of the bright Fixed Stars. 329 
It is thus easy to ascertain the total number of stars in the 
firmament for each grade of magnitude within Heis’s limits. 
The results are especially trustworthy, since every individual 
magnitude has been determined by careful and repeated com- 
parisons with established standards and the same scale; an 
there now arises the interesting question, how far the accurate 
numbers given by the two Uranometries, for stars as bright as 
the 6th magnitude throughout the entire heavens, would agree 
with the rougher estimates of a number of stars eleven times 
greater, but ‘Situated in the northern hemisphere only and 
including the 81 magnitude 
have therefore devoted some labor to the independent 
determination of a formula which should represent as well as 
possible the results derived from the Uranometries alone, upon 
the hypothesis already stated. The best value which I have 
been able to deduce for the constant ratio of the light of stars 
of successive magnitudes is 0°4988, the degree of accordance of 
which with observation upon our fundamental assumptions may 
be inferred from the appended table, which gives the number 
of stars for each half unit of magnitude, as deduced from the 
Uranometries, and from the formula 
Zim=8'2384 (80184), 
together with the peer oh coda tarot as in the preceding 
table. Those stars of r Heis’s Uranometry which are 
oie for the fractional shins ¢ of. a magnitude, are combined to 
form the numbers for the fractional halves in our table; a 
eee procedure, but the only practical one under the circum- 
s 
NuMBER OF STaRs IN THE HEAVENS. 
Uranometries. ' 
Mag. Formula. Difference. 
N 8 Total 
1 . 6 14 153 | +10 
14 7 4 cB LT +35 
2 25 20 45 395 —53 
24 35 33 68 51 SS 
3 55 41 96 9 — 8 
34 103 87 190 155 — 33 
4 133 108 240 269 +18 
44 254 154 408 467 4-17 
5 392 240 632 811 +22 
5} 563 | 1259 || 1409 +16 
6 1374 1075 449 ' 0 
64 fee 2022 ener e566} cS 
7 ease 3317 pe een 7392 Sona 
The formula 
Various — 8 suggested by this table. 
corresponding to ou theses differs greatly from the former 
ones, both in the fo} es and the ratio. The degree of 
