808 



• KNO^A/'LEDGE • 



[Vbb. 3, 1882. 



[Lol r bu rato jtor poanil per moDth, bo Ihut ul tho rnd of a month 

 lil bonimnK £ (1 -f r). Tlion, ut end of tirat mouth i! - in ilao ; at 



end of Kuiond JC- + (l + r)JC-; at end of third, C-+ (l + r)£" 

 fi 6 5 5 



+ (1 + r)'Jt- ; aiul. liiially. "t end of twenty months- 

 5 



|l + (l + r) + (l + r)»+ + (1 + r)»-'] i- ' 



-ilfl)!l-i4.[(,.r)«-ni:« 



1 T r— 1 5 Or 



Now, JtlOO nt rnt.' 



.L'l |>cr ninntb, compound iutenst. 

 Hhould bo equal in viiliio at ond of twenty months to £- paid 

 0, for twenty months. Thnt is 

 (1 + r)»£100= [(1 + r)»-l]£' 



monthly, ns above, for twenty months. Thnt is — 



.5r 



(1 + r)" (6-500r)=lJ 

 Henoo 20 log. (1 + r) + log. (G - 500r) == lop. C. 



Wo can find r tentatively from this equation. It is cleiU' r cannot 

 bo (i^oater than (i^-.'jOO. — El).] 



[26]--What will .010 annually at r pur .£1 per annum compound 

 interest amount to to in twenty years ? — J. R. — [We presnmo this 

 is onr correspondent's question. Tho method applied to previous 

 qiiefition gives for this amount at tho end of twenty years 

 [(l + r)" -1] (iilO-T-r)— Ed.] 



[27]--Tho value of a diamond varies as tho S(|uare of its weight. 

 A diamond falls and breaks into three pieces ; what proportion does 

 their probable value bear to that of the original diamond ? — P. A. 

 MacMaiion. 



[28]— E(JCATION.— 



a+x a—x — 



i/a + '/(a. + x) \/a—^a — x 



Maihematiccs Novocasteokcm. 



[The Equations of "RHeverte"in our last seem to have been 

 made " pie " of. We very carefully corrected the second (the first 

 was rightly given), wi-iting out in margin the left side of the equa- 

 tion afresh, but now tlie right side b.is entirely disappeared, and 

 the first equation has gone wrong. It .should be, I think. 

 x' 1/' a? V 



— +r =~ +~ =o + 6 



a X y 

 I cannot recollect what was on the right side of the (Jther 

 equation. Will " Kncvcrtc " oblige by repeating it ? Readers must 

 not imagine that fonnnlas which appear wrongly have been care- 

 lessly written or corrected. When I note that I had to corroot 

 several sheets of my book on Cycloids five or six times, and that 

 even then errors appeared, they will see how difiicult it is to secure 

 oorrectnese in the printing of mathematical matter. — Ed.] 



©m Cbc<>5 Column. 



THE following problem gained tho first prize in the late Problem 

 Tournament of Design and Work. It is taken from the ('/i,.« 

 Player^ Chronicle. 



By B. G. Laws. 



Wbitb. 

 White to play and mate in three mOTes. 



UAME AT ODDS. 

 First game in n match iM'twcen McMm. ff. Hrakine and W 

 ut the oddn of I'awn and two moves. 



NOTES BY MEPHISTO. 



(") The intention of bringing the B. to B.2. is good enough, bnt 

 we hardly think that Black can afford the neces.sary time for this 

 manoeuvre, we should prefer P. to K.3. followed by Q. to K.2., a 

 line of play favom-cd by Mr. Potter. We, however, freely confess 

 some ignorance as to this most cruel of all openings. A modem 

 treatise on these and other odds woirid be welcome. In a game 

 between Mr. Wayto and Mr. Ilooke, at Leamington, the following 

 occtirred : — 



P. to K.4. ^toK.B.4. Kt. to K.B.3. P. to K.5. 

 P. to K.3. P. to Q.4; P. to y.B.4. 



this line of play resulted unfavourably for the attack. 



C") White's attack relaxes a little, he ought to have Ca-illcd and 

 then played P. to K.B.4 . 



(=) Black has emerged fairly from the first attack, and Castling 

 at once would have been his best course. For, considering the odds 

 given, he ought not to dread White's attack on his King's side, with 

 th£ King in comparative safety. 



('') Sad loss of time. 



I') Well played. Should Black play y. to B.sq., White would 

 also obtivin a strong position. 



(') Black misses a good chance of somewhat equalising matters. 



Ho ought to have played 17. P. takes P., followed by B takes Kt. 



and Castles Q.R. ; he would then have cither remained with Bishops 

 of opposite colours or with Kt. against a B., and would have had a 



fair chance of drawing, e.g., 17. P. takes P. 18. P . takes P. (P. to 



P. takes B. 

 K.5. would not be good play.) jj t^^.^ jjt. ^ ^»' Castles Q.B. 



P. to K.B.5. _j^ P. t akes Kt . ^, Q. takes P. 



CaatlesQ.R. 



or if 19. 



20. 



21. 



ith a 



P. taJces P. "" B. to K.4. 

 ,'ood game. 



(K) A desperate course, but there seemed no possibility of ex- 

 tricating the Knight from its helpless position. 



(*) White conducts his game with good judgment. 



(') Black could not gain anything by playing his Queen away from 

 his King's side. 



