Aug. 11, 1882.] 



• KNOAVLEDGE ♦ 



189 



divided by a function. We will deal with it both ways, as more 

 effectively illustrating this part of our subject. 



Let 2/ = ?^ 



cosa- 



By the first rule we get at onco the first portion of the required 

 coefficient. For, treating cos a: as a constant, we take the differential 

 coefficient of sin x, that is, cos x, and get the first portion, viz., 



^2!_^orl. 

 cos X 

 For the second part we treat sin ar as a constant, and have to 



multiply it by the differential coefficient of the other factor 



cos X. 

 By what was shown in the preceding case, this is 



-_l_x-,;nrr.or?L'Lf. 

 cos" X 



cos'x 



This multiplied by sin x gires for the second portion 

 the required differential coefficient is 



nc 



This would be obtained at once from' rule C, which states that 

 where one function is divided by another, the differential coefficieEt 

 is equal to 

 numerator's dif. coefficient _ numer. x denominator's dif. coefficient 



denominator (denominator)'' 



or we may, as more symmetrical, put the differential coefficient of 

 a fraction in the form — 



dif. coef. X deuom. — denominator's dif. coef. x numer 



(denominator)" 

 yVe have now had a good deal of rule-stating and rule-illustrating. 

 In our next we shall apply some of the rules to a few' problems 

 of maxima and minima. Probably some readers who have begun 

 to grow weary may be induced, when they see the value of the 

 rules, to master them more thoroughly than they have yet done. 



dBuv C&esfs Column. 



By Mephisto. 



SEVENTH GAME IN THE MATCH BETWEEN MESSRS. 

 A. A. BOWLEY AND W. T. PIERCE, OP BRIGHTON. 



GlUOCO PlAXO. 



White. Black. 



A. BOWLET. 



' to K.5 



Whits. 



1. P to K-1 



2. KKt to B3 



3. B to B J. 



4. P to QB3 



5. P to Q4 

 G. B to K3 (r) 



7. B to QKto 



8. B to E4 



9. P takes P 



10. Kt to B3 



11. B to Kt3 



12. Castles 



13. P takes B 



14. P takes B (<?) KKt to K 



15. K to Rs(| Kt to R4 

 IG. R to KKtsq 1' to R3 



W. T. PlEECE. 



Pto K 4 

 QKt to B3 

 B toB4 

 P to Q3 (a) 

 B to Kt3 (b) 

 B to Kt5 

 P to QR3 

 P takes P 

 B to R4 (ch) 

 P to QKt 4 

 Q to B3 

 QB takes Kt 

 B takes Kt 



IS. P takes P 

 IS). B to B2 



W. T. PlKBCl 



P takes P 



Q to B3 (f) 



K to Qsq 



Kt to Kt3 



Kt to K4 



! 20. B to Q4 



21. P to KO 



22. P takes P (ch)K takes P 



23. B to K4 Q to K3 

 2 1. Q to B2 (/) P to Kt4 



25. QR to Ksq QKt to B3 



26. QIJtakesKt(.j')Kt takes B 



27. B to B5 Q to QB3 



28. R to K3 (;.) KR to Ksq 



29. B to Q7 (0 R takes B 



30. Q to R7 (ch) K to Bsq 



31. Q to R8 (ch) K to B2 



32. Q to R7 (ch) 

 Drawn (j). 



NOTES. 



(a) Inferior to 4Kt to B3. 



(6) 5. P takes P is to bo preferred. 



(c) G. P takes P, Q to K2 (best). (If P takes P or Kt takes P, 

 Black loses a Pawn.) 7. P takes P, Q takes P (ch). 8. Q to K2, 

 y takes Q. 9. B takes Q, P takes P, and White's game is slightly 

 to bo preferred. 



(<i) White ought to have taken with the Queen, as the exchange 

 of Queens would be iu his favour, considering he has a strong centre 

 and two Bishops. 



(e) If Q takes P, then B to Q4 with a strong attack. 



(/) White's play is very good, but he now misses his chance. Ho 

 ought to have plaved 24. P to KB4, which would have won, i.e. : — 



24. P to KB4 24. P to QB4 (We see nothing better.) 



25. B takes Kt 25. R takes Q 



20. QR takes R and White will win in a few moves. 

 The Black Queen is threatened by B to Q5, and in reply to Q or K 

 moving, White will play E takes kt P, Ac. 



(g) Probably played absent-minded, for B takes QKt wins a 

 piece. 



(h) White cannot take the Knight on account of Q takes P (ch) 

 followed on R interposing by R to Q8 (ch), and winning the Queen. 

 28. R to Kt3 would also have been bad on account of 28. Kt takes 

 P. 29. B to K4, Kt takes R, 30. Q to Kt3 (ch) would be useless, as 

 the Black Queen would cover on B5. 



(i) An ingenious move, which secures a draw. 



(j) Black cannot depart from his position, for if he played K to 

 K3, then Q to Kt6 (ch) would win the Queen, i.e., K to Q4. Q to 

 K4(ch). KtoQ3. R to Qsq (ch), and wins. Again, if 32 K to B3, 

 then Q takes RP (ch), and on Kt interposing, Q takes KtP (cb). 

 K to B2, Q to B5 (ch), Ac. 



PROBLEM No. 50. 

 By Alfeei) B. Palme 



WHITB. 



White to play and mate in four i 



End Position, No. 46, by Leonard P. Recs, p. 139. 



R to<J7 (ch) 

 Q to B7 (ch) 

 Kt to B6 (ch), Ac. 



Problem No. 

 Kt toKt2 

 R takes P 

 R to K5 mate 



Kt to B 1 and B mates 



Kt (oh) and 3B mates. 



1. K takes R 



2. E or Kt interposes. 



by Muzio, p. 139. 



1. K to B4 



2. K to Ktl 



(a) 1. K to Q3 

 ((.) 1. B takes P 



ANSWERS TO CORRESPONDENTS. 

 •,• Please address Chess-Editor. 



Leonard P. Eces. — Thanks for Problem and Game, 'i'ou anj 

 right about Problem No. 45. Thanks for your offer, but the in- 

 debtedness is really on our side. Wo, however, accept, under the 

 condition that " we make thee judge," for which purpose we would 

 send you all solutions received. 



Ffynono Club.— Colour of men is merely n matter of mutual 

 understanding, but for convenience of notation it is preferable for 

 the first player to have White. 



Berrow. — Problem received with thanks. 



Alfred B. Palmer.— (ianie received with thanks. 



Correct solutions received of Problem No. -18 :— Herbert Jacobs, 

 J. A. Bower and C. H. I.vlle, J. K. Milne, Tofsir, Edward B. Norton, 

 Geo. H. Bonner, W. A. Lee. No. 49 :— Alfml R. Palmer, Schmenko. 

 J. J. Kave, John Watson. From Squire, J. K. Milne, J. G. (Dublin), 

 A. R. Johnson, G. Woodcock, Kit, Berrow, A. U. Cooke, E. J. J., 

 Geo. H. Bonner, W. A. Lee. 



W. Mead. — No, wo have not forgotten. 



E. C. II. — Solution wrong. 



A Reader wishes to play a game by correspondence. 



SiXfEXCE each will be paid for copies of No. 3 of Knowledge. 

 Apjily, or addre8.H, Wyman A Sons, 74 and 5, Great Qneon-stnect, 

 London, W.C. Tlic publishers have on hand, for sale, a few copies 

 of Knowledge, Nos. 5, G, and 7. Price Bd. each. 



