Roche — The Quadratic Vector Function. 103 



Expanding, eq^uating coefficients of tr, 



or ^' afse\<7f)',,je\e'i'e\,T = i ; 



If we put Wi2 VXfi = rii{nu V{d\~^X9'2~^it + (i'.'^XB'i'^fi) by method analogous 

 to that of § 2, using results of § 5, we get 



(A„) ■^,, = a,,9', - mS\e\-'Q\ 



and or becomes 



1 



= - »fl'«2 Qfl/ ft/ ^ ■ 



OO 1(7(7 ;(rS7i2C 



Thus, this monomial form is completely solved. 



28. Another particular example is 



X(pp) = CT = V{<i)ip4>,p + ct>2p4'3/> + 't>:ip4'ip), 



we have 



Sa<f>ip = S4>ip(j}2p4>3f = Sp4>\<y 

 Sac^ip = S4'ip^iii^ip = Sp4>'2(j ; 

 Sp (<^'i(T - <^'j(t) = and Sp (4>'it - 4'\<y) = 0. 



where x can be found by substitution as above. 



29. Dr. Conway has defined the central axes of the function as those 

 vectors which satisf}' Vp^ipp) = 0. So 



= V^paiSp<f>ip + VpaiSp'i>2p + Vpa^Sp'i'ip, 



and we get two scalar equations for p 



Spfip _ Sp(p2p _ Sp(j)sp 

 SuoOip SazGip SoiO^p 



E.I. A. PEOC, VOL. XXX., SECT. A. L^"^] 



