Feb. 2, 1863.] 



♦ KNOWLEDGE ♦ 



77 



But, by Euclid 11. 3, M K.MF = M K.K F + M K', and by 11.5, 

 MC' = DK.KC + M K' 

 .•.MK.KF = DK.KC 



Now, if A B C D be inscribed in a circle Tvhose centre is (), and 

 which cnts EG in I', Q, wo have (Euclid III. 35) UK.KC = 

 PK.KQ.-.MK.KF = FK.KQ, and a circle drawn through 

 P, P, y, will pass through M. In the same manner it may be 

 shown to pass through N, the middle point of A B. But the circle 

 described upon F as diameter passes through M, N, since O M F 

 and O N F are right angles. And as only one circle can pass 

 through the three points F, SI, N, it follows that P, Q lie on the 

 circle who diameter is F O. Therefore, OFF, O Q F are right 

 angles, and P, Q are tlie points of contact of the tangent from F. 

 Q.E.D. 



[Note. —The theorem is easily shown to be true for any conic 

 section, for the circle O may be projected so as to become any given 

 conic on another plane, and the lines P B A, F C D (which are quite 

 arbitrary) may bo so taken as to be projected from the same centre 

 apon any given pair of lines catting the conic. Tlicn all the lines 

 and points of contact and intersection in the two figures will 

 necessarily correspond each to each.] — J. C. S. 



Eebatum. — At p. CO, col. 2, I. 14 from bottom, for i G.G A rea<l 

 B G.G A. 



<!^ur 21236 ist Column. 



By " Five of Clubs." 



WE give this week one of the finest hands at Whist ever played. 

 Z was Cavendish, and the game is number XXXVIII. in his 

 book. We shall have some ntore notes and general remarks tu 

 make on this well-played partie next week. 



r. 



Hearts — 5, 4. 

 Spades — A, Kn, 6. 

 Diamonds — Q, Kn, 9, 



8,5. 

 Clubs — i, 3, 2. 



A. 

 Bearts—9, 7. 



Diamonds — 10, 7, G, 4, 2 

 Clubs— Q, U. 



The Hands. 



B. 



Hearts— A. Q, 10, 0. 

 Spades— Q, 10, 8. 

 Diamonds — A, 3. 

 Clubs— A, K, Kn, S. 



Hearts— K, Kn, 8, 3, 

 Spades— K, 3, 2. 

 Diamonds — K. 

 Clubs- 10, 9, 7, 5. 



Score. — Four all. 



A Y 







o o ♦ o 





^fij 1 * 1 1 1 1+7+ 

 ^m * ♦ * + 



^^ I + 1 1 I [+_+ 



♦ +1 1+ +1 1*^ [+~+ 



♦ ♦) [+ + l^sS I i! + 



o*ol PHi I o I ^ 



+ ' + 



+ 

 +^+ 



NOTES AND REMARKS. 



NOTK.— The card undirlinpd wins the 

 trick, and card below leads next round. 



1. A leadf penultimate of his 

 long suit. Queen lies with V; 

 Three with B, unless 1 is signall- 

 ing (.4 alone knows this). H has 

 probably no more. 



2. B knows that probably Z has 

 no more Diamonds, while the Two 

 has not appeared. But there is a 

 strong probability that ,4 has led 

 from a live-card suit (since ten 

 Diamonds lie between A and Y). 

 It is, therefore, not likely that Y 

 has begun a signal. Of course, Z 

 may be signalling from King, 

 Queen, but it is unlikely. 



3. We donbt whether A should 

 have returned his partner's lead of 

 trumps. Strength in trumps is 

 manifestly divided between B and 

 Z, and very great strength, for 

 nine trumps lie in these two hands. 

 ,4 knows, therefore, that though 

 B may have been strong enough 

 to lead trumps, Z may bo stronger. 

 A puts B in a bad position by re- 

 turning trumps. A would have 

 done bettor to load Club Queen, 

 in the hope that B may be strong 

 in Clubs. This would have won : 

 though that proves nothing. Two 

 tricks were already made. Three 

 more would have been made in 

 Clubs. A would have made the 

 sixth trick by ruiling Clubs ; and 

 the Ace of trumps would have won 

 the odd trick and the game. After 

 trick three, as plnj'ed, B knows 

 that Y has no more trumps, nor A 

 (note the trnmp card). Z knows, 

 also, that neither A nor Y have any 

 more trumps. 



4. B wisely gives up trumps. 



5. After this B knows the fourth 

 round in Clubs must go to the 

 enemy. 



6. ,4 and B now want only one 

 trick to win, and it looks as if they 

 must get it. 



7. B leads A's suit. 



8. Very good play by Z. The 

 position is plain enougli, though 

 how many Whist playeis fail to 

 recognise such things. 1 he second 

 best trump lies with B, so that if 

 Z has to lead trumps, Y Z must 

 lose. The King of Spades is 

 absolutely useless to Z, for if he 

 takes a trick with it, the enemy 

 must make a trick in trumps and 

 the game. If .-1 J? have the Ace, 

 the game is gone any way. If Fhas 

 the Ace and wins the King with 



it, 1' Z may still win ; but how apt Y would be not to win his 

 partner's King ! Therefore, to simplify his partner's jilay as much 

 as possible, to " leave no jioint of strategy to partner to which he 

 can attend himself," Z throws away his useless King. 



9. But now another danger lurks in store for Z and his partner. 

 Z has got rid of one winning card too many, but he still has another, 

 his third trump. If Y make the ninth trick, Z must win the 

 tenth or eleventh trick (it matters not which) and lose the game. 

 Therefore, Z plays the grand coup : ho trumps his partner's 

 winning Diamond. 



10 leads losing Spade, and thus enables his partner, after 

 winning trick eleven, — 



12 to lead up to Z's tenaoe, giving Y Z the odd trick and the 

 game. 



10 





Erratum.- — ^Whist game, p. 15, last two tricks, interchange C 10 

 andD 9. 



