506 



Sir G. Greenhill on tl 



le 



6. The Bessel Functions of real or imaginary argument^ 

 denoted by ber and bei in Kelvin's notation, are dis- 

 tinguished here by a mere change of sign in the argument a? 

 of the Clifford Function. 



Thus the Clifford Function has no negative root : it 

 would not be possible for the revolving chain in § 2 to 

 stand erect. 



But by supposing each link to contain a coaxial flywheel 

 in rapid rotation, a gyroscopic stiffness can be given to the 

 flexible chain, to enable it to hold itself upright, as in 

 the reported rope trick of the Hindoo conjurer, and behave 

 as what may be called a gyrorope (yvpopoTrrj). 



Denote for each infinitesimal link, of length ds, at 

 an angle 6 with the vertical, the weight and moments of 

 inertia, axial and transverse, by a. C, A, estimated per unit 

 of length, so that a is in lb/ft, C and A in fb-ft 8 /ft, 

 that is in lb-ft ; and so C/cr, A/a are in ft 2 ; by R the 

 angular velocity of each little flywheel. 



>Y->2dY 



Y+^dY 



The vector GH in the figure of the horizontal component of 

 angular momentum (A.M.) is given, in gravitation units, by 



GH 



=( 



ri R . n A co . n 



(J — sin u— A - sin cos 

 9 9 



e)iU, 



(1) 



and in steady bodily motion, equating its vector velocity ? 

 GH . &), to the couple due to the reaction at each end of the 



