l6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 66 



If we substitute this value in the above-mentioned equations, then 

 they become at once modified appropriately for the proposed solution. 



It may finally be noted that in the case of observations made at one 

 place the zenithal attraction for the correction of the radiant can only 

 be determined hypothetically, for we must use the zenith of the 

 terminal point which is unknown, and we must know the relative 

 velocity. For this latter the place of observation can be adopted and 

 no great error will result. Instead of the unknown velocity, we gen- 

 erally use the geocentric velocity corresponding to the parabolic orbit. 



II. COMPUTATION OF THE ORBIT RELATIVE TO THE SOLAR 



SYSTEM 



The co-ordinates of the apparent radiant a', df freed from zenith 

 attraction, and relative to the ecliptic, will be designated by A', ^'. 

 These and the relative geocentric velocity 1/ are found by the combi- 

 nation of the heliocentric motion of the meteor with the velocity v in 

 the direction indicated by the analogous co-ordinates A, /? combined 

 with the magnitude and direction of the heliocentric motion of the 

 earth at the node of the meteor's orbit. A, ^ determine the true 

 radiant point and v is the heliocentric velocity at this point. The very 

 unimportant influence of the earth's rotation on its axis can here be 

 left out of the consideration. 



As the unit for the measurement of v and 1/ when no other kind is 

 noted, we use the velocity of the earth at its mean distance from the 

 sun. The quantities expressed in kilometers will be reduced to this 

 unit with sufficient accuracy by dividing by 29.59. 



For the radius vector, or the distance of the earth from the sun, 

 the unit is the average distance or the semi-major axis of the earth's 

 orbit. For that position of the earth's orbit at which the longitude 

 of the sun is O the corresponding distance of the earth expressed 

 in this unit is 



r=i-l-^'cos(0 — tt). 



In this expression we may for a long time adopt with sufficient 

 accuracy ^' = 0.01676 and if T denotes a year, we have 



7r=IOI° I2.8'-1-I.03'(T-I900). 



The radius vector r is given for every day in every astronomical 

 ephemeris. 



If 0' indicates the longitude of the direction of the normal at that 

 point of the earth's orbit for which the longitude of the sun is O, then 

 we have 



0'= O -t- -^-,sin(0 -tt) = O +57'6 • sin(0 -tt), 

 arc I ^ 



