NO. l6 METEOR-ORBITS IN THE SOLAR SYSTEM — VON NIESSL 21 



common focus which possess parallel asymptotes on one side. In this 

 case one orbit is direct, the other is retrograde, and their perihelia lie 

 on opposite sides of the radius vector. 



Since one of the two perihelion distances is ordinarily very small, 

 the attendant radiant is generally in that portion of the sky covered 

 with sunshine. For the parabolic orbits the true positions of the two 

 associated radiants lie diametrically opposite one another. 



The expressions above given for the determination of the orbit in 

 the present condition of the art of observing meteors go far beyond 

 the needs of the accurate computations. They can therefore only be 

 appropriately applied when we are concerned with the further de- 

 velopment of definite theoretical views. In the working up of obser- 

 vations we attain our object sooner and without appreciable loss in 

 accuracy when we assume in general that for the earth's orbit we 

 have e=o, r=i, ©'=©, and also that the velocity of the earth is 

 always equal to unity, in short, we take the orbit of the earth as 

 circular. 



It is easy to simplify all the previous expressions by means of these 

 substitutions, only we must say that it is not important to seek for the 

 true radiant when we can attain the ordinary elements in the shortest 

 way. We find, in fact, 



v^ = v'^-i-i-2v' cos/3' sm(0-X'),^ 

 cos T= — ^cos^' cos(0 — A'), I 



sini=: — tan ^' • cot T- sec(0 — A'), ") 



cos,-^ i+z;cosrtan(Q-V) ^ f (36) 



V sm T 



I 



and the calculations may be carried further by making the indicated 

 substitutions in the known formulae. For the determination of the 

 sidereal starting point /, b, we have 



o- w sm T , 



tan — = —. , where 



i-f-mcosT y^2_2 



= m. 



^^o/o ^ 2+(z/2 — 2)cos 



(27) 



whereupon / and b are found from (30). The velocity for p= 00 is 

 Vo=Vzr^ — 2. 



The simplification of the inverse problem to find / and b for the 

 radiants from A', P' does not here need any further explanation. 

 Computational results from the elements of the orbit from the velocity 

 determined by the observations are almost useless because the basis 



