80 C. V. L. Cliarlier 



^020 = + ^2 i) 



which substituted in the differential equations (187*) give 



(X -)- 2v) — V &j — V Cj = — «2 ' 



(191) — V a, + (X + 2v) 6j — v Cj = — 6^ , 



— V — V + (X + 2v) = — , 



and 



(X + 2v) «2 — V 62 — V C2 = 0, 



(192) — V «2 + + 2v) &2 — vc2 = 0, 



— V «2 — V ?;2 + + 2v) C2 = 0, 

 or, using the value X = — 3v, 



ftg = v(ai + + cj, 

 (192*) = v(«j + + cj, 



^2 = H«i + + cj, 

 whereas the three equations (192) all take the same form 



0 = v(a2 + + C2). 

 As, according to (192*), = c^, we hence get 



(/g = &2 = C2 = 0 , 



and it remains the relation 



(193) a, + + = 0. 



Two of the quantities a^, h^, c, may be arbitrarily choaen; the third being 

 then determined by (193). 



The solution of (187*) is now 



•^200 ^'0 ~r ^ . 



. , — Svt 



^002 I ^1 ^ ' 



where 



«1 + ^1 + ^1 = 0, 



(194*) ^ T 



V = A — 



We know that T, and lience also v, is positive. 

 It now immediately follows from (194) the following theorem: 

 If t increases towards -f- co , then the coefficients ^200 ' ^020 > ^002 uppi'oach 

 asymptoticaUy to the same limit . 



