of Deposit of a Submarine Cable, 15 



subtract the second. The remahider gives 



0=l-e^ -^ ■' .„ 01-0=1- -^ 



^-- ^a+f^) = eT,or^ = ^{e^ + l)-l 



and with this value of/ the equations are satisfied. It will be 

 seen that / is the trigonometrical tangent of the angle made by 



the cable with the horizon, or -^ that of the angle made by the 



cable with the vertical. It is to be remarked, that this angle is 



independent of the fractions -j- and — . 



27. If e=3, j^= Kj ( "7" ) ~~ 2' ^"^ *^^ angle made by the 



cable with the horizon is 28° 1' 10". If e=3, ^= \/(^^) -\, 

 and the angle made by the cable with the horizon is 18° 55' 0". 



28. To find the tension, we may take either of the final equa- 

 tions of Art. 25 and integrate it : the first equation will be the 

 more convenient. The arbitrary constant will be determined by 

 the consideration that the tension at the place of contact with 

 the bottom =0 ; and therefore when a? = 0, T = 0. Thus we find 



or, if we prefer to express it in terms of the vertical ordinate y, 



"■- a' U v{\+fy f ^^' w{i+rf' 



-^ a' U v/(l+/V / '^' 



Ife = 2, 



and 



Ife = 3, 



and 



^^^^^=3-514, VHW-, =0-883; 



T=y- ^x 8-514 x(^ -0-883) xy. 

 T =y- |- X 27-760 x (— - 0-946)' x y. 



