372 OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



or by putting s' equal to unity, and substituting the respective num- 

 bers, we obtain 



area efcd = a = 700 X 0.27 189 square inches. (283). 



459. Consequently, by having the area of the trapezoid efcd, 



and one of its parallel sides dc given, the other parallel side ef and 



the perpendicular depth Q H can easily be found ; for by the nature 



of the figure and the property of the right angled triangle, we have 



D C / - 7 20 



= b=piV * 



900+ 189 3o| 6 inches. 



therefore, by the property of the trapezoid, we have 



3(30 + c)=r 189, 



or by separating the terms and transposing, we get 



3c = 189 90=99, 



and by division, it is 



99 

 ef= c=--=33 inches. 



u 



460. We must next endeavour to discover the point k, in which 

 the primary and secondary water lines intersect each other, and for 

 this purpose, 



\)utfk nr y, then by subtraction, we have e k = 33 y ; 

 but by the rules of mensuration, it is 



and by restoring the above values of fk and e k, it becomes 



yXki = (33 y)Xkh. (284). 



Through the point c and parallel to PQ, draw en meeting ef per- 

 pendicularly in n\ then it is manifest, from the principles of Plane 

 Trigonometry, that 



*"*=="= 



which corresponds to the natural tangent of 75 57' 49". 

 But by the principles of Geometry, the exterior angle cfn is equal 

 to both the interior and opposite angles fki and fik ; consequently, 

 by subtraction, we have 



angle fik = 75 57' 49" 15 = 60 57' 49", 



