Oct. 3, 1884.] 



* KNOV\ALEDGE 



285 



^^ 



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SOLUTION OF FIGURE PUZZLE (13?8). 

 [1423]— Let X be the number. Writing the figures in order 

 B C D E F A is equivalent to multiplying x by 10, adding A and 

 subtracting 10' A. 



/. 10!t + A-10«A = 3a;. 



DK. LARDNBR AND TRANSATLANTIC NAVIGATION. 



[1419] — May I be permitted to point out that the late Dr. 

 Lardner gave an emphatic denial to the statement (which I have 

 before heard, and which he takes pains to rebut as a popular 

 error), i.e., that he asserted Atlantic steam navigation to be im- 

 possible. He says that at the British Association Meeting in 1836, 

 he advocated one of the projects. At p. 118, Vol. X., of the Museum 

 of Science and Art, appears an extract from the Times of 1837, 

 showing his ideas on the subject, which were simply that too much 

 should not be immediately expected, and that caution should be 

 used. I do not know if he ever held a different opinion, but it not, 

 I consider it only fair to his memory to notice these facts. He 

 adds : — " What l" did .affirm and maintain in 1836-7 was, that the 

 long sea voyages by steam which were contemplated, conld not at 

 that time be maintained with that regularity and certainty which 

 are indispensable to commercial success, by any revenue which 

 could be expected from tratBo alone, and that, without a Govern- 

 ment subsidy of a considerable amount, such lines of steamers, 

 although they might be started, could not be permanently main- 

 tained." He then goes on to notice what was the actual subse- 

 quent fate of the earliest Atlantic steamers, which quite corroborates 

 what he had advanced. He likewise mentions that, " long ante- 

 cedent to the epoch now adverted to, the Atlantic had actually 

 been crossed by the steamers Savannah and Cwrofoa." 



Simplex. 



ORTHOGRAPHIC MAPS. 



[1420] — In an oblique orthographic map of a hemisphere, if 

 yon cross the ellipse that represents the equator, by an equal and 

 similar one, turned the contrary way, this ellipse will pass through 

 the foci of all the traces of meridians, and afford a wonderfully 

 ready way of both finding their ends and striking them all with 

 one trammel. I should like to see this demonstrated. E. L. G. 



THE WICKED PLEA. 

 [1421] — " The Wicked Flea" and all other insects hate creosote' 

 which I find is more effective than Keating's Powder. 



John Alex. Ollaed. 



AN INVALID ON THE COVENTRY CHAIR. 



[1422] — If Mr. Browning could put himself in the place of an 

 invalid, I don't think he would talk of the " Coventy chair " super- 

 seding the present Bath chair. He would know that " a crawling 

 pace of about two miles an hour " is more suitable to the nerves of 

 an invalid than the tearing pace of a tricycle. Besides, the 

 "Coventry chair" would be excluded from the parade and the 



pier favourite resorts of invalids at seaside places — and would 



have to keep in the road, where the fear of collision with horse- 

 vehicles is very distressing to an invalid who cannot stir from his 

 place, whatever happens. If he wishes to go only in the roads and 

 streets, he had better go for a drive in an ordinary carriage, which, 

 being of a larger size than a Bath chair or tricycle, can hold its 

 own against other vehicles. I speak feelingly, for, even in this 

 quiet place, I am always in a state of trepidation till my chair 

 reaches the parade. E- C. H. 



Worthing. 



Similarly, 



C = 



7x=(10«-l) A 



30x + B-10« B = 2ac 

 14ai 



D = 



562 



A= 



B 



E 



999999 



^_28a_ 

 999999 

 35a; 



999999 999999 



But F-i-lO E-^10=D■^10' C + 10'B-HO^ A = ^!; 



999999 



„ ^ 999950 



F = 



999999 

 49 



7r 



999999 142857 

 Now F must be an integer less than 10, and 7 is prime to 

 142857 .'. j; must = 142857. 



.". 142857 is the number required. Kit. 



[1424]— About a fortnight ago a friend sent mn the puzzle given 

 by E. Bidders in letter 1398. It appeared, I think, in the Liverpool 

 Courier. 



I recognised it as a curious property of the number formed by 

 the recurring decimal representing the vulgar fraction f . 



i=i42857 

 AB C DE F 

 ABCDEF = 142857 = the number 

 BCDEFA = 4 28571 = 3 times the number 

 CDEFAB = 285714 = twice 

 DEFABC = 857142 = 6 times „ 



EFABCD = 571428 = 4 times „ 



FABCDE = 714285 = 5 times „ 



R. B. 



[Correct solutions, mainly, it would seem, by the system of trial 

 and error, have also been received from E. C. H., H. K., C. J. B., 

 F. B. Whitmore, F. G. S., P. P. G. Goolden, E. 0. H., G. H. Howe, 

 J. McD., T. K. H., and others.— Ed.] 



COINCIDENCES. 



[1425]— Seeing in your issue of July 25th last a letter headed 

 " A Coincidence," it has struck mo that an experience of mine m 

 the same direction may amuse some of your readers. 



One night several years ago I went to a dance in town. I dressed 

 at a well-known hotel, only going there just before the dance, gave 

 no name, left my luggage, on which there was no name, and 

 returned to sleep about 3 o'clock. Next morning, on commg dowjn, 

 a porter addressed me by name, and handed me a card. It bore the 

 printed name of a man whom I only knew by name. Over the 

 name was written in pencil my name, initials all correct, and on 

 the back, also in pencil, a direction to an address curiously like 

 mine (the number identical, and one being Old Square and the 

 other Old Jewrv). and in a very similar handwriting to t^i^t of, and 

 signed with the initials of, a man whose whereabouts I did not 

 know and whom I was anxious to see. I asked the porter how he 

 knew it was for me ; he said it had been left while I was out for a 

 gentleman who was expected that night, and I was the only one 

 who had come. 



Now I never was in that hotel before or since. I only made up 

 mv mind to go ten minutes before I went. The card was meant 

 for some one "else, who bore (as I found out by a directory) my 

 exact name in initials and only with a small variation m full. That 

 person was expected there that night and did not come. The card 

 belon<red to a man of whose existence I Imew. The writing on the 

 back Resembled that of, and the initials were the same as those of 

 a man whom I wanted to see, but who was then in India (as 1 

 found out later), and the address given was curiously like mine. 

 And yet my connection with the whole thing was a pure accident. 

 A document so going astrav in a play or novel would be set down 

 as an improbability ; but this was what did happen m the case of 

 this card. I may add that none of the names were common ones, 

 and one is a particularly uncommon one. It seems to me to be a 

 nest of " coincidences." EssUL. 



■ years since, I was waiting for a train to arrive at 

 arge town, that I might go on by it. I saw an 



[1426]— A few ; 



the station of a large , „ „ -, , j i, j i 



elderlv gentleman, whose face struck me and who looked iiard at 

 me. We soon recognised each other, though we had not met for 

 forty-two years. After talking for some time of old days, the train 



