10 



♦ KNOWLEDGE ♦ 



[November 1, 1887. 



SELF-CHARTED STARS. 



N considering such a cliart of stars as appeared 

 in the number of Knowledge for May 1886, 

 considerations of singular, one might almost say 

 quaint, significance are suggested to the mind. 

 Among all those discs representing stars, and 

 each telling the same wonderful and complex 

 story, no two represent the same time. The 

 story told by that star-chart is not simultaneous. It bears 

 the same relation to a record presenting matters as they 

 actually are at a given moment that a story told by a news- 

 paper bears to a chapter in ;i volume of history. When we 

 are looking at one star-disc, we contemplate the self told 

 record of a suu as that sun was many years ago ; when we 

 turn to another sbir-disc, we see a similar record, also 

 relating to a long past epoch, but not to the same epoch. 

 One of the star-discs, regarding it as in a sense a portrait of 

 a remote sun, may be hundreds of years older than another, 

 though both were taken at the same instant on the photo- 

 graphic plate. Pi-obably within the range of this one 

 picture, with its two thousand stars, we have records 

 extending over many hundreds of years. It is true that 

 the picture represents a rich region of the Milky Way, 

 and my own theory of the Milky Way, adopted and 

 supported by such independent thinkers as Herbert 

 Spencer * in England, and Oscar Peschule in Germany, 

 recognises the whole rich galactic mass like that seen 

 in Cygnus as in reality what it appears to be (that is, 

 as truly a stellar cloud, whose farthest portions are not 

 relatively much farther from us than the nearest). Yet 

 it can hardly be but that in the same field of view are seen 

 many stars which do not belong to that cloud, but shine 

 from beyond depths far more remote. Even as regards the 

 great star-cloud itself, moreover, we have a wide range of 

 time to deal with. Judging from the length and width of 

 the great clustering aggregation of the Milky Way in 

 Cygnus, from the heart of which the chart has been taken, 

 we may infer a depth corresponding to more than one-tenth 

 of the distance of the .star-cloud regarded as a whole. 

 Supposing this distance, then, to correspond to a light- 

 iourney of one hundred years — a very moderate assumption 

 when we remember that Sirius lies at a distance of about 

 twenty years' light-journey from us — we find that the 

 farthest stars of the cluster tell us their story ten years 

 after the nearest stars. 



Thus the strange thought arises that while the chart 

 does not represent the actual state of the pictured stars at 

 the moment when the photograph was taken, it does not 

 even represent the state of those stars — either as to relative 

 position or relative lustre — at any epoch whatsoever. For 

 aught we can tell any star taken at random in the chait 

 may have been extinct many years before it painted its 

 record on the photogi-aphic plate ; or it may at the moment 

 when its light reached us have been in reality very much 

 brighter or very much fainter than its pictured record 

 would seem to show. Stars may in the meantime have 

 shone forth which are not shown in the chart, because the 

 extremities of the light-pencils by which alone their discs 

 could hi delineated had not reached within many thousands 

 of millions of miles of our solar system. Then, again, not 

 a single star in the whole chart is shown in its true 



* As regards important portions of my theory of the universe I 

 was anticipated by Mr. Herbert Spencer — though I only learned 

 this long after I had advanced that theory. But I am speaking 

 above of the Milky Way regarded as a congeries of stars, iu which 

 aspect I believe I may say that I alone established those details in 

 which my theory differs from that of the Hersohels formerly 

 accepted. 



position, and no two stars are shown in their proper rela- 

 tive position. For every star of the two thousand travel- 

 ling along through space must have some thwart motion, 

 greater or less (we may exclude as impossible the case of a 

 star moving e.ractli/ towards the solar system) ; and no two 

 stars can have exactly the same thwart motion. 



Hence have we this strange result, that a photographic 

 record which the astronomer justly regards as a most 

 marvellously exact star-chart, far more exact than any such 

 record as the most skilful astronomers can obtain observa- 

 tionally, nevertheless neither represents what is now, or 

 what ever was — precisely as here shown — at any moment of 

 time. 



MAGIC SQUARES. 



By W. Holden-. 



?s I have not been hitherto " A Constant 

 Reader of your valuable Periodical," I do 

 not know if you have dealt with the sub- 

 ject of " Magic Squares " or not ; but I 

 have thought that the enclosed would be 

 interesting to your readers. They appear 

 to me to be marvels of ingenuity. About 

 fifteen years ago the methods of construct- 

 ing these " Magic Squares," so called, was discussed in 

 " The Riddler " columns of the Addnkh Observer, of which 

 columns I have the editing. It appears that the rules for 

 constructing squares, of which the root is an odd number as 

 7 X 7, is very simple. Thus 1 have in my possession a 

 square il X 27, containing all the numbers from 1 to 27^, 

 and of course the sum of every horizontal, vertical, and 



,. , r • 1- 27- -f 1 

 diagonal line is 2/ x - 



= 9.855. But the method of 



constrttctiug it is so simple that the figures may be written 

 down consecutively without the slightest hesitation. The 

 case, however, is very difierent when the root is an even 

 number, and especially so when it is the double of a prime 

 number as 14 x 14. But at the time to which I refer, 

 Mr. E. J. C'atlow, who was then engaged as a shepherd in 

 the interior of this " island continent," turned his attention 

 to the subject, and discovered the rules for constructing 

 .squares of every kind, no matter how large. He subse- 

 quently told me that if he had not turned his attention to 

 the subject, and to the German language, his occupation 

 was so monotonous, and the solitude so profound, that he 

 feared he would have gone insane. 



Some time after his discovery of the rules referred to. 

 Ml-. Catlow wrote a paper describing thtm, and sent it to 

 Mr. C. Todd, C.M.G., our Postmaster-General and Govern- 

 ment Astronomer. The paper was read by Mr. Todd before 

 the Adelaide Philosophical Society, and he stated that in 

 all his mathematical studies he had never met with any 

 rules of the kind app'icable to all numbers. 



Curiously enough, however, while Mr. Catlow was study- 

 ing the suViject in the far north, Mr. J. B. Bassett, a school- 

 master of Willunga, thirty miles south of Adelaide, was 

 doing the same thing, and the result was the discussion in 

 the Adelaide Observer as to priority of discovery, to which 

 I have referred. 



Mr. Catlow and Mr. Bassett have both •' joined the 

 great majority," but among the papers of the latter was 

 the square of which No. 1 is a copy. You will observe 



* Although iu the earlier volumes of Knowledge we had a great 

 number (some said too large a number) of magic squares, and 

 have in MS. snlutions of the still more complex pu;;zles presented 

 by magic cubes, we print Mr. Holden's paper unhesitatingly, as 

 presenting novel and interesting developments. 



