304 OF THE POSITIONS OF EQUILIBRIUM. 



conditions is answered, and we shall shortly see, whether or not the 

 data are sufficient to satisfy or fulfil the other condition. 



By extracting the square root of 58.944, we get 



w=-V/58.944 = 7.677 nearly; 

 therefore, by addition and subtraction, the values of x, are 



a: = m + 72 = 24.429 +7.677 = 32. 106, and x m n 24.429 

 7.677 zz 16.752 inches. 



Now, we have seen by equation (234), that the corresponding 

 values of y are expressed in the same terms, having the signs of the 

 second member reversed ; hence we have 



y = 16.752, and y = 32.106 inches. 



But here we have m -\- n zn 32.106 inches, being greater than b the 

 downward side of the transverse section, which by the question is only 

 28 inches ; it therefore follows, that with the proposed data and under 

 the specified circumstances, there is only one position in which the 

 body can float in a state of rest, and it is that which we have already 

 determined, where the base of the section, or the extant side of the 

 body, is parallel to the surface of the fluid. 



But we may here observe, that notwithstanding the values of a: and 

 y, as we have just assigned them, do not satisfy the conditions of the 

 question, yet they are not to be considered as being useless ; for they 

 actually serve, with a slight modification of the body, to furnish posi- 

 tions in which it will float at rest, although those positions do not 

 agree with the case, in which only one angle of the figure falls below 

 the plane of floatation. 



387. The positions of equilibrium corresponding to the preceding 

 values of a; and y, are 

 as represented in the an- 

 nexed diagrams, where 

 E D is the horizontal sur- 

 face of the fluid, ABC 

 being the position which 

 the body assumes when 

 x is equal to 32.106 and 

 y equal to 16.752 inches, 

 and abc the correspond- 

 ing position when y is equal to 32.106 and x equal to 16.752 inches ; 

 these being the respective values as obtained by the above numerical 

 process. 



