January 1, 1900.] 



KNOWLEDGE. 



in 



shell the external limit of which is the maximum dis- 

 tance at which a star of the first degree of intrinsic 

 brightness is just visible, and within this shell only 

 stars of the first degree of iutriusic brightness will be 

 visible with the same aperture. But will an increase 

 of aperture render visible all the stars of the second 

 degree of intrinsic brightness, i.e., all the stars lying 

 within the shell ? It will not, because some of the 

 stars — viz., those near the outer surface of the shell — 

 will be so faint that their feeble rays will be either 

 entirely absorbed, or so much absorbed by our atmo- 

 sphere and telescope, that the limited sensibility of ou'- 

 eyes or photographic plates will be unable to show 

 them. But it may be argued that these second degree 

 stars may be bright enough to be seen with the larger 

 apei-ture even from the outer surface of the shell. Tliis 

 may be true in the limited case we are considering, 

 but not when we consider infinity. 



In all probability stars consist of 100 or 1000 degrees 

 of intrinsic brightness. Wc must therefore consider 

 100 or 1000 shells around the inner sphere, in each suc- 

 ceeding one of which, with a given aperture, fewer stars 

 are seen. If the feeble rays from a star of the 100th 

 degree of intrinsic brightness bo just able to pene- 

 trate our atmosphere from, say. the .50th shell, then all 

 the 100th degree stars beyond this distance will be 

 quite invisible with any aperture. Stars of the 100th 

 and 99th degrees of intrinsic brightness will be visible 

 beyond the 51st shell; those of the 100th, 99th, and 

 9Sth degrees beyond the 52nd shell, and so on till we 

 come to the 150th shell, where stars of the 1st degree 

 of intrinsic brightness become invisible, and which 

 therefore forms the limit of the visible stellar universe. 

 Must we not, then, expect a thinning out of faint stars 

 somewhat similar to that shown in fig. 2, p. 154 (July) :- 

 And may we not therefore brush away those " clouds 

 of cosmical dust which conceal eveything beyond " our 

 faintest stars ? 



But, even disregarding absorption altogether, is the 

 question of sky-light from an infinite number of stars 

 so simple as Mr. Burns assumes ? Someone has 

 defined " nothing " as " a bung-hole without a barrel " ! 

 Similarly, a star at infinite distance is a star without 

 a magnitude. For if it be at infinite distance it must 

 be infinitely faint, and its disc infinitely small, i.e., 

 like a geometrical point, without magnitude. How, 

 then, can an infinite number of such points cover any- 

 thing at all, much less the entire sky ? And again, 

 could the light of a star at infinite distance ever reach 

 us ? Would not the star be at a finite distance if it 

 did ? Nor will the excessively faint stars that are at 

 finite distances produce any apparent brightness, for 

 the image of each star falls upon a different point of 

 the retina ; and since each is invisible, they will bo 

 collectively invisible. 



Must we not therefore conclude that although the 

 stellar universe may be infinite, the visible portion of 

 it must be finite ; and that no reasoning, from 

 numerical data or otherwise, can ever advance us a step 

 further ? 



It seems to me that the ciuestion is not " Is the 

 stellar universe finite?" — that we can never know— - 

 but " Is it probable that within the finite visible 

 universe stars are uniformlv distributed?" 



Madeira. Wm. Anderson. 



TO THE EDITORS OF KNOWLEDGE. 



Sirs, — Having read the article in last month's issue 

 under the above heading, it occurred to me that the 



writer, Mr. Burns, would go a good way iu answering 

 the question if he were to define in what sense he uses 

 the word " infinite." 



When scientists speak of the number of the stars 

 being infinite, they either mean indefinite, or givo to 

 the word its strict philosophical meaning. Taken in 

 the first sense the word infinite is quite intelligible as 

 applied to the number of the stars, man's power of 

 observation being so limited. To adopt the second 

 sense is to put forward an absurdity. 



It is scarcely necessary to observe that the idea of 

 infinity in the strict sense docs not admit of circum- 

 scription ; of either increase or decrease ; and accord- 

 ingly excludes the idea of extension or multitude. 



Surely this sense of the infinite eannol, be predicated 

 of tiie stellar universe, made up as it is of units. 



R. J. CONNELL. 



[Mr. George H. Hill (Streatham), writing on this 

 suljject, "Is the Stellar Universe Finite?" challenges 

 Dr. Burns' conclusion (Knowledge, November, 1899, 

 p. 'J49), that " if the number of stars were infinite we 

 should have the whole sky one blaze of light," on the 

 ground that Dr. Burns assumes that what is lost in 

 stellar radiation by distance, is gained in number. He 

 writes: — "But if the illuminating area were to de- 

 crease owing to increase of distance, more rapidly than 

 it increased, owing to greater numbers, surely how- 

 ever infinitely the process might be continued it would 

 never give us a blazing sky." This is of course true if 

 the rate of decrease be sufliciently high, and simply 

 expresses in other words my own criticism of Dr. Burns' 

 fourth hypothesis. Mr. Hill gives my suggestion more 

 at length, and conceives of space " as containing prac- 

 tically isolated stellar groups or systems (on a colossal 

 scale), every star visible to us belonging to but one 

 such system, while other (exterior) systems appear to 

 us only in the form of nebulae." He further suggests 

 that there would naturally be a tendency to thin out 

 towards the margin of such a system, in accordance with 

 Mr. W. H. S. Monck's remark (Knowledge, August, 

 1899, p. 179) that "a thinning out commences at 

 (comparatively speaking) no great distance from the 

 earth or sun." It must be borne in mind that the 

 idea that the irresolvable nebulre were " external 

 galaxies " was refuted long ago by Herbert Spencer, 

 Proctor, and others. The clustering of nebulse round 

 the poles of the Milky Way is a clear proof that they 

 form an integral part of the samei structure with it ; as 

 their occurrence with stars in the Nebecula Major is a 

 proof that they exist at substantially the same distances 

 from us, as do the stars.] 



The " Seas " op the Moon. — Mr. James Macgeorge 

 criticises Mr. J. Gr. O. Tepper's paper on "The ' Seas ' of 

 the Moon " (Knowledge, November, 1899, p. 251), on 

 the ground that Mr. Tepper has not shown that the 

 Moon ever had an a+mosphere sufficiently dense to sup- 

 port any form of organic life, and calculates the amount 

 of atmosphere which it would have possessed had it 

 attracted to itself a proportion of atmosphere, as com- 

 pai-ed with that of the earth, corresjionding to its 

 gravity. As the figures may bo of some little interest 

 I give them here more precisely than Mr. Macgeorge 

 has done. Taking the diameter of the earth as 7,926 

 miles and of the Moon, 2,160 miles; wc have the earth 

 ,3.67 times the Moon in diameter, or 13.47 times in sur- 

 face area. Its mass, however, is 78 times as great. If 

 then the total mass of the earth's atmosphere be 78 

 times that of the Moon we shall have 5.8 times the 



