Si pa Be glieger TR Se Pee ke ee ee 
ATES nee geen he) Ae oe SAC x za ratleeas fo 
Sy eee lta Me ee aa 
: ee : eee 
t a a 
254 A. C, Twining on Meteoric Rings as 
from the ecliptic. But in the plane uv, such is the direction of 
the deflections or effects in the line uEv that, even if the radial 
distances were not in or near the ecliptic, neither a retrocession 
nor an advance can be consequent upon them. 
uming the expressions and quantities from (C); viz. # and 
y the transverse and conjugate diameters and v the miles tray- 
ersed in a second, putting also } for the assumed initial distance 
upon the asymptote from the centre, so that 2 . shall measure the 
time from the initial to the terminal places by the uniform and 
undisturbed initial motion, the nodal motion which applies indi- 
vidually to all the meteors of the cylinder will be expressed by 
26 2\2 2\% : : 
(1.41 [1+(14+4) +0455) \53 in which @ is con- 
stant, ¢ is the earth’s velocity, and J. is the symbol for the Napier- 
ien logarithm; and which, when differentiated with reference to 
the spaces, gives | 
2b $2 y2 $ y? $ e 
2(. 445 [3— (1455) je f+(145) | : 
for the average of nodal effect upon the entire cylinder to the dis 
tance of 7 on every side. The same is equivalent to a retrograda- 
tion of m, m, r, r (which are next the earth) to the distance of 1370 
miles; while the advance nq in the plane Esr is only 254 miles 
on the ecliptic preceding and: 228 on the side following. Yet 
advance is nearly constant, while the recession diminishes with the 
distance, and down toa very moderate average for the entire mass. 
ferential expression < (1+c?.1 = eos. D) 2d cos, D; in which a8 
a constant derived from the inclination of the relative line and 
the amount of tangential perturbation, reduced to the plane of the 
Ting, ¢ is the natural tangent of that inclination, and D is the ar 
of the meteors’ relative position in the normal cylindric section 
taken from the line of section of the latter with the ecliptic, SO that 
is effect upon the nodal position, averaged for such a cylinder, 
= be comprehended ith eutlinaeat closeness in the express! 
35 (1+e)?; also, Sater* sin.?D gives the same for any ind: 
dividual meteor. The factor therefore is the fraction 4, negle’ 
ing @ small term with a double sign which eliminates itself from 
the average b: appearing in opposite senses on opposite 
