Jas. 26, 1883.] 



KNOWLEDGE ♦ 



61 



AOE (for z G15E= / AOE, and Z BEG= / OEA), we see 

 that the resolved part alont; E O of the attraction of small elliptical 

 section at B on particle at E = ;jxita mass x cos B EO-i-(BE)' 

 =/iprir (GB) 2?>» see OBG cos BEO + (BE)', where /i repre- 

 sents the attraction of a nuit of mass at a unit of distance ; and 

 since B G = B E O, while 



GB:BE = OA:OE = r:ii 



attraction ol element at B on particle at E = — ' in direc- 



tion E O. 



In other words, it is the same as though there were a spherical 

 shell, of radius r and thickness r, around G as centre, and the 

 element of this shell intercepted by conical surfact- having vortex 

 at (; and small vertical angle 2^, were transferred to O. 



The same may be proved of the resolved part of attraction of 

 element at A on imrtiele at E, in direction E O. The resolved parts 

 of the attractions of elements at B aud A, at right angles to E O, 

 are equal and opposite, and need not, therefore, be considered. 



This being true of all such sections as wo have supposed at B 

 and A, is true for the whole spherical shell, — which, therefore, 

 attracts the particle E, as if the whole mass of the shell were at (). 



Cob. — As a homogeneous sphere, or a sphere whose density varies 

 according to any law with the distance from the centre, may he 

 supposed made up of an indefinitely great number of concentric 

 shells of small thickness and uniform density, it foUotcs that the 

 retultant attraction of a sphere of either kind on an exterior particle 

 is the same as though the whole mass of the sphere were collected at 

 the centre. 



^r Cl}f99 Column. 



By Mephisto. 



THE following game, which was recently played, will be found 

 to contain interesting positions for study : — 

 YIEXXA OPEXIXG. 



■WTiile. 

 Mephiato. 



1. P to K4 



2. Kt togB.3((i) 



3. P to B ► 



4. Kt to B3 



5. B to Kt5 



6. P to Q3 



7. B takes Kt 



8. P takes P 



9. KttakesP(J) 



10. Kt to Kt 4 



11. Q takes Kt 



12. K to B sq (</) 



13. Q to Kt3 (i) 



14. B to B4 (J) 



Bl.ck. 

 U. E. Bird. 

 P to K 4 

 B to B4 (i.) 

 P to Q-l 

 Kt to QB3 

 B to Q? (r) 

 Kt to B3 

 B takes B 

 P takes P 

 Q to Q5 (p) 

 Kt tiikcs Kt 

 CastIesKK( f) 

 P to B4 (h) 

 P takes P 



White. Black. 



Mephisto. U. £. Bird. 



E to KR sq. (r) P to KKt4 

 R to K6 (s) R to B4 

 K to B sq (0 K to Kt2 



R to R3 

 R toK3 

 P to Kt3 

 P to R4 



K to B2 

 R to Kti (i') 

 K to R4 

 P to Ktt 



15. 

 16. 

 17. 

 18. 

 19. 

 20. 

 21. 

 22. 

 23. 

 24. 

 25. 



Bl 



R takes R 

 Q toB2 

 Castles (0 

 R takes Q (n 

 R to K4 (p) 

 R to B sq 

 R to K2 

 Kt to K t 

 R takes B 

 K toQ2 

 K to K2 



K takes B (I) 

 B toQ3 

 Q to Kt5 

 P to KG („>) 

 ) P takes Q (r,) 

 R to KB S(| 

 B takes P (q) 

 B to Kt6 

 B takes Kt 

 P toKR4 

 K to R2 

 P toRa 



R takes B (i) 

 R takes P 

 P takes P 

 R to Kt4 

 R to QB4 

 K takes P 

 P to Kt3 (ch) 

 R to B4 

 PtoB4 

 R to B7 

 PtoQ4 

 P toQ5 

 P to B5 

 P toQG 

 P takes P 

 I' to <J7 

 K to B sq 

 P queens 



P takes R 

 P takes J' 

 K to Kt3 

 K to R4 

 P to Kt5 

 K to R5 

 K to R6 (if) 

 R to QBi 

 R to KR4 

 R to Rsq (.) 

 K to R7 

 R toRG 

 R to R3 (v) 

 P takes P 

 K to R8 (:) 

 R to R7 (ch) 

 R to R sq 

 Resigns 



NOTES. 



(a) Safer than the King's Knight's Gambit. 



(b) Admissible ; cautious players, however, prefer Kt to QB3. 



(c) Best. In this jjosition it is not uncommon for players to drop 

 into a, bad variation by playing instead — 



5. Kt to B3 I 7. B takes Kt P takes B. 



6. P to Q 3 Castles | 8. Kt to QR4 



Threatening Kt takes B, which will either triple the Pawns on the 

 Bishop's file or win the King's Pawn. 



(d) A dangerous capture, therefore not advisable. 

 (c) Initiating a strong attack. 



(/) A very good move, and better than 11. Q to B 7 (ch), for 

 after 12. K to Q sq. Castles ; 13. Q to B3, Black's chance of attack 

 is diminished. 



(g) In consequence of Black's good play the position is full of 

 difficulties. Black threatens the dangerous move of P to B4, and 

 thereby to open up the KB file for his King's Rook, or even the 

 K's file for his Queen's Rook, which would bo fatal. The only 

 other possible move seems to be Kt to K2, wliich, however, would 

 also result badly, i.e., 12. Kt to K2, Q to B7 (cli). 13. K to Q sq, 

 P to B4 (if Q retires P takes P with advantage). 14. P takes P, 

 Q takes KtP, aud Black must win the exchange by 15. Q takes Q, 

 B takes Q. 16. R to K sq, B to B7. 



(/i) Brave, and destroys White's hopes for peace and quietness. 

 Watch the following ingenious combination : — If in reply to P to B4. 

 13. R takes P, B to Q2 ! 14. R takes R, R takes K, now White's 

 Queen is attacked and Black also tlireatens check «-ith the 

 Queen followed by the Rook, which must result fatally. For 

 instance, it 15. Q to Kt 5 (apparentlv his best), then follows Q to- 

 B7 (ch). 16. K to Q sq, Q to B s" (ch). 17. K to Q 2, R to B7 

 (ch), and mate in two moves. 



(i) White of course expected an attack when he ventured oa 

 9. Kt takes P, but when there is an attack there is also a defence. 

 This move must be taken in connection with the following one as 

 being the soundest reply. 



(.)■) If now P takes P, then Castles, White will recover his Pawn, 

 and tnrn a dangerous j)osition into one of comparative safety. 



(i) Black was not justified in trj-ing to overcome White's tena- 

 city by such impatient means ; he might still have retained a good 

 game "by the following play : -14. P takes P. 15. Castles, B to- 

 Q3 (best). 10. B takes B (forced), P to Q7 (ch). 17. K to Kt sq. 

 P takes B, and Black has the better game. 



(/) The best way of meeting Black's attack ; had White attempted 

 to preserve his Rook, then Q takes KtP would had involved him in 

 difficulties. 



(m) A fine specimen of Black's noted brilliancy. If B takes R, 

 18. Q takes B, and White stands somewhat better. 



(n) The only move to avoid loss. 



(o) We can now better point out Black's plans, and why he did 

 not take the Rook. He now threatens the Rook as well as B takes 

 KtP. If to prevent this White plavs 19. R to KKt4, then follows 

 R to KB sq. 20. R to B sq, P to KR4. 21. R to KtG, K to R2. 

 22. R takes B (best), B takes KtP (best). 23. R takes P (best), 

 R takes R. 21. R to Q7, B to B3. 25. R takes BP, R takes RP, 

 and Black has two passed Pawns. 



(p) The right move ; it avoids all danger, and if Black takes the 

 Rook, White remains with a fair ending of Knight against Bishop. 



(q) Although B lakes R was sound play, we cannot condemn 

 this bold move, because with the Pawn on B7, Black could fairly 

 reckon upon drawing the game, but it also left him a (very) 

 remote chance of winning. Had he played B takes R he would 

 have had notliing left but to play for a draw. 



(r) The ensuing ending is most interesting. Wliite must now 

 endeavour to utilize his advantage — by no means an easy task. 

 R to R sq is the beginning of a series of moves to an-ive at a 

 favourable position to sacrifice a Rook for the Bishop with 

 advantage. 



(s) A most important move, as it cuts off the King from the 

 Bishop and wins time ultimately. If White takes the Bishop 

 (the only way of winning) he would lose unless ho could also 

 get some Pawns. There would be no hope of doing this if the- 

 King were near the Bishop. 



(t) To render the Rook on R sq available. 



(i() As will be seen, this and the following moves force White's 

 hands, as Black obviously threatens to break through White's 

 Pawns. It would, of course, not have been good to play R takes 

 B now, for Black threatens to play havoc amongst White's Pawns. 



(••) An opportune moment, and promising the utmost possible- 

 advantage. 



(h) Black has shown all along that he disdains to play for a 

 draw, but the move in the text positively loses. 



\x) " Hope springs eternal in the human breast." If 43. R 

 takes P, then I! to B sq (ch), followed by K takes P. 



