16 The Astrouomci- Royal on the Conditions 



If e=Q (that is, if the ship is stationary), and if / have the 

 concsponding value x (that is, if the cable hang vertically down, 

 which makes the tension the least possible), T = y. 



29. The tension is the greatest possible when the cable is 



delivered with the least speed possible, that is, when — = 1. 

 This gives, for e = 2, 



T=//x{t-|xO-117|; 

 and, for e=3, 



T=yx{l-|x008l}. 



30. The tension will be diminished by increasing the speed of 

 delivery of the cable ; but without fixing upon a numerical value 



for -r- (the proportion of the coefficient of longitudinal re- 



A. 

 sistance to that of lateral resistance), no statement of its value 

 can be given more intelligible than those in the formula of 

 Article 28. The tension will be made = if we can make the 

 second term of the expression = y. This gives, for e=2, 



(^_0-883y=^^-4^, 

 \n J Bx8-514 



or 



-= 0-883 + 0-3427a/^ 

 n V ii 



(the other root of the quadratic being inadmissible, as it makes 



— < 1). Thus, suppose -r = T> the tension is if — =1 68 ; 

 n ' ^ A 4 n 



or if the cable is delivered with a waste of 0'568 on the geogra- 



B 1 . . . m 



phical length. \i -r=.-. the tension is if — =1'911. 

 ^ ° A 9 n 



For e=3, the tension will be =0 if 



(!?L_0-946Y = ,^ 

 \n J B X 37- 



760' 



— =0946 + 0-1898 



n 



\/w 



If — = -, the tension is if — = 1-326, or if the cable is de- 

 A 4 n 



livered with a waste of 0*326 on the geographical length. If 



-r- = r:> the tension is if — = 1*516. 

 A 9 n 



