156 



KNOWLEDGE 



[August 1, 1891. 



Sir John Hersehel extended the observations of his 

 father to the southern heavens, and showed that 

 there was a simihir ckistering of the smaller nebuhc 

 on the southern side of the Milky Way, and a similar 

 intimate connection between the distribution of stars 

 and the distribution of nebuhe in the southern 

 hemisphere (see Cajv Observations, p. 134) ; but it 

 was not till 1858 that the obvious conclusion from 

 these observations was drawn by Mr. Herbert Spencer 

 in a remarkable paper on " The Nebular Hypothesis," 

 pubhshed in the WctitminMcr Ecrieir. He remarked, " If 

 there were but one nebula, it would be a curious coinci- 

 dence Avere this one nebula so placed in the distant regions 

 of space as to agree in direction with a starless spot in our 

 own sidereal system. If there were but two uebuliP, and 

 both were so placed, the coincidence would be excessively 

 strange ; what then shall we say on iinding that there are 

 thousands of nebuhe so placed '? Shall we believe that in 

 thousands of cases these far-removed galaxies happen to 

 agree in their visible positions with the thin places in our 

 own galaxy? Such a behef is impossible." 



Mr. Herbert Spencer's paper was not illustrated by 

 charts, and the force of his reasoning was not generally 

 perceived till some ten years afterwards, when Prof. 

 Cleveland Abbe drew attention in the Monthly Xotkrn of the 

 Eoyal Astronomical Society for May, 1867, to the intimate 

 connection between the distribution of nebula:' in space and 

 stars ; and Mr. Proctor, in 1869, constructed some charts 

 on an equi- surface isrojection, which graphically put his 

 readers in possession of the facts and carried conviction to 

 all who read his remarks. 



The theory that the nebulae were distinct galaxies in- 

 volved the assumption that light can reach us fi-om regions 

 many thousand times more remote than the stream of 

 stars which compose our own galaxy ; and it also involved 

 the assumption that the matter of the universe is aggre- 

 gated into clusters, separated by immense barren spaces, 

 in which we must assume that there are very few luminous 

 stars, and but few dark stars which would absorb hght, as 

 well as comparatively very Uttle opaque matter distributed 

 as meteors are distributed in the region of space we are 

 familiar with. 



We have evidence that the greater part of the lucid stars 

 belong to the galactic system, but the large proper motion 

 of some stars, taken in conjunction with their small 

 parallax, afibrds endence, as Prof. Simon Newcomb has 

 pointed out, that they will in time pass away from our 

 galaxy.'- The regions outside our galaxy cannot, therefore, 

 be absolutely barren, but however sparsely luminous stars 

 are distributed through space, if there were no absorption 

 of light iij its passage through the ether, and no opaque 

 bodies to blot out the light of distant stars, it would be 

 impossible, as Olbers long ago pointed out, to draw a 

 Ime in any direction which would not in an infinite 

 imiverse pass through some luminous star, and the whole 

 heavens ought to shine with the average brightness of 

 such stars. 



That the heavens are comparatively dark may, there- 

 fore, be taken as proof either that the light-transmitting 

 ether is not perfectly elastic, or that there are numerous 

 dark bodies in space that blot out the light which we 

 should otherwise derive from the more distant parts of the 

 universe. 



* Prof Simon Xewcomb lias shown in liis Fopxdar Asfronomv 

 that making tlie most liberal assumptions as to the number and 

 masses of the stars of our galactic system, the highest speed which a 

 body could attain if it fell from an infinite distance through such a 

 stellar system would be 25 miles a second, a velocity which is 

 certainly smaller than that of many stars. 



THE MAGIC SQUARE OF FOUR. 

 To the Editor of Knowi^edge. 



Deab Sir, — It may Interest some of your readers to 

 know that the deficiency of 32 squares (short of Frenicle's 

 total of 880), mentioned in my letter in the April number 

 of Knowledge, has been supplied by Dr. .1. Willis, of 

 Bradford, who has seen Frenicle's collection and given it 

 a careful examination. It appears that Type C {riik my 

 article in March number) really has 801 varieties, and not 

 merely 272. I may as well mention at the same time, in 

 justice to Mr. Cram, that it was through an oversight that 

 I obtained only 80 extra squares of this type from him. 

 He meant to have given me seven instead of five, in which 

 case I should have had 7x16 instead of 5x16 extra. 



The following analysis of Frenicle's number may, there- 

 fore, be now considered as correct: — A, B, D, each 48 ; C, 

 304; E, F, each 96; G, I, J, L, each 56; and H, K, 

 each 8.— Total 880. 



Whilst writing, I may perhaps be allowed to make two 

 other corrections in my article. The first is a misprint ; 

 page 47, first column, the first row of the square (1) should 

 be 1 6 11 16, not 1 6 11 6. Lastly, the first sentence in 

 the last paragraph in the same column is wrong. The 

 four varieties mentioned in the third hue are obtained by 

 transposing for 8, and 4 for 12, and (("(•(' virxa (which 

 doubles the number of squares), and then transposing the 

 two centre columns (which again doubles the number), 

 thus making four varieties. 



In conclusion, it may be worth while to quote Dr. 

 Willis's opinion, that " it is extremely improbable that 

 other squares of four exist in addition to these 880, as 

 Frenicle appears to have proceeded by finding by trial all 

 those combinations which satisfy the conditions that the 

 sum of the fom- corner numbers, as well as that of the fom* 

 numbers in the middle of the square, must equal the 

 normal 34." 



T. S. Babrett. 



[P.S. — Frenicle's articles, in which his 880 squares 

 occur, may be seen in the British Museum. They are 

 printed in a volume entitled " Divers Ouvrages des 

 Mathematique et de Physique, par Messrs. de TAcademie 

 Koyal des Sciences ; Paris, 1693." This book is cata- 

 logued under the name Frenicle de Bessy, and its library 

 mark is 49 f. 1.] 



Mr. P. F. Kend.\ll, F.G.S., wishes us to announce that 

 a Committee has been formed for collecting information 

 mth respect to masses of Kock or Boulders distributed 

 over the North-West of England. Mr. Kendall, whose 

 address is 16, Leegate Road, Heaton Moor, Stockport, is 

 acting as Secretary of the Committee, and will be glad to 

 communicate with anyone willing to collect information in 

 their district for the Committee. 



THE OBSERVATION OF RED STARS. 



By Miss A. M. Clerke, Authoress of " Thf System of the 



Stars," and " The History of Astronomy duriiig the 19th 



Century," dr., de. 



'• "T" 'jr 'T'HY should not stars change in colour as in 



% /% / light?" Baron Von Zach asked tentatively 



\l \t close upon seventy years ago, and the 



" f remark gave point to his re-publication, in 



1822, of " Lalande's List of Red Stars," the 



first compiled with the help of the telescope. Now, 



excellent reasons might be found why such objects should 



