102 



KNOWLEDGE 



[Aug. 1, 1884. 



through the point x^ y^ (i) must be satisfied when Xo is written for 

 X and 1/2 for i/, thus 



'./; — i/i = m (^2— a^i) 

 that is 



substituting this value of m in (i) we obtain the required equation, 

 viz., 



2/-Vl=^2Zli (a; -a:,) (ii) 



X« — Xi 



an equation which may be written in the easily remembered form 

 V-V i_ x-x^ 

 y2 — V\ ^2— a:i 

 CoK. — We may write (ii) in the form 



y{x^-x,) +y^{x — x.2) + y.,(xi — x)=0 (iii) 



This amounts to the statement that if « v be the co-ordinates of 

 any point on the lino through Xji/, and Xay^, then the area of the 

 triangle formed by joining the points aJii/,, x.^y^ and x y ia zero, — a 

 consideration from which we might have deduced the equation 

 required. 

 Since (iii) may be written 



x(yi-y-:) +y(x2—Xi) + x0« — y,x.. = O 

 the intercepts on the axes of x and y are 



X2V1 - -f l!/2 



and 



iToj/i — ^iy» 



Vi-y^ x,-x.2 



(To he continued.) 



(Bur Cf)t65 Column. 



By Mephisto. 



SELECTED PROBLEMS. 



No. 120. 



Buck. 



Whitb. 

 White to play and mate in two moves. 



Xo. 121. 

 Black. 



Whits. 



Keprinted from p. 80 on account of misprint. 



^Vhite to play and mate in two moves. 



Ending from actual play. 



Amateur. 



Black. 



Whixb. 



Mr. Waters.- 



White to play and win. 



ANSWERS TO COKRESPONDENTS. 



,*, Please address Chess Editor. 



Geo. W. Thompson. — You are quite right; we ought to have pub- 

 lished the reply to Black's defence of Kt to Bsq — that is, Kt x P in 

 Carpenter's problem. 



E. W. Young. — Regret to say problems not suitable. 



W. — You say that yon would cheer/idly have played 50. P x BP 

 in the ending given in Kno^vledge of July 18, expecting 50. P x HP 

 51. P to B5, when, I am afraid, on Black playing K to Q4, yon 

 would have become rather sad. No doubt we have seen the 

 problem, but cannot recollect it. Is it not unsound ? 



Walter. — We reprint the position correctly. 



Conect solutions received from M. T. Hooton, Chas. T. Wilbra- 

 ham, G. W. Thompson, Uncle John, C. T. G., The Owl. 



The Norwood Revien: says that a new Chess Club in in course of 

 formation ; it will assemble in a locality near the station, and will 

 begin in September next. 



OONTKNTS OP No, 143. 



FAGB 



Dreams. V. By Edward Clodd ... 65 

 The .4.ntarctic Kegious. By E. A. 



Proctor 66 



Sensation in a Severed Head 67 



The Electro-Magnet. By W. Slingo. 



(Itlu>.) 



Other Worlds than Ours. By M. 



de Fontenelle. With Notes by 



Eichard A. Proctor 



NoTel Tricycles. By John Browning 



68 



69 

 70 



riam 



The International Health Exhibi- 

 tion. IX. (niut.) 71 



Thunderstorms 73 



BcTiews 76 



Miscellanea 76 



Correspondence : Dickens's Story 

 Left HaU Told (No. 139)— The 



Solar Glow, 4c 77 



Our Mathematical Coloma 79 



Our Chess Column 80 



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