METEORS OF AUGUST AND NOVEMBER. 129 



X, = G, COS {[L + 90°) 



(7) Y, = G, sin (^ + 90°) cos « 



Z,=z— G, sin {[L + 90°) sin ^ 



and 



X = G cos i cos jB = Xo + X, 



r= Gsinicos JB= ^0 + r, 

 Z = G sin 5 = + Z, 



z = g cos Z cos h — G cos i cos .6 + y cos ^ cos /? = X + ^ 



(8) y = 9 sin / cos 5 = G sin i cos 5 + y sin ;i, cos ^ = Y +7^ 

 z ■= g %m.b = G sin B + y sin ^ = Z + ^ 



If we add together the squares of the three equations (§) -v^ being the angle 

 of elongation of the convergent point from the observer's true direction, we 

 obtain 



g^= G' + f + 2Gy [cos B cos ^ cos {L^X) + sin B sin /?] 



^^ = G' + y' + 2 G y cos 4- 



(9) • -n • 



cos '4' = COS 5 cos (3 cos (i — /I) + sin B sin /3 

 y = — G cos i]^ ± v (^^ — Gr^ sin^ ■^) 

 In Table VI. 4' comes out in the second quadrant both for the August and 

 November meteors. Hence both signs before the radical are possible, and the 

 only geometrical limit which these equations furnish, in order that g, G, and y 

 shall be positive and rational, is that of the true normal velocity ( G sin 4'- ) 

 This being necessarily the minimum of the true velocities, and the minimum 

 required by the condition that y must be rational, we have for its limit 

 (10) g = G sin 1^ 



Marking with a negative sign at top the quantities that result from the use 

 of the lower or negative sign before the radical in the last of (9) we have the 

 following geometrical limits of the values of g and y : 



Maximum of ^ = + ao 

 g=G 

 " y = + CD 



(U) Minimum of ^ = G sin 4' 



'* ^ = G sin tJ^ 



" y = — G cos 4' 



" y = 



VIII. — 2 H 



