OF THE POSITIONS OF EQUILIBRIUM. 



which, when the triangle is equilateral, becomes 



7 



s = =0.4375, 

 16 



1 and the arithmetical mean of these, from equation (247), is 



327 



Let therefore this value of s be substituted instead of it in the 

 expressions, class (252), and we shall obtain 



x = 25.95, and x = 16.05 inches, 



the corresponding values of y being 



y =z 16.05, and y =. 25.95 inches. 



412. The positions of equilibrium, as indicated by these values of 

 x and?/, are as represented in the annexed diagrams, where IK is 

 the horizontal surface of the fluid, ABED, abed the immersed, and 

 DEC, dec the extant portions of the section corresponding to the 

 positions ABC and abc, in which CD and ce are each equal to 25.95 

 inches, and CE, cd equal to 16.05 inches, being the respective values 

 of x and y, as determined from equation (252). 



Bisect A B and a b in the points F and f, and draw the straight lines 

 FD, FE and fd, fe intersecting the horizontal surface of the fluid in 

 the points D, E and d, e ; then, when the body floats in a state of equi- 

 librium, the lines FD, FE,/C? and/e are equal among themselves. 



This is very easily proved, for since the triangle ABC is equilateral, 

 the angle ACB is equal to sixty degrees, and consequently its half, or 

 the angles ACF and BCF are each of them equal to thirty degrees; 

 therefore, by the principles of Plane Trigonometry, we have 



DF 8 =CD 2 -4-CF ? 2CD.CFCOS.30, 



and similarly, by the same principles, we get 



F E 2 HZ C E 4 -4- C F 2 2C E.C F COS. 30 ; 



