OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 375 



Let this value of km be added to that of kt already determined, 

 and the aggregate will give the value of mt; therefore, we have 



mt = d= 11.0345 + 11.01 =22.0445 inches. (287). 



464. With respect to the value of the remaining quantity S, we 

 have only to observe, that from the nature of the trapezoid, the posi- 

 tions of the points G and g can easily be ascertained, and the distance 

 between them, is therefore expressed by the following equation, viz. 



g _ D . 



Now, according to the conditions of the question, we have 6 = 40 

 inches, ft nr 30 inches, and D zrz 20 inches ; and moreover, by com- 

 putation, we have found that ^=33 inches, and QHzrG inches; 

 consequently, by substitution, the above equation gives 



* on C 20(40 + 60) 6(66 + 30)7 - . - , 

 d =i 20 ) ; ~ - L j i - IL - L J. z= 7.43 inches very nearly. 

 I 3(40 + 30) T 3(33 + 30) } (288 ). 



Let therefore the values of d and S, as obtained in the equations 

 (287 and 288), be substituted in equation (286), and we shall obtain 



' 



which being reduced, gives 

 x = 4.25 1 .923 =. 2.327 inches. 



This is the length of the equilibrating lever, but the whole weight 

 of the body in cubic inches of water, is 



(40 + 30) 10 X 12 X 14x 0.27 = 41752 cubic inches, 



which being reduced to Ibs. gives 

 41752X62.5-^1728=: 1510.125 Ibs. ; 



hence the momentum of stability is 

 S= 1510.125X2.327 z= 3514.054 Ibs. 



Such is the method of calculating the measure of stability, when 

 the transverse sections are all equal and similar figures ; but when 

 this happens not to be so, as in the case of ships and other vessels 

 designed for the purposes of navigation, the difficulty of calculation. 

 is greatly increased, for the several terms of which the equation is 

 constituted, must have their values separately determined by intricate 

 forms of approximation, the nature of which can only be known from 

 the circumstances which regulate the particular constructions, to which 

 the investigations are referred. 



