of the bright Fixed Stars, 327 
_ The discordances between the numbers obtained by enumera- 
tion from the Durchmusterung and the empirical values deduced 
from Professor Littrow’s formula, vary satisfactorily in sign ; 
Zm=0°6098 (8:5295)™. 
To these I add the values corresponding to another formula, 
which I have deduced for the purpose of giving a somewhat 
better representation to the stars brighter than the 3} magni- 
tude. In this the light-ratio for each magnitude is 0-4523 and 
the number of stars comprised in the half-magnitude m is 
Zm=1:0691 (3:2878)". 
The residuals appended to each of the empirical series repre- 
sent the excess of the computed numbers over the observed 
ones, expressed in hundredths of the former. 
Stars OF THE NORTHERN HEMISPHERE. 
According to the Durchmusterung. 
Mag. | Counted, yg orahar ty Difference. Pen A Difference. 
6 3 54 — 
14 4 4 64 | +38 
2 22 12 —90 
24 12 14 +14 21 +43 
3 5 27 —89 38 — 
3¢ 60 50 | —20 69 | +413 
4 128 _ 125 +2 
44 140 178 | +21 232 | +40 
5 379 —13 411 tf 
54 463 628 +26 745 +37 
6 1242 1179 — 5 1350 — 8 
64 2231 2215 —1 2 +9 
7 4608 4161 —Il 1 — 3 
"4 7817 +12 52 | +14 
8 14525 14686 1 14600 cs sae | 
84 28486 27590 —2 26474 — 8 
9 78185 51830 
The marked defect of the computed numbers for stars of the 
%th magnitude has led me to include the several values for 
this magnitude in the table, although they were intentionally 
Omitted in deducing the formulas. I do not think that any 
. 
