Sept. 2l', 1882.] 



• KNOWLEDGE • 



285 



8elf-rcstraint in legitimate pleasure-taking may be better em- 

 ployed (and 13 all wanted) in resisting temptation to what is 

 really wrong — if it be only to bad temper. I believe in 

 a doctrine of mental and moral correlation as surely as 

 in the correlation of physical forces, and hold that the self- 

 conceit, detraction, and sour temper of ascetics (to say nothing of 

 subtler defects) are directly due to their waste of moral energy in 

 resisting and rejecting innocent pleasures. — Alg. Bbay. You are 

 right. The (p-t-1) is in the numerator. Your letter appeared 

 because it was the easiest way of indicating the problem. I 

 could not afford time for an answer which would have been 

 of no use to any other reader. I do not think you have 

 quit© caught the answer to the parados. Tlie paradox arises 

 in reality from our assuming knowledge that does not exist. 

 The proof for the series 1- +2= +3^ -Hie, has occurred to others. 

 It shall appear; though, probably, after some delay. — A. H. wishes 

 to know how photographs are produced in which the figures stand 

 out brilliantly white, like statuary, against a dark background ; 

 also to know which are the best books for Stage 10 Mathematics of 

 the Science and Art Department. — J. P. "We could not venture to 

 give an opinion without seeing the planisphere. The course you 

 propose would be the best. — Loeesmith. Thanks. — J. C. L. There 

 is some mistake, certaiEily. The H. A. of mean sun quoted is not 

 exactly that of the mean sun at noon at Greenwich on May 28, 

 187i; the seconds should be 25.1.3, not 25.73 ; but it is near enough 

 to be very far from the R. A. at noon at New York. — Iota (1). The 

 moon appears larger near the horizon, through an optical delusion 

 only ; when measured with any angle-measuring instrument, the 

 moon is found to bo smaller near the horizon. (2.) The moon turns 

 on its own axis once in every Inaar month. — G. M. The question is 

 rather too wide to be dealt with in this section; may be made the 

 subject, of an article. — Haltaeds. Are not all those cases expli- 

 cable as mere coincidences ? Considering how many thoughts arise 

 in us and how many events occur to us, such coincidences must be 

 always occurring. Why should we wonder when they do occur ? 



MATHEMATICAL ANSWERS. 



GwERFYL. If you had worked correctly, you could not have an 

 error of five millions in deaUng with numbers of 8, 9, or 10 digits. 

 Give some example, and the matter may be explained. 1 do not 

 know of an eight-dec. -place logs. The seven-decimals suffice for all 

 ordinary purposes. The calculation of logs is a subject rather too 

 complex and requiring too much space to be dealt with in Answers. 

 — R. N. Thanks for solution of Problem 44. It avoids the diffi- 

 culty you point out in mine. The other point you notice is obviously 

 an erratum. Will find space for solution if possible ; but we are 

 already much in arrears with mathematical matter, and conse- 

 quently short of space. 



0ut aaa&i'st column* 



By "Five of Clubs." 



THE following game illustrates early lead from a sIk 

 trumps when the long suit is established, and there 

 re-entering cards : — 



The Ha.nds. 



A. 



Hearts— X, :i. 

 Clubs— K, 10. 9. 



3. 

 Diamonds — A. S. 

 Spades— .\. K. 



Hearts~K, Kn, 1. 

 Clubs- -A, 7. 

 Diamonds — Kn, 10. ; 

 Spades — Kn, ;i, iJ, i. 



T. 



Hearts — Q, 7, 2. 

 Clubs— Q, 8. 

 Diamonds— 6, 5, 



10, 8, 7, 



ireu.-ts~\i>, 9, 8, 0, 5. 

 Clubs— Kn. 2. 

 Diamonds— K, Q, 9, 8. 

 Spades — Q, 2. 



CiVTlox — Bfwsro of Ihe Pnrty ofTerini; limitations of tho "Dig Wavwlev" 

 and Big J •■ Pen. Sold by all rospectablc Stationers throughout the world. 

 •' Thev come as a boon and a bleasinc to men. 

 The Piokwick. the Owl, and the Warerley Pen." 

 Also the Hindoo Pens, Diagonal Points, Ifos. 1, 3, and 3. Sample Box with all 

 ine kinds, Is. Id. by post. Patentees of pens and penholders, Macnivcn & 

 BT„Tr,"'K ;S"; , r i'"j l"" ?I»i"'J-'s Government. Offices, 23, Blair-slreel, 

 Edinburgh. (Eslabhshed 1770). 



A T B Z 



4. 4-1 ,^**\ I II 4- 



1 1 '? I !<? t? 



1^ 



It round. 

 EEMAEKS, INFERENCES, itc. 



1. A having seven Clubs, leads 

 the antepenultimate. 



2. B having no very good suit, 

 returns his partner's load ; from 

 tho fall of the cards he sees that 

 all the remaining Clubs are with A. 



3. Although with only two 

 trumps, A having five winning 

 Clubs, two winning Spades, and 

 Diamond Ace, leads trumps, hoping, 

 by forcing, if necessary, to get out 

 trumps and bring in bis long suit. 

 He leads Ace to ensure two rounds 

 of trumps at least. 



4. B knows from A's play that 

 A has not led from a long suit of 

 trumps. For if A had had five 

 trumps, headed by tho Ace, ho 

 would have led trumps first round. 

 B should have helped A in getting 

 out as many trumps as possible, 

 by playing his King and leading 

 the Knave. Tlie finesse succeeds, 

 as it happens, but it was not good 

 play. 



5. Remaining trumps are with Z. 



6. B leads Spades in response to 

 .4's discard of a Diamond. 



7. A forces Z, of course. Y dis- 

 cards from his weakest suit ; B 



9. A again forces Z. 



The rest of the game plays itself. 



O O 



Answees to Coeeespondents. 

 J. MoTLE and L. Pa.nteex.(?) 

 Whist will continue weekly (or 

 perhaps only fortnightly) later. 

 — A. GoEHAM. 1. See No's, follow- 

 ing 13, in which Ps play of the 

 Ten is discussed at length. My 

 corrected opinion is that the play 

 was not good, except under tho 

 particular circumstances. 1' knew 

 his partner would draw the desired 

 inference. Y and Z had played 

 much together — that was the only 

 excuse for Y's departure from rule. 

 2. In the first case under this 

 heading, Z having enacted one 

 penalty, no other can bo enacted. 

 B can take the card again into his 

 hand or leave it exposed, it can 

 scarcely matter which. In the 

 .second case, where the other 

 iieualty is enacted, tho card can 

 Im- called either as a lead, or in its 

 t uni (if playable without a revoke) 

 to a trick. 3. In No. 43, p. 22, A 

 has already shown that ho holds 

 but three Diamonds by leading 

 Queen and following with a smaller 

 one. What now information can 

 ho give by playing Si.x instead of 

 Two second round ? B knows that A has not moro than three 

 cards, and also that ho must have had three at least ; for there aro 

 no possible conditions under which Queen would be led from Quoeii 

 and another at the first round. 4. Honours are counted, I imngino 

 (though tho game without honours is far better.aiid moro scientific), 

 because inferior players would have but a poor chance were it not 

 for the cleineut of chance introduced by counting honours. Count- 

 ing half honours, that is, two for four honours, and one for three 

 honours against one, would be a fair comiiromiso. if tho clubs 

 could agree in recommending it. — Nemo, (i.) I know nothing of 

 Bezicpio. (ii.) A having already won the trick. B, on taking his 

 partner's trick, seeing A about to lead, snys : " Partner, the trick 

 is mine; don't play?" Is the remark allowable? It seems to 

 us B is not only allowed but bound to prevent kis partner, if 

 ho can, from loading out of turn. But it would have been bettor 

 to say simply, " ily lead, partner."— FiVK or Ci.l;BS. 



® 



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