Bessel- Clifford Function, and its applications* 503 



ax n+l 

 With a line density ax n , and T= -- — ^, the condition 

 , " n + 1 



changes to 



d l <rx u+l dy\ co 2 <rx n jj = Q ^. 



dx \ n -+- 1 <£#/ # ' 



a g + (» + 1) ^ + (» + 1) f = 0, «/ = AC„(n + 1) ? (4) 



instead of the complicated expression in • Bessel Functions/ 

 p. 222 ; and I is still the subtangent of the curve at the 

 lowest point. 



3. Lecornu's problem of the small oscillation of a 

 weight W, raised or lowered from a crane by a weight- 

 less chain, requires the differential equation of angular 

 momentum, 



d 2 y d 2 x A . . 



d 'aW-^dt^^=^ ' ' ' • ' (1) 



where x is the length of chain out. 



Then with constant vertical acceleration /upward, 



J= -/; * = t/(T»-*») $ f=i-jp, • • (2) 



d 2 ' 



and with - T -- = v. 

 dt 



(T»-«»)j^+ 2(l+^ = 0, . . . (3) 



|(f^)J + »(» + l), = 0, . . . ,4) 

 Legendre's differential equation for 



v = bP n {!^, with n(n + l) = 2(l-ff.); 



^ J n{n+l) K J dt 



Changing to the variable x in (3) and (4), 



*(«-* )^-i*t+*C 1 +?)y = °' 



differential equations (O.K.) o£ the hypergeometric (H.G.) 

 form. 



2 N 2 



and then « 1 ( f r 



(H) 



