Bessel-Clifford Function, and its applications. 



507 



link, with components, vertical and horizontal, X — %dX r 

 Y— -JdY at the top, —X — ^dX, — Y — ±dY at the bottom 

 (to split the difference), 



or 



GH . co = Xds . sin 6— Yds . cos 0, 



' 9 9 



<R ■ A „\ tan0 



X tan 0-Y = ( C — -A- cos flWii 6 

 \ 9 9 



= ((J?— Acostf) 



(2> 



ith 



; 



g = /«-. 



Resolving vertically and horizontally for tbe relative- 

 bodily equilibrium of the link, 



(X+idX)-(X-idX) = dX = <rd*, X=<™, . . (3) 



(Y + K5T)-(Y- WY) = dY = a^yds = a- Us, 



-?;■ 



yds. . (4) 



fl?A' 



With the chain nearly straight, take s = x, ^-= cos 0=1 



then eliminating X and Y, 



\ ft) / / tf.r tf# / J " 



or, putting C A = ala, and differentiating 





, ri ta — x\ d// b ~ (a—X\ 



dy 



The first root of d, making f = Q, is 



° ax 



■ ■ (5) 



• • (6.) 



. . (7> 



oiven bv 



a — x 

 the first root of J\ = 0, 



fa — x_ 



'Z A / 1 O 0()1I, Ulll; 1HOI LVJV7H V.H- ^J ^, J 



Thus a length x of the gyroscopic chain can be 

 made to stand upright, given by ,r = a — ?riu I, so that 



T =l C^ — A ) --.., must be made io exceed 3*67. 

 / \ to / err 



With a weight W balanced on the top, the second 



function D would be required in the solution, and the 



constants adjusted for the relative equilibrium of W. 



