H. A. Newton— Biela Meteors of Nov. 27th, 1885. 421 



Suppose the directions of the luminous paths regarded as 

 right lines to be first corrected for the earth's attraction and 

 rotation as heretofore indicated, and the corrected lines to be 

 produced indefinitely. They will intersect the celestial sphere 

 in and near the constellation Andromeda. The most of the 

 points will lie in an area comparable in size with the area 

 dotted over by the assigned radiants, as shown in the figure on 

 p. 417. Probably the points would be somewhat more widely 

 distributed than the assigned radiants, 

 since these latter are centers of radiation 

 deduced each from many observed 



paths. Let an area R be taken on the 

 celestial sphere that shall contain the 

 principal part of the points so deter- p , 

 mined, an area that for convenience may 

 be taken of an oval form. To this area R corresponds a se cond 

 area R', such that R' bears the same relation to the motion of 

 the meteoroids relative to the sun as R does to the undisturbed 

 motions relative to the earth. The area R' may be thus con- 

 structed. Let P be the point of the celestial sphere from 

 which the earth is moving. To any point in R will correspond 

 a point in R r co-planar with P and conversely. Hence great 

 circles from P touching R will be tangent to R'. If u be the 

 earth's velocity, and v the meteoroids' velocity relative to the 

 sun (which may be assumed to be the same for all the meteo- 

 roids), then by the law of composition of velocities, v. u : : sin 

 PR : sin RR'. The dimensions of R' for the Biela meteors will 

 be easily found to be in one direction about f , and in the other 

 about •§ of the dimensions of R. Therefore for the shower of 

 Nov. 27th, R' is measured by degrees rather than minutes. 



If the orbits of the Biela meteoroids were nearly (or quite) 

 co-planar the area R' would be a narrow oval (or a mere line). 

 And if S be the earth's place as seen from the sun at the time 

 of the shower the major axis of the oval (or the line) would be 

 co-planar with S. 



But to each point in R r corresponds a point in R, and if R A 

 is a narrow oval (or line), R will also be a narrow oval (or line, 

 which would be in fact, a portion of a sphero-conic). The 

 lengths of lines in R will be to the lengths of corresponding 

 lines in R' in ratios not much greater than 9 :4, nor much less 

 than 3:2. 



Now the thickness of the dense part of the stream subtends 

 at the sun as was seen, an angle of about 3 /- 7. Therefore, 

 either there is something like a nodal point of the meteoroid 

 orbits near where the earth's orbit cuts them, or else the devia- 

 tion of the planes of the orbits from their mean plane is 

 generally not greater than one-half of 3'*7. Because a large 

 group of orbits whose planes intersect the mean plane at angles 



