Dec. 1, 1882.] 



KNOV/LEDGE • 



443 



(or u)= /i/ij!, may be taken to 



Therefore the statement, area 



mean that ive get the area between A Q, O X, and certain boundary 

 ordinates, by summing a multitude of very thin rectangles like Pn 

 between the corresponding ordinates. This is an indefinite state- 

 ment, and fy dx is called an indefinite integral. When we take 



definite limiting ordinates as An, Q X corresponding to x = Oa, and 

 1 = X (say x=a and i = b respectively), we get the definite area 

 A Q N a'; and we write 



area A Q X n = / y dm 



which me.ans that from the value of /•; dx when h is written for x, 



is to be subtracted the value when a is written for x, to give the 

 area of the space between the ordinates corresponding to these 

 values. 



Be it noticed that what we have here said about areas applies to 

 any quantity which might be represented by an area, and there- 

 fore practically to any quantity whatsoever. If we can obtain an 

 expression for the small increment of any quantity » corresponding 

 to any small increment of the variable, and can ascertain by any 

 process what quantity that is which has such increment, we can 

 determine « by the process of integration. 



Examples wlU, however, best show the value of all this. 



iBuv 2236 1'St Column. 



By " Five of Clubs." 



A WHIST CA.SE. 



A and B are partners at Whist against Y and Z. A and B are 

 four by honours, each having two. They claim two by honours and 

 score them. Towards the end of the deal A says to B, "you had 

 not two honours, had yon, partner ? " Before B replies in the 

 affirmative the trump card is turned and quitted. A and B claim 

 to score four by honours. Y Z assert that the claim is too late. — 

 Hazard. 



[It appears to us that the claim is good, provided ^'s question 

 was addressed to B in such a way as to be unmistakably the in- 

 itiation of a claim. Z had in that case heard enough to know that 

 a question was raised as to the honours, and he should either have 

 waited, or gone on dealing with the understanding that the claim 

 was made in due time, whether he finished his deal or not before 

 the position of the honours had been fuUy recalled. If A being in 

 doubt says " I think we had four by honours," he ought not to be 

 worse o£E than if he had said " We claim fonr by honours." Law 50 

 seems clearly to imply that the adversaries by questioning the score, 

 interrupt the dealer (that is, that he ought to" hold his hand till the 

 question is settled) and that they may legitimately do this if they 

 can establish their claim. Had" X stopped when A spoke, and A 

 failed to establish his claim, A" would have been free to deal again, 

 had he mis-dealt in consequence of the interruption. We may infer 

 that X should have stopped. — Five of Clubs.] 



OUB esteemed correspondent, Jlr. F. H. Lewis, has kindly 

 selected and annotated three games of singular interest, on'p 

 illustrating the advantage under certain conditions of keeping back 

 the winning trump ; the second, the advantage under other con- 

 ditions of playing the winning trump; and the third, the necessity 

 of keeping back the best of a plain suit at a critical stage in the 

 game. The first of these games runs as follows : — 



Clubs— 8, 4, 3. 

 Diamonds— 8, 6. 

 Spades— 6, 5, 4, 2. 

 Hearts- A, Q, 9, 5 



KEEPING BACK THE WIXNIXG TRUMP, 

 r. The Haxds. B. 



Club.-'— Kn, 5. 

 Diamonds — A. K, Q. 



A. 

 auhs—A, Q, 9, 2. 

 Diamonds— 7, 5, 4. 

 Spades— Q, 3. 

 Hearts— Kn, 7, 6, 2. 



Z. 



^^H^),^— K,io,7,G. 



Diamonds— Kn,10,9,5 

 Spades— A, 10. 

 Hearts— K, 8. 



THE PLAY. 

 ITOTB. — The card underlined wina the trick, and card below leads next round, 

 MK. LEWIS'S NOTES. 

 1. A leads from his longest suit, 



3. B, trusting to his partner to 

 protect the Heart suit, and being 

 strong in both the other plain suits, 

 leads a trump. Z having turned 

 the Ten, properly heads the Knave. 



4. .4 having the finesse in trumps,, 

 waits for another lead from B, but 

 he should not have continued the 

 Heart lead. B cannot be strong in 

 trumps, and A knows that he can 

 liave no strength in Hearts. A's 

 proper lead here was the Spade- 

 Queen. 



5. r having no rentree card, 

 gives Z a discard. He properly 

 abstains from continuing with 

 Heart Ace. The discard of the- 

 Spade Ten shows Y that his part- 

 ner had great numerical strength 

 in Diamonds. It was open to Z to 

 discard a Diamond, as the lead of 

 trumps was from the adversary, 

 but having four trumps originally, 

 he had hopes of utilizing one of 

 them. 



7. B is in a difficulty. He knows 

 Heart Ace to be with Y, but he- 

 knows also that he can have but 

 one more Diamond, if any. As A 

 continued the Heart suit, he pro- 

 bably wants the finesse in trumps. 

 B, therefore, plays trump. 



8. As Z discarded Spade Ten, B 

 discards Spade Knave to show that 



lowest Spade is equal to the- 

 Ten. 



9. Acting upon this hint, A plays 

 Spade Queen. 



10. Z can count B's hand. If 

 he leads the winning trump, and 

 draws the Club Two from A, he 

 can then lead only Diamonds, and 



O O^J o 



6 O O O ^^ 



o o| lo^ol ,^^ I o 

 *~+l [*~+] I*~*] f*~4^ 



7 *4-| * * + 



his 



11. B here properly plays Spade 

 Eight. If Z passes it, B continues 

 the suit, and A getting the discard 

 of the Heart, Z loses the game. Z 

 is not to be trapped. He knows 

 he can save the game by forcing 

 A, who has the losing Heart. 





Q. T. Y. asks why, at trick 7 

 (p. 410, col. 2), B should know 

 that A had four trumps. " Correct 

 Card," he says, indicates the higher 

 as the proper card to play first, to 

 show four trumps. What " Correct 

 Card " says is, " Should partner 

 lead trumps and you have four or 

 more, make the signal," &c. and 

 the signal consists in playing un- 

 necessarily a higher card before a 

 lower. Precisely: in plaijitig such 

 a card, not in Icadintj it. As we 

 lead the highest of a sequence and play the lowest, so to show four 

 trumps we play a higher card before a lower, but return a lower 

 card before a higher (this last being also the settled rule for 

 showing that we held originally fonr cards of the suit). Thus, if my 

 partner leads a small trnmp, and second player puts the Queen on, 

 I holding Ten, Eight, Three, Two, play third hand the Three, and 

 in the ne.xt round the Two, whether leading or plivjing to the trick ; 

 the play, of the Three first round shows I hold £(>ui m the suit, so 

 soon as the Two has appeared. But if, with the same cards, secouu 

 hand plays a small card, and my Ten makes, I return the Two, and 

 the third round then shows that I held four originaUv, — Five op 

 Clcbs. 



X.—" A and B are partners. B leads when it is A's turn j 1' and Z 

 call on A to lead from a particular suit, and B takes up the card 



