101 



• KNOWLEDGE * 



[Dec. 2, 1881. 



Wo can rondily nbtnin approximate volutions by lognrithmR, thus : 

 — Kor r, wo liuvo ; — 



Ipjr. 51000-67- 4-7i;t210l 

 ouo third of which - 1 57 10701 = log. .37-215 

 whence x = 37-215 feet, 

 and FL = 40— ,T =. 2-755 feet. 

 For I/, we have :— 



log. 39333-33 = 1-5017608 

 one third of which = 1-5315809 = lo';. .11 COS 

 w-hencc >i = 3 1008 feet, 

 and YM = 10— i/ = 5992 feet. 

 Thus— 



YL = 2-755 f t . ; L.V = 3237 ft. ; ' and MX = 1008 It . 

 In )iracticc, I suppose it would be more convenient to know 

 whereabouts the planes of section respectively cut the lines Dl}, 

 I'd, EH, t'.l. For this purpose all we have to do is to divide each 

 of these four lines in the same proportion as the line XY. This, 

 w-hether it is done by construction or by computation, is too simple 

 te need further explanation. I may just note, however, that — 



liD' : YX'::(ioy+{Yliy : (40)» 

 ::iG32 : 1600 



::5i :50 



so that, for the divisions along DB, FO, EH, and CA, the above 

 values for YL, LM, and MX have all to be increased in the ratio 

 i/sT '. v'so" or api)roximating as 101 to 100. Increa.siiig tliem by 

 one-hundredth, we get, supposing Im, the required points of 

 division along DB-Bt = 2783 ft.; (m = 3-209 ft.; and »i = 4018 ft. 



#ur €l)t^^ Column. 



The Two K.\ight.-j' Defence. 



WE take next a sounder form of this opening, where Black, 

 instead of retaking the Pawn at his fifth move, plays away 

 his Qneen's Knight to Queen's Book's fourtli. The game opens 



R. to K. I. Kt. to K.B.3. B. to Q.B. t. 



thus :— 1. p j^ jj ^ 2. Kt, to Qu_3_ 3. Kt. to K.B.3. 



Kt. to K.B.5. P. takes P. 



"*• pTtTQi: ^- Kt. to Q.B.l. '"''""^ '"'^ "''^' "^° '""^^ °f 



play; he may cither check with the Bishop or play P. to Q.3, de- 

 fending the Bishop while leaving it to protect the forward Queen's 

 Pawn. The first, which is the better play, will now occupy oiu- 

 attcntion. Note, that whatever play is adopted, White's attack is, 

 for the moment, over. Ue has to provide for the safety of his 

 King's Knight, in attacking which Black can dcvelope his game. 

 The opening proceeds thus : — 



6. 



B.Q.Kt.Sch . 

 P. to Q.B.3. 

 P. takes P. 

 P. takes P. 

 B. to K.2 

 P. to K.K.3 ' ^ 

 Kt. to K.B.8 

 P. to K.5 • 

 Kt. to K.5 



Qrt^"Q^ ' "'■ 



P. to K.B.l. 



11. to Q.IM 



(A) 



In position 1 ^Vliite, Hocnis to be the better off. Black has his 

 game more open, and, in fact, the attack rests for the moment 

 with him. But the attack docs not seem suflicient to compensate 

 for the Pawn which Black has lost. It will be obsenecl that at 

 move 12 Black hud to provide against the move P. to Q.B. 3, attack- 

 ing Queen, followed by P. to Q.Kt.-l attacking Iwth Knight and 

 Bishop. He might have done this by playing Bisho|> instead of 

 Q. to Q.'s third. In this case White would" still pnsh Q.B. Pown, 

 attacking Q., and on her retreating to Q.'s fourth, her best 

 move, would play P. to Q.Kt.'s fourtli. with decided advantage. Or 

 Black might have played away his Q.Kt. to Q.Kt.'s second, leaving, 

 however, his Q.B. P. undefended, and on White taking it, Black 

 Queen has to retreat to Q.'s tliird. 



On the other hand, in position 2, Black's game seems as good as 

 White's. He is a Pawn short, but his forces are better situated. 



Next week we shall carrv on the variations A and B, arising from 

 White's plaving 8. B. to" Q.R.4, or 8. Q. to K.B.3, instead of 

 B. to Q.2. 



Young players will find it a useful exercise to play several games 

 from each of the positions 1 and 2, taking the attack and defence 

 alternately, and, in everj- case, playing through the opening moves 

 till cither position 1 or position 2 is reached. 



Instead of 11. P. to K.B.4, bj- which position 1 is reached at 

 twelfth move. White may play 11. Kt. to K.Kt.4. On this Black 

 takes the Kt. with his Q.'s Bishop, White retakes with Bishop, and 

 Black plays Kt. to Q.B. 5. This leads to an even game. 



Several of our readers appear to find considerable difficulty with 

 Mr. Healcy's little problem at p. 41. two declaring flatly that there 

 must be some mistake. The solution is simply — 



■HTjito. 

 1. E. to Q.Kt. 7 (ch.) 



2. R. to Q.Kt.5. 



3. R. to Q.B.5 (ch.) 



Black. 



1. K. to B. sq. (If K. to 



R. sq., there follows 

 ]>erpetual check, unless 

 K. goes to B.sq. 



2. P. Queens. 



3. Q. takes B., stalemate. 



The other position, and Ponziani's position in oiu- last number, 

 are easy enough. Black's choice is divided between perpetual 

 chock and stalemate. 



We give, in conclusion, a little problem of our o^vn invention. 

 It presents no difficulty whatever for those who are at all proficient 

 in problem-solving ; but may amuse, for ten minutes or so. those 

 who kave not given much attention to that department of Cl.i -., 

 (The very feature which makes the problem interesting for i' , - 

 directs the former at once to the solution.) 



-PrMlileii! l)v the Editor. 



White to play and mate in two moves. 



&m- e©I)ts;t Column. 



By "Five of Cluds." 



A (IAIN we give a simple whist g-ame, taken from actual play. 

 -/r\. It is boiTow-ed from the "Westminster Papers" for 1877. 

 The first player, A, was our correspondent (and friendly critic), Mr. 

 Lewis, whose Double Dummy problems long formed so marked n 

 feature of the '' Westminster Papers." We give this time B'( 

 inferences, with notes on the play as before. The game is interest- 

 ing as showing how a good jilnyer may be led by the fall of the 

 cards in the first two or three rounds to lead out trumps even when 

 short in them, and when one of the adversaries probablv holds four. 



