104 Mr. HOLDITCH, ON SMALL FINITE OSCILLATIONS. 



••• F3=-r, +r„ 

 F, = - F, + r, ; 

 and taking the limits, V=a, 

 r, =0, 

 Fj = »• - a, 



F, = a - r + j-2, 



^ g- \ V 4A;- 16 l6.(r-a) 48 (r-a)VJ 



Etjoample. An ellipse with its axis major horizontal. 



Here r = 



1,= 



= r„ + '>\.e + r^.- + . 

 A«6 



and T = — . V -• '{l + ^^ ■ — rvr; + rrj— ? • 



ae ^ ^ I V4A:-6- Ihb" I] 



The same principles may also be applied, with great facility, to the oscillations of floating bodies. 



H. HOLDITCH. 



