METEORS OF AUGUST AND NOVEMBER. 131 



greatest velocities in Table VI., both observation and theory, in their present 

 state, require us to restrict the anniversary meteors to elliptic orbits. Analogy, 

 also, leads us, in the case of sporadic meteors and isolated clusters, to make the 

 same restriction. The value of 12.0, however, for the December meteors, is 

 too small to include all the values of Table I. in a periodical orbit, unless ob- 

 servation should show that, on the occasion of a high angle of deflection of the 

 convergent point, the value of ^ / falls below the average in Table I. The 

 limits of (11) and (is) give for elliptic or periodical orbits 



Maximum of ^ = V (:^ — ^-^-^ ) 



" a = + 00 



1 



(13) 



a = 



Minimum of ^ = G sin 4* 

 " g = G sin t^ 



" y — — G cos 0^ 



fy = 



1 



a = 



— G^ sin^ 4/ 



R 



The limiting value of g^, or "^, is adopted by Olbers*^ and Professor Erman, 

 Jun.," for the orbits of these asteroids. Their reasons for the restriction are 

 not, however, stated. Professor Erman, Jun., has overlooked the limits which 

 have the negative sign over them, and has, therefore, too much restricted 

 the limits of the elliptic elements of these anniversary asteroids, possible ac- 

 cording to the principles of the geometry of position. This oversight pervades 

 the results and conclusions throughout that interesting paper. Its effect is 

 particularly manifest in the formulse there given for computing the maximum 

 motion of the convergent point in a finite period, which he makes about 0°.l 

 per hour in a retrograde direction. Now, by applying the proper limit to the , 

 reciprocal of y, which Professor Erman makes a coefficient of this motion, 

 (since the limit of y is 0, and that of "^ is -f- o) ,) we may have, without any 



*^ See passage already quoted. ^' Astr. Nachr. 385. 



