218 Prof. F. Elgar. The Variation of 



for the extreme light and loaded conditions, and one or two inter- 

 mediate ones, to construct cross-curves, from which the ordinates of 

 a curve of stability at any draught between the two extreme ones can 

 be readily measured off. In order to do this, the curve of stability 

 already described has to be analysed, and dealt with under a different 

 form. The ordinary curve of stability, as illustrated in fig. 9, is a curve 

 showing the variation in the length of GZ in fig. 8 or the arm of 

 the inclining couple with the angle of inclination. P in fig. 9 is 

 the length of GZ in fig. 8, at the angle of inclination a. But 

 GZ=BR-BT=BR-BGsm0. Therefore Pa in fig. 9 is the 

 difference of these two quantities at the angle of inclination . The 

 curve of stability, or curve of GZ, is a curve whose ordinates are 

 equal to the differences between the corresponding ordinates of two 

 curves, one of which represents the variation in the length of BR 

 with change of inclination, and the other is a curve of sines with 



FIG. 10. 



radius BG. Thus if Opb, fig. 10, be a curve, of which the ordinates, 

 such as px, are equal to the length of BR at the angle of inclina- 

 tion a. ; and Qp^a a curve of sines from to 90 with radius 

 oc=BG ; then the differences between the ordinates of these curves 

 will give the corresponding values of GZ, or the ordinates of the 

 curve of stability. Thus pp l is the length of GZ at the angle of 

 inclination , and is equal to the ordinate P of the curve given in 

 fig. 9. 



It will be obvious that after calculating three or four curves of BR 

 for a vessel, including those for the two extremes of draught, no 

 further calculation is necessary for obtaining a similar curve at any 

 intermediate draught, since it is only requisite to construct cross- 

 curves at given angles of inclination say at intervals of 10 

 and from these cross-curves to measure off the ordinates of the 

 curve BR for the draught required. Having thus obtained the curve 

 of BR for the draught in question, the ordinary curve of stability, 



