222 



♦ KNOWrLEDGE ♦ 



[Oct. 5, 1883, 



duced into the elements of algebra — projection, correlation, 

 motion accepted as aids to geometry — the mind of the 

 student quickened and elevated and his faith awakened 

 by early initiation into the ruling ideas of polarity, continuity, 

 infinity, and familiarisation with the doctrine of the imaginary and 

 inconceivable. It is this living interest in the subject which is so 

 wanting in our traditional and mediaeval modes of teaching." If 

 from this point of view we now look towards the work of the Asso- 

 ciation for the Improvement of Geometrical Teaching, the result is 

 not as satisfactory as might have been wished. There is veiy little 

 of the influence of modern ideas to be found in the diiterent 

 syllabuses which have been published. Even in the one headed 

 "Modern Geometry" there is nothing of the genius of modern 

 thought. The subject-matter is partly taken from modern geometry, 

 but for modern methods one looks in vain. Nevertheless, it is 

 satistisfactory to see that the use of the syllabus on plane geometry 

 has spread pretty widely, and it is to be hoped that it will continue 

 to do so. 



A thorough reform, in the direction indicated, will be a difficult 

 task, and it will, perhaps, be a long time before it is possible. At 

 present it has not even been settled which series of axioms will 

 ultimately be adopied. Possibly, many attempts have still to be 

 made before a new Euclid finds the material sufficiently prepared 

 for him to raise the hoped-for edifice. 



#ur Cbess Column. 



By Mephisto. 



PROBLEM.— By the Kev. H. Eoltok. 



The Arabians. 



Black, 



White. 

 White to play an 1 mate in fourteen moves. 



PROBLEM Xo. 101. 



By W. Fcr.n-ivai,. 



Black. 



^y^ITE. 

 White to play and mate in three moves. 



SOLUTION OF PROBLEM 99. 

 1. K to KB8. Thi-eatening 2. ^t to Q,7 (ch ) ^^ ^ Kt (fr om 

 Kt3) to QB5, mate. 



1- Q , , — zyrTp ^°^^ '^°^ prevent this, as the Q will be pinned. 



This checkmate position is very beautiful. 



Black's defences are Q takes Kt or P takes Kt. 

 Q to KR2, 



If 1. 



2. 



Q takes Kt. 



ifi .-, Q to QR7, ■ 



" ^- P takes Kt. -• *<=■ 



This is doubtless an exceedingly beautiful problem, but there is a 

 slight blemish in the fact that in answer to several of Black's 

 possible first moves (viz., P to QR6, P to K7, P to KB6, Q takes Q, 

 Q to B8, Q to Q8, Q to Q7, Q to K7, Q to KB7, Kt to R6, Kt to 

 Q7) White can play either 2. K to K7, or 2. Kt to Q7 (ch). Fritz's 

 problem, however (unnumbered, on page 61), has some dual solu- 

 tions on the second move. I do not think No. 99 bears away the 

 palm from Fritz's composition. In the former the White K is 

 evidently scanted ou K7, and the fact that he must not travel by 

 KB7 suggests KB8. In the latter, KR8 is apparently such a use- 

 less position for the Queen that one is hardly likely to try it until 

 it is suggested by the failure of Q to KRC and Q to KR4. The 

 almost exact balance of pieces is also a point (though a small one) 

 in favour of the first prize problem. But the ideas and combina- 

 tions in both are so elegant that the only reason why Berger's 

 problem is not the best, is that Fritz's is such an uncommonly fine 

 problem. The similarity in the methods of getting the White Q 

 round an awkward coi'ner wiU not pass unnoticed. W. 



ANSWERS TO CORRESPONDENTS. 

 *»* Please address Chess Editor, 



J. A. Miles. — Problem received ivith thanks. 



Correct solutions received. — Problem 99, John Watson. No. 100, 

 W., B. Gleam, John Watson. 



John.— In Problem 99, if 1. Q takes Q, Kt to B6 (a very fine 

 defence). 2. Kt to R5, Kt to Q4. Or, 2. Q takes Kt, P to BG, and 

 there is no mate. 



Contents of No. 100. 



PAGE 



A Naturalist's Tear. Blackberries 

 are Ripe. By Grant Allen 193 



The Chemistry of Cookery. XIX. 

 By W. Mattieu Williams 194 



The Antiquity of Man. By W. Pen- 

 gellv 195 



The Sim's Distance. By Professor 

 E. S. Ball, LL.D 19; 



The Morality of Happiness. IV.— 

 Eight and Wrong. By Thomas 

 Foster 199 



Tast Sun Spots. (7Zte».) 201 



PAGE 



Chemistry of the Cereals. By W. 



Jago, P.C.S 201 



Poker Principles 203 



The Philosophy of Mathematics. 



Part I. By Professor A. Cayley 204 



Commas and Colons 205 



The Face of the Sky. ByF.E.A.S. 206 



Editorial Gossip 206 



Correspondence: High -Wheeled 



Tricycles i\ Low Wheels— The 



" Sun and Planet " Bicycle, &c... 806 

 Our Chess Column 208 



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