1902.] on Magic Squares and other Problems on a Chess-Board. 63 



books and documents of the old Mathematical Society of Spitalfields 

 (1717-1845) for the purpose of extracting something which might 

 interest or amuse, if it might not instruct, the audience I addressed in 

 Section A of the British Association for the Advancement of Science at 

 Glasgow last autumn. It is an arrangement for the first eighteen 

 numbers on five connected triangles ; the magical property consists 

 in the circumstance that the numbers 19, 38 and 57 appear as sums 

 in a variety of ways. The number 19 appears nine times, 38 twelve 

 times and 57 fourteen times (Fig. 15). 



I should say that I feel conscious that I have not been able to 

 introduce the subject of my lecture without occasional and, perhaps, 

 in the circumstances, unavoidable obscurity. For the rest, I have 

 felt somewhat doubtful as to the interest I might arouse in these 

 problems, but the managers honoured me by inviting me to display 

 to you some of the chips from a pure mathematician's workshop, and 

 I felt no hesitation in accepting. 



