not, it is
certain that the arguments are far more effective than if the writer
had presented them in the form of an essay. Mr. Dodgson had a wide
experience as a teacher and examiner, so that he knew well what he was
writing about, and undoubtedly the appearance of this book has done
very much to stay the hand of the innovator.

The scene opens in a College study--time, midnight. Minos, an
examiner, is discovered seated between two immense piles of
manuscripts. He is driven almost to distraction in his efforts to mark
fairly the papers sent up, by reason of the confusion caused through
the candidates offering various substitutes for Euclid. Rhadamanthus,
another equally distracted examiner, comes to his room.

The two men consult together for a time, and then Rhadamanthus
retires, and Minos falls asleep. Hereupon the Ghost of Euclid appears,
and discusses with Minos the reasons for retaining his Manual as a
whole, in its present order and arrangement. As they are mainly
concerned with the wants of beginners, their attention is confined to
Books I. and II.

We must be content with one short extract from the dialogue:--

_Euclid_.--It is, I think, a friend of yours who has
amused himself by tabulating the various Theorems which
might be enunciated on the single subject of Pairs of Lines.
How many did he make them out to be?

_Minos_.--About two hundred and fifty, I believe.

_Euclid_.--At that rate there would probably be within
the limit of my First Book--how many?

_Minos_.--A thousand at least.

_Euclid_.--What a popular school-book it will be! How
boys will bless the name of the writer who first brings out
the complete thousand!

With a view to discussing and criticising his various modern rivals,
Euclid promises to send to Minos the ghost of a German Professor (Herr
Niemand) who "has read all books, and is ready to defend any thesis,
true or untrue."

"A charming companion!" as Minos drily remarks.

This brings us to Act II., in which the Manuals which reject Euclid's
treatment of Parallels are dealt with one by one. Those Manuals which
adopt it are reserved for Act III., Scene i.; while in Scene ii., "The
Syllabus of the Association for the Improvement of Geometrical
Teaching," and Wilson's "Syllabus," come under review.

Only one or two extracts need be given, which, it is hoped, will
suffice to illustrate the character and style of the book:

Act II.,