instrument will photograph, and the other only to take in those to the eleventh magnitude. Of the latter it is intended to prepare a catalogue. Some portions of the German and English catalogues have already been published, and their results will be made use of in the course of the present work.

one star

But

Closely connected with the work of cataloguing the stars is that of enumerating them. In view of what may possibly be associated with any Numbering planets with intellectual beings the Stars. inhabiting them—the question how many stars there are in the heavens is one of perennial interest. beyond the general statement we have already made, this question does not admit of even an approximate answer. The question which we should be able to answer is this: How many stars are there of each distinguishable magnitude? How many of the first magnitude, of the second, of the third, and so on to the smallest that have been estimated? Even in this form we cannot answer the question in a way which is at the same time precise and satisfactory. One magnitude merges into another by insensible gradations, so that no two observers will agree as to where the line should be drawn between them. The difficulty is enhanced by the modern system-very necessary, it is true-of regarding magnitude as a continuously varying quantity and estimating it with all possible precision. In adjusting the new system. to the old one, it may be assumed that an average star of any given magnitude on the old system would be designated by the corresponding number on the

new system. For example, an average star of the fourth magnitude would be called 4.0; one of the fifth, 5.0, etc. Then the brightest stars which formerly were called of the fourth magnitude, would now be, if the estimate were carried to hundredths, 3.50, while the faintest would be 4.50. What were formerly called stars of the fifth magnitude would range from 4.50 to 5.50, and so on. But we meet with a difficulty when we come to the sixth magnitude. On the modern system, magnitude 6.0 represents the faintest star visible to the naked eye; but the stars formerly included in this class would, on the average, be somewhat brighter than this, because none could be catalogued except those so visible.

The most complete enumeration of the lucid stars. by magnitudes has been made by Pickering (Annals of the Harvard Observatory, vol. xiv.). The stars were classified by half-magnitudes, calling

Number of Stars.

For the northern stars, Pickering used the Harvard Photometry; for the southern, Gould's Uranometria Argentina. A zone from the equator to 30° south declination is common to both; for this zone I use Gould. The number of each class in the entire sky, north and south of the celestial equator, is as follows:

It would seem from this that the number of lucid stars in the southern celestial hemisphere is 315 greater than in the northern. But this arises wholly from a seemingly greater number of stars of magnitude 6. In the zone o° to 30° S., Pickering has 214 stars of this class fewer than Gould. Hence it is not likely that there is really any greater richness of the southern sky.

The total number of lucid stars is thus found to be 5333. But it is not likely that stars of magnitudes 6.1 and 6.2 should be included in this class, though this is done in the above table. From a careful study and comparison of the same data from Pickering and Gould, Schiaparelli numerated the stars to magnitude 6.0. He found:

For most purposes a classification by entire magnitudes is more instructive than one by half-magnitudes. From the third magnitude downward we may assume that forty per cent. of the stars of each half-magnitude belong to the magnitude next above, and sixty per cent. to that next below. We thus find that of

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 between three and four times that of the order next brighter. 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, 7647, of stars to the magnitude 6.5, we see that it is fortyfold, 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. There is, therefore, no evidence of any falling off in the ratio of increase up to the tenth magnitude.