Here it is to be remarked that under magnitude 6 are included many other than the lucid stars, namely, all down to magnitude 6.4. The last column gives the entire number of stars down to each order of magnitude.
It will be remarked that the number of stars of each order is rather more than three times that of the order next higher. How far does this law extend? Argelander's 'Durchmusterung,' which is supposed to include all stars to magnitude 9.5, gives 315,039 stars for the northern hemisphere, from which it would be inferred that the whole sky contains 630,000 stars to the ninth magnitude. Comparing this with the number 7,647 of stars to the magnitude 6.5, we see that it is forty-fold, so that it would require a ratio of about 3.5 from each magnitude to the next lower. But it is now found that Argelander's list contains, in the greater part of the heavens, all the stars to the tenth magnitude.
On the other hand, Thome's Cordoba 'Durchmusterung' gives 340,-380 stars between the parallels -22° and -42°. This is 0.14725 of the whole sky, so that, on Thome's scale of magnitude, there are about 2,311,000 stars to the tenth magnitude in the sky. This is more than three times the Argelander number to the ninth magnitude.
It would, therefore, seem that the ratio of number for each magnitude must exceed 3, even up to the tenth. If a ratio of only 3 extends four steps farther, the whole number of stars in the sky down to magnitude 14.5 inclusive must approach 200 millions. Until the international photographic chart of the sky is subjected to a detailed examination, it is impossible to make an estimation with any approach to certainty.