(14) 



, 22 RESEARCHES CONCERNING THE PERIODICAL 



contradiction from the geometry of position, a motion of the convergent point 

 in a finite period of time indefinitely great, instead of 0°.l. There are other 

 variable elements omitted in Mr. Erman's formulae for computing this motion, 

 which will be referred to in the next section. It remains to point out the use 

 of the formulae of (8) in computing the elliptic elements from observed values 

 of y, ?i, and /?, and the known values of X, Y, and Z. These equations may 

 assume the following well known forms : 



tan I = ^ + 7 ^^^ ^ <^Qs ^ = Y + ^ 



X + y cos ;i cos /? X + ^ 



tan b = ^±^>^ ^. cosl= %±\. cos I 



X + y cos /I cos p X + ^ 



^Z + y_sin| ^.si^^^^.sinZ 



r + y sm ;i cos p F + )? 



_ X + y cos % cos /? _ X+ ^ 



^ "" cos I cos S "" cos I cos 5 



_ F + y sin ^ cos /? _ F+ >7 



"" sin / cos h ~~ sin / cos b 



^ Z + y sin (3 ^ Z + g 



sin J sin 5 



In making the computations, either of the formulae (9) may be used as a 

 check to test the accuracy of the computation. The subsidiary quantities, G^, 

 Lo, and Bo = 0, are readily obtained thus : 



® = the earth's longitude 

 £ =z " eccentricity 



= sun's longitude = © + 180° 

 R^ = earth's radius vector 



(15) 



^(1_,^)= G, i?o sin (L, — ®) 

 {^) = 39°.95 



G, = 0.011644 = 365.2564 x sin is cos (^) 

 Now the quantities L and B differ from Lo and {Bo = 0) by less than a degree, 

 and the deflection of the convergent point from the plane of the Lo and Bo, or, 

 in other words, from the ecliptic, being in a southerly direction, and also south- 

 erly with respect to the plane of L and B, the true motion of the meteor must 

 be southerly, and it must be tending towards its descending node. Also, the 



