g^5 Mode of calculating the 



as the {lability of the veflel, which will be pofitive, nothing, 

 or negative, according as the point S is above, coincident 

 with, or below, the point G. If now we fuppofe W to re- 

 present the weight of the whole veflel and burden (which 

 will be equal to the fection MM CD multiplied by the 

 length of the veflel), and P to reprcfent the required weight 

 applied at the gunwale B to fuitain the vefTel at the given 

 angle of inclination; we {hall always have this proportion: 

 as VS : SW :: W : P; which proportion is general, 

 whether S W be pofitive or negative ; it muft only in the 

 latter cafe be fuppofed to acl upward to prevent an overturn. 



In the redtangular veflel, of given weight and dimenfions, 

 the whole procefs is fo evident, that any farther explanation 

 would be unnecefiary. In the trapezoidal veflel, after 

 having; found the points G and R, let AD, BC be pro- 

 traced until they meet in K. Then fince the two feclions 

 MM CD, EFDC are equal, the two triangles M M K, 

 E F K are alfo equal ; and therefore the rectangle E K X 

 KF=KMxKM = KM 2 ; and fince the angle of incli- 

 nation is fuppofed to be known, the angles at E and F are 

 eiven. Confequentlv, if a mean proportional be found 

 between the fines of the angles at E and F, we {hall have 

 the following proportions : 



As the mean proportional thus found: fine Z_E : : KM : KF, 

 And as the faid mean proportional : fine Z_F :: KM : KF; 

 therefore ME, MF became known; from whence the area 

 of either triangle MXF or MX-F, the difiance n n, and 

 all the other requifites may he found. 



In the mixtilineal fection, let AB — 9 feet = 108 inches, 

 the whole depth = 6 feet = 72 inches, and the altitude of 

 MM the line of floatation 4 feet or 48 inches ; alfo let the 

 two curvilinear parts be circular quadrants of 2 feet, or 24 

 inches radius each. Then the area of the two quadrants = 

 904-7808 fqnare inches, and the diitance of their centres of 

 gravity from the bottom = 13-8177 inches very nearly; alio 



the 



