. The point R is always the centre of gravity 

 of the feftion MM CD, which, if confiding of different 

 figures, muft alfo be found by dividing the fum of the 

 momenta by the fum of the weights as common. Thefe 

 two points being found, the next thing ncceflary is to de- 

 termine the area of the two equal triangles M XE, M X F, 

 lheir centres of gravity 0, 0, and the perpendicular projected' 

 diftance n n of thefe points on the water line EF. This 

 being done, through R and parallel to EF draw RT — a 

 fourth proportional to the whole area MM CD, either 

 triangle MXE or MXF, and the diftance n n; through 

 T, and at right angles to RT or EF, draw TS meeting 

 the vertical axis of the veflel in S the metacentre; alfo 

 through the points G, B, and parallel to ST, draw NGW 

 and BV; moreover through S, and parallel to EF, draw 

 WS V meeting the two former in V and Wj then SW« 



as 



