LE, J. Parsons—Elliptic Elements of Comet 1882, I. 33 
The differential coefficients with respect to the six elements 
being computed for the six normal places gave twelve equa- 
tions involving the following unknown quantities, 
x=10000 dT, 
‘ AES ee ag 
M sin y=d log qg (Briggian) or Yee a! 
z=dy'=da' + cos 7’dQ! v=dQ)' 
sin u=de or de=——, w=di'. 
sin 1 
It was not thought worth while to apply weights systemati- 
cally according to the number of observations, but as the last 
normal place seemed to have considerably less precision than 
the others, the last two equations were given a weight of 0°5012 
“ic ghana as a convenient approximation to a weight of one- 
alf. - 
The twelve resulting equations being solved according to 
the method of least squares give the following values for the 
unknown quantities: 
w= 4°4771-4-1'°468 u=— 2'°2662+0'°877 
Y= 2°4213+4 4°214 V= +10°952 42°495 
@=—1°42954 0°875 w+ 9°035 4+2°739 
Substituting these values in the equations of condition gives 
for the sum of the squares of the residuals [vv] =22°02. In the 
solution of the normal equations [nn°6]=22°09. 
ese unknown quantities the following corrections to 
the preliminary elements are found 
@T= +0°000448 +0°000147 de=—0°00001098-+-0°00000425 
d log g= + 0:0000051--0-0000089 dO’=+10'-952  4:2'495 
do =—8'"024 26440 di’ = 4+ 9085 = 2739. 
These corrections give as the most probable values of the 
elliptic elements, ; 
T=June 1052953 G. M. T. 40°00015 
log g=8°7836432 +-0°0000089 
e€=0°99998902-+-0°00000425 
G@=208° 59’ 33"-792 
O=204° 56’ 29"-49 | Mean Equinox and Ecliptic 1882-0 
t= 73° 48’ 417-82 
co' = 196° 51’ 16”°-49-+4-2"°644 : 
Q’=210° 29’ 12”-254-2"-495 } Referred to Equator. 
a= 52° 57’ 417-04--2"°739 
Rectangular equatorial codrdinates, 
x =r [9°9611023] sin (126° 22’ 497°33 He 
y=r |9°8608362] sin ( 61° 11’ 5804+ 
z=r | 9-9021280] sin (196° 51’ 16"°49+%) | 
Am. Jour. So.—Tump Senres, Vou. XXVIT, No. 157. —Jax., ime 
