KNCV/L-EDGE 



137 



Let us btndy this result a little. 



Remembering that the differential coefficient of a quantity ex- 

 presses the rate at which the quantity is increasing, wo see that 

 the above result implies that as wo increase the angle the sine in- 



creases, until X is a right angle 



But after x has passed this 



value, cos. x is negative. This implies that the sine thenceforth 

 diminishes ; and we know as a matter of fact that the sine does 

 diminish as the angle passes the fight angle. 



Again ; notice how the differential coefficient implies the rate of 

 change. We know that cos. x is unity, or has its greatest value, 

 when a; = 0. As »■ changes from then the sine changes fastest. 

 Again ; cos. x is nought when .r is a right angle, and very small 

 when X is near!}' a right angle. Hence the sine changes very 

 slowly as the angle is passing the right angle. All this, of course, 

 is very obvious without any reference to the differential calonlns. 

 But it serves well to illustrate the application of the calculus to 

 more difficult inquiries. 



I leave the reader to prove by a similar construction that, 



,hj 



"bvionslv also, if 



®i\t miln^t Column* 



SIU,— I send you a game from actual play, which I iiopo will be 

 both interesting and instructive to your readers. I have 

 annotated the play for the benefit of the less experienced players. — 

 Yours, Ac, Frederic H. Lewi.-s. 



Temple. 



We commend the following game to the careful study of our 

 numerous Whist students. 'Ihe play is good throughout, except the 

 mistake on Y'a part, to which Mr. Lewis calls attention in his re- 

 marks ; but Y'a intention was excellent, and it was only A's deeper 

 play which foiled it. V had to take several things into account, .ind 

 he took all points carefully into account except one : viz., that the 

 lead could bo thrown into Z'shand. The abundant signalling in the 

 game is worth noticing, as also the way in which B omits the usual 

 signal for length in suit headed by Ace, Queen, Knave. 



Tiu: IIaxi.s. 



Diamonds — (J, C, o, ■ 

 Spades— 8, G. 

 Hearts— K. 

 Clubs— Kn, 10, .-,, ••!. 



Diamonds— H. 

 Spades— 10, 5, I, 

 Hearts— A, Q,Kn 

 Clnbs— A, fi. 



ViamoniU-K. 7. 

 Spades— Kn, 7. 

 Hearts— 10, 7, 5, I 

 Clubs— K,Q,S, 4. 



Diamnnds—A, Kn, 10, 



Spades— A, K,Q,9,3. 

 Hearts— fS. 



C:ubs— !i, 7. 



tangent BT, tho angle ABT is a right angle. Wo know this to ho 

 not approximately, but exactly true ; but the reader must not be 

 eatislicd until he sees that tho line of reasoning given here jiroicn it 

 to bo so. 



THE PLAY. 

 Dtlcrlineil wine the tritli, and card bflow leads next round. 

 REMARKS, INFERENCES, Ac.» 



1. With five trumps, and five 

 comparatively small cards, A pro- 

 perly leads from his plain suit 

 [playing the penultimate, though 

 if the score were different, a trump 

 lead would bo permissible, and, 

 according to Polo, advisable, but 

 tho rule " always lead a trump 

 from five," is open to question]. 

 The fall of tho nine from Z shows 

 A that Z either has no more Clubs 

 or is signalling [unless, which ia 

 less likely, Y held Queen only; in 

 which case Z may have the King, 

 and B have four Clubs left.] 



2. B opens his strong suit. 



3. B, although he has six Hearts, 

 continues with tho Queen, rather 

 than with the Knave [seo Leads, 

 ic] in order that A, having 

 dropped the King, may not be in 

 doubt. A refuses to overtrump Z, 

 because it is clear to him that Z'b 

 hand consists of Sjiadcs and 

 trumps : he therefore discards a 

 Spade. 



4. Z sees his Spades in danger, 

 and apparently from the weak 

 hand. He plays, therefore, to find 

 the King in his partner's hand, or 

 linesso on tho return. [A plays 

 tho penultimate trump, showing 

 his partner (next round) that he 

 held five originally.] 



5. Z is obliged to play the Ace, 

 so as to get the first force on A 

 before he est-blishes his Club suit. 

 [Tho care with which Z attends to 

 this little matter will seem strange 

 to those who think it a Whisb 

 offcnco of tho first magnitude to 

 give the enemy a chance of ruffing 

 — they nover call it " forcing," 

 by the way — or to fail to give one's 

 partner such a chance. It may 

 bo worth their while, if such there 

 bo among our readci-s, for these 

 unwise players to try tho effect of 

 Z's omitting to force.] 



8. r passes, in the expectation 

 that .1 will continue the Club, in 

 which ho maintains the tcnacc. 

 Ho thinks if he takes it, ho mast 

 force Z at tho risk of his being 

 overtrumped. But ho did not 

 take into account that Z's trumps 

 nuLst bo Knave, Ten, for if A had 

 had tho two best, ho would pro- 

 bably have drawn the trumps. Y'n 

 play was to win tho Clnb, force Z 

 with the Heart, thus keeping the 

 second best Club when .1 was 

 forced in return with the Club, so 

 winning tho game. Z completes 

 his signal. 

 Oand 10. [Well playod, A !] Tho play of Yin the last trick lets A 

 into the whole of his hand. It is clear to him that Y is keeping up 

 tho tenace, and that he has not the best Heart, v^'splay is then very 

 luotty. By jilaying the Queen of trumps he throws, in tho next 

 trick, the load into Z's hand, taking tho chance of finding B with a 

 winning sjmdo. Tho rest of the hand plays itself. 



CnA.MBS OF Hoi-niNG Certain Ha.vds at Whist. — The following 

 calculation will show what is the chance of holding a hand at Whist 



Tho notes within brackets are by " Fire of Clubs." 



