THE PROGRESS OF SCIENCE. 



761 



of the resulting cosmologies may be, 

 they must, nevertheless, be regarded as 

 little more than guesses, since the sci- 

 entific data necessary to a sound con- 

 ception of the problem are still lacking. 

 The chief elements required are the 

 determination of the number, distribu- 

 tion, constitution, brightness, distance 

 and motions of the stars. All these 

 determinations are now possible to 

 science, at least in part, although only 

 a few decades ago several of them would 

 have seemed impossible. 



A recent contribution of great im- : 

 portance in this line is a study of the 

 ' Distribution of Stars,' by Professor 

 Edward C. Pickering, director of the 

 Harvard Observatory. The memoir 

 forms Part V., Vol. XLVIII., of the 

 Annals of the Observatory. This re- 

 search was rendered possible only as a 

 result of the extended work in stellar 

 photometry which has been carried on 

 by the author during the last quarter 

 of a century. Nearly two million ob- 

 servations of the brightness of the 

 stars have been made by him and his 

 assistants at the Cambridge and 

 Arequipa stations of the observatory. 

 Upon these results especially, and also 

 upon the various Durchmusterungs, 

 and the work of Father Hagen, the in- 

 vestigation is based. 



Two very important facts are 

 brought out by this research. Hither- 

 to it has been supposed that the 

 proportion of faint stars to the whole 

 number is much greater in the milky 

 way than in other parts of the sky. 

 This may still be true for very faint 

 stars, but Professor Pickering shows 

 conclusively that, for all stars whose 

 magnitudes have been determined, the 

 proportion of bright and faint stars is 

 practically the same in the milky way 

 as elsewhere in the sky, and that the 

 stellar density is only about twice as 

 great. 



From theoretical considerations Pro- 

 fessor Pickering derives the formula, 

 log N = 0.60 M + A, in which N is the 

 number of stars brighter than a given 

 magnitude M. A comparison of the 



results of observation, however, shows 

 that the coefficient of M is never 

 greater than 0.52, and that this value, 

 which is fairly uniform for the brighter 

 stars, grows rapidly less for the faintest 

 stars whose magnitudes have been de- 

 termined. An inspection of Table 

 XXI. of the memoir shows that for 

 the stars visible to the naked eye, the 

 whole number brighter than a given 

 magnitude is from three to four times 

 as great as that of the next lower 

 magnitude; that is, for example, there 

 are 3.3 times as many stars of the 

 fifth magnitude and brighter, as of the 

 fourth magnitude and brighter. For 

 fainter stars the ratio steadily de- 

 creases, until for the twelfth magni- 

 tude the number is little more than 

 twice that for the eleventh magnitude. 

 This curve of distribution is remark- 

 able. If the rate of decrease continues 

 with equal rapidity for successive mag- 

 nitudes, it would lead apparently toward 

 the ratio unity at the eighteenth or 

 twentieth magnitude, which would im- 

 ply the limit — possibly very ill-defined 

 — of our universe. This conclusion is, 

 however, still very uncertain, since 

 reliable observations of brightness are 

 available only to the twelfth magni- 

 tude. Professor Pickering is careful 

 to draw few conclusions beyond the 

 reach of actual observation. He says, 

 however, ' As estimates are given 

 which are still more uncertain than 

 these, it may be stated that the 

 number of stars corresponding to the 

 magnitude 15, or which would be visible 

 in a telescope of 15 inches aperture, 

 would be about eighteen million, and 

 the increase for larger apertures would 

 be surprisingly small.' With the mount- 

 ing of the great five-foot reflector at 

 Cambridge, however, there seems to be 

 little doubt but that the determina- 

 tions of brightness will be extended 

 to the faintest stars which can be 

 reached at the present day. Before 

 many years we shall perhaps know 

 whether our universe is simply a 

 limited region in the infinite. 



