76 BOVEY ON THE BENDIKG 



Eliminating m.^ from 2 and 3, 



nil— ISm^— 4?M, = — ^(!y., + !«3 — é.îi'a + î^'J (x^) 



Eliminating m^ from 4 and x-^ , 



II 



?)!, + 56.mj + 15.^5= — -( Wj + î*3 — 4.W3 + u\ + 15.^1 + w^ ) (.xj 



Eliminating w^ from 5 and x.^ , 



Wj— 209^5 — 5C.m^=—_ ( m;^ + w^ — 4:.ic^ + w^+\f).w^ + w^ — M.w^ + wj {x.,) 



Finally, by successively eliminating tos, m^,, m„_2, 



= — J- |m'2+«'3 — 4.M'3 + «',+ 15.M)^ + !<'5— +a,„_4.?(V-3 + ?<'„- 



T««-3-Wn-2 + M',i-l±««-2-«'n-l+W»| (î/) 



the tipper or lower sign being taken for the terms within the brackets according as n is 

 odd or even, and the coefficients a„_i, a„_2, a,^_^.^.... being given by the law, 



a„_i = 4.a„.o — a„_3 < 



a„_2 = 4.a„.3 — a„_4 



a^^=4:.a^ — «3^209 



«3 = 4. ft, — rt, = 15 

 fl2^4.ai = 4 



flj =1 

 Commencing with equations n — 3 and n — 2, and proceeding as before, 



i^ ( . . 



= — ^- Y^n-2-W^ + ?i'2 — «„.3.M;, +^3 + rt„-.l.M'3 + 7(',— 



± 15 . M'„_4 + ^,,-3 ^ 4 . w„.s + w;„_2 ± w'n-2 + w.-i I (2) 



the upper or lower sign being taken for the terms within the brackets according as n is 

 odd or even. 



