374 OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



But we have already found that/A zz 15. 94 inches, and k zzz 17.687 

 inches; consequently, their squares are 15. 94 2 rz 254.0836, and 

 17.687 2 zz312.83 respectively; therefore, we have 



kw \ <J 1 133.8272 /z 2 , 



and the value offi 2 is found by the following logarithmic operation, 

 angle fik =60 57' 49" - - log. cosec. 0.058334 

 angle fki 15 00-- log. sin. - 9.412996 

 side-fk 15.94 inches - log. 1.202488 



Sum of the logs. = 0.67381 8 



/t* = 22.2657 nat. number - - twice the sum zz 1.347636; 

 therefore, by substitution and reduction, we obtain 



k w = W 1 133.8272 22.2657 zz 16.68 inches nearly. 



But by the property of the centre of gravity as referred to the plane 

 triangle, we know that k o zz -f & w ; hence we have 

 Aozzf-of 16.68 ml 1.12 inches, 



and by a well known theorem in the doctrine of Plane Trigono- 

 metry, we have 



from which, by substituting the numerical values, we get 

 312.83 + 277.89 5.5664 



2X16.68X17.687 

 consequently, by multiplication, we get 

 kt = 11. 12X0.99231 = 11.0345 inches. 



463. Returning to the triangle hke, we find that e = 33 

 15.94 zz 17.06 inches, and kh 0.9703x17.06 zz 16.55 inches; 

 therefore, by Plane Trigonometry, 



sin.75 57' 49" : sin. 15 : : 16.55 : he, 

 which being actually reduced, gives 



Aezz4.415 inches. 



Therefore, by pursuing a train of reasoning, similar to that by 

 which we discovered the value of k t, we shall obtain 



he 9 



from which, by substituting the numerical values, we get 



291.0436 + 821.707519.4923 

 m= - - - zz 11.01 inches. 



