H. A, Newton on November Star-Showers. 59 
shows a decided tendency toward o position of sign of the re- 
mainders, and hence the first must be considered as the more 
probable velocity. This opposition of signs and its significance 
was pointed out to me by Mr. J. W. Gibbs, to whom I am in- 
debted for other valuable suggestions, 
_ 16, If the annual motion of the group is 1+ 53,; revolu- 
tions, we may determine the orbit. Between ‘the shower of 
A.D. 902, and that of A. D. 1888, were 365 x 9381+283+19°25, 
that is, 340067:25 days. During this time the group has made 
931 + 28 revolutions, excepting a small fraction of one revolu- 
tion to be determined from the procession. ‘The procession is 
26° 33', of which 12° 58’ is due to the precession of the equinoxes, 
The remainder is to be reduced to the plane of the orbit, and 
regarded as described with a radius vector greater than the mean 
‘stance. Hence it may be called th of a revolution. The 
time of a sidereal revolution of the group around the sun is, 
then, 340067-25 + 958-96, or 354621 days, 
16. The accuracy of this periodic time is worthy of notice. 
The principal uncertainty arises from the assumption (2) that the 
shower of A. D, 902 occupies the same place in the cycle as that 
of A. D. 1883; in other words, that the earth passes through the 
Same part of the group in those two years. An examination of 
the remainders in the eighth column of the table leads me to 
believe that the probable error of this supposition would be less 
than one year. Now if this error was one year, plus or minus, 
the periodic time would be ee 27 or 354-621-011 
days. This error of the periodic time would be only about 16 
minutes. There is a similar accuracy in each of the other possi- 
eriodic times, 
€ cause of this accuracy is evident. The periodic times of 
the group and of the earth are like the two divisions of an im- 
mense vernier, extending back nearly a thousand years, and we 
measure from the twenty-ninth coincidence. eit : 
17. Each body of the group must have its own elliptic orbit 
about the sun, this orbit being, of course, slightly modified by 
the action of the rest of the group. The major axes of all these 
llipses are I. For otherwise the bodies would soon scatter 
themselves along the whole circuit of the ring, and there would 
be a display every year. A very slight deviation from a common 
y 
axis is evidently | eos + or 098049, the mean distance of 
ab 5°25 ‘ 
the earth being unity. The earth’s radius vector, at the time of 
& shower, represented below by 7, is 098887. The velocities of 
the earth, and of any member of the group, are represented 
