382 OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



depressed by it ; then, if the solidity of each segment is multiplied 

 into the distance of its centre of gravity from the horizontal line 

 passing along pp', and produced both ways to the head and stern of 

 the vessel ; the aggregate of the products thus arising, will constitute 

 the value of the numerator dv of the fractional term in equation 

 (282 a ), where the momentum of the vessel's stability is 



<dv 7 



,=:< o sm.d>>?tf. 



L \ r y 



Consequently, since the several quantities w, v, S and 0, are either 

 given d priori, or determinable from the circumstances of the case, it 

 follows, that the momentum of stability for any angle of inclination, 

 and for any form of body, can be found by the above formula ; but 

 the labour and intricacy of the calculation, increases with the irregu- 

 larity of the body to which such calculations are referred, and in 

 particular cases, the labour required to accomplish the purpose is 

 immensely great. 



PROBLEM LXII. 



473. The vertical transverse sections of a ship, taken at the 

 distance of five feet from each other along the principal longi- 

 tudinal axis, are thirty-four in number, and are bounded by 

 curves approaching to a parabola of a very high order ; cor- 

 responding to these are twelve horizontal sections between the 

 keel and the plane of floatation, taken at intervals of two feet 

 on the vertical axis, the first section occurring at the distance 

 of nine inches from the upper surface of the keel : 



It is required to determine the measure of stability, when 

 by the action of the wind, or some other equivalent external 

 force, the vessel is deflected from the upright position through 

 an angle of thirty degrees; the ordinates corresponding to 

 the several sections, being as registered in the following 

 table. 



