296 OF THE POSITIONS OF EQUILIBRIUM. 



Now, by substituting the numerical values of a, b and c, as given 

 in the question, and the value of d as deduced from calculation, the 

 absolute values of cos.0 and cos.0' will stand as below. 



Thus, for the absolute numerical value of cos.^>, we have 

 4(784-f649) 324 



and for the absolute numerical value of cos.^', it is 

 649) 324 



Let the numerical values of cos.^> and cos.^' as determined by the 

 above computation, together with the numerical values of a, b, c, s, 

 and s', as given in the question, be respectively substituted in equa- 

 tion (229), and we shall obtain 



x 4 48.2S59* 3 4- 23894.7* =: 249408 ; 



but in order to simplify the resolution of this equation, it will suffice 

 to take the co-efficients to the nearest integer, for the error thence 

 arising will be of very little consequence in cases of practice, and the 

 modification will very much abridge the labour of reduction ; the 

 equation thus altered, will stand as below. 



x 4 4Sx s -f- 23895* = 249408. 



Therefore, if this equation be reduced by the method of approxima- 

 tion, or otherwise, the value of or will come out a very small quantity 

 less than 22 inches ; but taking it equal to 22, the result of the equa- 

 tion is 



22 4 48 X22 3 4- 23895X22 = 248842. 



By substituting the given values of b, c, s and s', with the com- 

 puted value of x, in equation (227), we shall have 



22000^ = 499408, 

 from which, by division, we obtain 

 499408 



22000 ' 



Consequently, from these computed dimensions, together with the 

 sides of the section given in the question, the prism may be exhi- 

 bited in the position which it assumes when floating in a state of 

 equilibrium. 



376. Construct the triangle ABC to represent the transverse section of 

 the floating prism, and such that the sides AC, BC, and AB are respec- 

 tively equal to 28, 26, and 18 inches; make CD and CE respectively 



