EXAMINATION ON THE THESIS 191 



Montagnes" and asked me to put the thirty or so questions on 

 the board and from them to construct the "Re'sume" Penta- 

 gonal." The task took considerable time, but I had visualized 

 it well, and set down the matter accurately. Then, still following 

 the book, he asked me to criticise the work as a whole. Fortu- 

 nately I had recently studied the essays of William Hopkins 

 of Cambridge University, in which there is an effectively dis- 

 tinctive study of the mean, showing that, taking account of the 

 departures of the general mountain axis from the lines described 

 by the several great centres of comparison set up by De Beau- 

 mont, the correspondences of the position of these axes with 

 these circles was no nearer than chance would bring about ; in 

 a word, that there was really no more mathematical order in 

 the alignment of these features than would be found in straws 

 thrown haphazard on a table. It happened that Peirce did not 

 know of Hopkins's work on this subject, and though I gave 

 the author full credit for the criticism, the sufficiency of it was 

 impressive, and finished my examination, save that at the 

 end he asked me a question. I have forgotten what it was, but 

 it appeared to me unfair. I said that I could give no answer, 

 and asked him what the answer should be. We had a sharp 

 colloquy, which ended in his good-natured acknowledgment 

 that he had put the question to see what I would do with it. 



I never shall forget the look of pleasure on my master's 

 expressive face as he watched the progress of this part of my 

 examination, which I knew was well done, for I was in an excel- 

 lent state of tension for the work and felt myself in perfect com- 

 mand of it. He had evidently been in some anxiety as to my 

 ability to face the questioning I should be subjected to by his 

 colleague. I had myself no serious doubts as to my ability to 

 meet the trial, though the purely nervous anxiety before it began 

 was a sore infliction. I won my degree summa cum laude by the 

 unanimous vote of my judges and that without much debate, as 

 I was told. I was asked to wait a moment and in a minute or 

 two the good news came to me, Benjamin Peirce being the first 



