100 



KNO^A/'LEDGE • 



[Dec. 2, 1881. 



lliiM to illimtrnto my particular difliciilty) of tlio rcinnrk (if a friend 

 who said ho know RoniothinK whirh " trnvclled " quicker than light, 

 and on beinn^ osked to exphiin, answered ni'jhl. I had some difliculty 

 in ex|ilninin|^ to him tlml sinht «ii« merely a mental interpretation 

 ■ ■f sensation produced on a ^ifuwin- orfjan by the light which had 

 iilreody "travelled" from the distant object to tho organ in 

 i;uestiun. 



Uidess I have been misinformed, tho present tendency of scientific 

 thought is to do awny with the idea of "attraction " altogether, as 

 a ligment of the inlcllcct. \Y\ial wo call gravity, or any other form 

 of BO-cnllcd attraction, is merely the tendency to fall in the direction 

 of least push. Thus, suppose a railway truck between two engines 

 lending to push it in opposite directions. It cannot move both ways 

 ot once. It therefore moves in tho direction of the weaker engine. 

 Something analogous to this is the modern explanation of attraction 

 so-called. A stone falls to tho earth because the pressures exerted 

 on it aro least in the direction of tho earth — no attraction at all in 

 nature — all push and strife. — Yours, Jkiinr.KsiiRouGii. 



[78] — 1 was much grutilied to find this (piestion raised in the last 

 nutnber ot Knowlepge. It is an exceedingly interesting subject, 

 and one I would like to sec treated in a competent manner. In an 

 article by yourself, entitled "The Mystery of Gravity," you inti- 

 mated that you might at son)e future time describe a method by 

 which gi-avity might be generated and propagated, founded on the 

 views of Lc Sage. I write from memory, and therefore cannot bo 

 certain of the exact words. Will j'ou kindly say whether this 

 promise has ever been fulfilled ? If not, would you kindly favour 

 the readers of Knowledge and myself by stating your views on this 

 truly great question. — Yours, &c., T. J. HiCKix. 



ELECTRICAL BELLS. 



[79] — As a subscriber to your promising weekly, I have come 

 across the extract from the Times, No. 1, page 14, wherein the 

 writer recommends electric bells for private houses. 



1 beg to say from long experience, electric bells arc very trouble- 

 some in private houses, however they may answer in hotels, where 

 there is generally a yearhj charge to keep them in order. 



There is a better system in use in Government offices, and that 

 system is tho pneumatic, which is so simple and durable, that I 

 wonder the Times should ignore "pneumatic" while writing up 

 " electric." 



I have pneumatic in my house, and the excellency of the whole 

 arrangement is, beyond question, worth bringing to tho front, cer- 

 tainly quite as much so as electric is by the Times. There is no 

 battery nor anything whatever to attend to. — Y'ours truly, 



M. Tester. 



THE FIFTEEN PUZZLE. 



[80] — I enclose a sTiorl proof, which I gave in the Bri-jhtrm Herald 

 for May 22, 1880. 



Take 15 tickets, numbered from 1 to 13, and arrange them in a 

 row in any order. Let every instance in which a lower number is 

 further on in the series than a higher number be called a disarrange- 

 ment. Note whether the number of such disarrangements is even 

 or odd. A cyclic interchange of any odd number of tho tickets will 

 make an even difference in the number of disarrangements, and, 

 therefore, no combination of such interchanges can convert an order 

 with an odd number of disarrangements into an order with an even 

 number of disarrangements. 



Now arrange the 15 tickets in a square, and bring the blank 

 space to the place it is to occupy finally. Then after this, the game 

 consists of the travels of this blank space over the board, finally 

 ending where it started. The route pursued consists partly of 

 tracks followed and again retraced, which make no ultimate dif- 

 ference to the number of disarrangements — and partly of closed 

 paths travelled round, which are cyclic interchanges of an odd 

 number of tickets. No number of such ojierations can make the 

 number of disarrangements zero if it happened originally to bo odd. 

 —Yours, A-c, AuTiifR Black. 



[81] — .\s you invite cin-respondence, I send yon the enclosed very 

 remarkable arrangement of figures. A year or two ago 1 sent thorn 

 to the publisher of juvenile books. I believe it was not attended 

 to. If so, I am of opinion that it is unknown. 



At first sight it seems a confusion of figures ; but, on examina- 

 tion, tho arrangement will be found to be very simple. 



You will perceive that the unit 1 is placed under the central 



square ; if yon follow the fignres to tho end, all confusion will 

 Tanisli. To understand it is a verj- different thing. 



West Brompton, Km: 11, 1871. H. S. 



The Hi|unre of all ndd numbers may be so arranged that the totals 

 of all tho columns — perjiendicidar, horizontal, and diagonal — shall 

 bo the same. And the totals will be the larger* half of the H|Tiaro 

 multiplied by the odd number. 'I'hus the totals of — 



5x 25-i-2 = 13x 5 = 05, the total. 



7x 49-»-2 = 25x 7-175 „ 



Ox 81-!-2-)l X 9 = 300 „ 

 11x121-4-2 = 01x11 = 071 ,, 



SqiAiiE.s OF "Onu" NiMBrn. 



5 tolaJ»=65. 



Square 25h-2 = 13 x 5 = 65, the total? 

 7 totals =175. 



Square — = 25 x 7 = 175, the totals. 

 9 totals=S69. 



Square of 9 x 81-i-2 = 41 x 9=369, the totals. 



[This is a known method of making magic squares. We find 

 in the magic stpiarc for the numbers 1 to 9 ; thus : — 



3 .". : 



in which also other methods of solution are indicated.— Eo. 

 • The larger half means the actual half plns-s J. 



