322 



OF THE POSITIONS OF EQUILIBRIUM. 



and similarly, the corresponding values of y are 



The practical rule for reducing the above equations must be omitted 

 in this case, the forms being too complex to admit of a clear and com- 

 prehensive description ; it is however presumed, that the attentive 

 reader will be enabled to understand the method of solution, by care- 

 fully tracing the several steps of the process as exhibited in the fol- 

 lowing arrangement. 



406. EXAMPLE. If the dimensions of the section be the same as in 

 the preceding example ; then, the value of s as computed from equa- 

 tion (247), becomes 



__(16X28 2 18 a )Xl8*__ 3959280 



0.2013 nearly. 



32X28 4 19668992 



Therefore, let the mean value of s as thus determined, together 

 with the numerical values of a 2 , b*, cos.0 and cos 2 .^, be substituted in 

 equation (248), and we shall have, in the case of the positive sign, 



*i=0.47347.v/4X28* 18 8 -f ^0.22417(4 X28 2 18*) 0.7989X28* 

 27.152 inches, 



and in the case of the negative sign, it is 



a: =: 0.47347 -v/4X28*18 2 V0.22417(4X28 2 18 2 ) 0.7989x28* 



HZ 23.06 inches, 



and the corresponding values of y, are 

 t/ 23.06, and y 27.152 inches. 



407. Now, the positions of equilibrium corresponding to the above 

 values of x and ?/, are as 

 denoted in the subjoined 

 diagram ; where IK is the 

 horizontal surface of the 

 fluid, ABC the position cor- 

 responding to x = 27. 152 

 and y zz: 23.06 inches, and 

 abc the position indicated 

 by x z= 23.06 "and y = 

 27.152 inches. 



Bisect AB and ab in the points F andy, and draw the straight 

 lines FD, FE and fd, fe intersecting the plane of floatation in the 

 points D, E, and d, e ; then shall the lines so drawn be equal among 



