310 LL. Boss—~Tail of Comet b, 1881. 
7 = Length of perpendicular let fall from the particle on r pro- 
duced at the time 
& = Distance from the foot of that perpendicular to the nucleus. 
gp = Angle whose sine is 4, or the angle between r prolonged and 
the line joining the nucleus and particle at the time M. 
As an example of the manner in which the theoretical lines 
of Plate VI have been constructed, the results of computations 
intended to represent the Ae ie ‘tail of Jane 26:805 (Berlin 
time) are subjoined. The of (1—y) is assumed to be 11°0; 
and the hyperbolical neni are eS eberpatel for particles emitted 
at perikiehion, rit for two designated dates subsequent to that 
M’ ~ June 167510 June 18°510 June 20°510 
M’ June 167510 June 18°359 June 20-205 
log E 0°0792 00791 0-0788 
I 4° 15’ 2° 29’ J fageh Og 
A 284 “102 110 
& 273 187 109 
” 077 041 018 
Pp 15°47 12°-4 9°°5 
From the values of 4, &, and y, the curve marked I in the 
figure for June 26 (Pl. VI) i is ae aractat From that curve we 
derive by a graphic process the values of g corresponding to 
the pene values of 4 at two points in’ the tail on that date. 
e thus 
A ’ ¢ 
June 26-805 210 12°-9 13°2 
Type I "187 140 12°3 
The agreement between the values of g’ and ¢ is even closer 
than could have reasonably been expected from the unavoid- 
able le ae error in the determination of ¢’. 
e diagrams of Plate VI, the point N represents the posi- 
coe of the nucleus at the respective ne of observation. 
N RB’ is the radius vector prolonged. The curves N [I are care- 
fully constructed in the original diagrams fi the computed 
positions of two or more partic! es, when (L—y)=11:0. The pre- 
vious dates of emission were so chosen that one or more com- 
puted points would fall near that which was actually observed. 
Che curves N II were constructed with (l—#)=1°4, and may 
represent the tail of Type I. The sweahiila between dates 
of emission and observation for like values of 4 are much 
greater in this case than in that for tails of Type I. The curves 
N are constructed with (l—#)=1-0; and N III” for July 
22, is based on (1—p)=0°6. The: dots enclosed in small circles 
indicate the positions of points in the tail actually observed. 
