their hateful presence the fancy that would fain be pure.  Against all these some real mental work is a most helpful ally.  That “unclean spirit” of the parable, who brought back with him seven others more wicked than himself, only did so because he found the chamber “swept and garnished,” and its owner sitting with folded hands.  Had he found it all alive with the “busy hum” of active work, there would have been scant welcome for him and his seven!

It would have robbed the book of its true character if Lewis Carroll had attempted to improve on the work done in his head, and consequently we have the solutions exactly as he worked them out before setting them down on paper.  Of the Problems themselves there is not much to be said here; they are original, and some of them (e.g., No. 52) expressed in a style peculiarly the author’s own.  The subjects included in their range are Arithmetic, Algebra, Pure Geometry (Plane), Trigonometry, Algebraic Geometry, and Differential Calculus; and there is one Problem to which Mr. Dodgson says he “can proudly point,” in “Transcendental Probabilities,” which is here given:  “A bag contains two counters, as to which nothing is known except that each is either black or white.  Ascertain their colour without taking them out of the bag.”  The answer is, “One is black and the other white.”  For the solution the reader is referred to the book itself, a study of which will well repay him, apart from the chance he may have of discovering some mistake, and the consequent joy thereat!

A few extracts from the Diary follow, written during the early part of 1894:—­

Feb. 1_st.—­Dies notandus._ As Ragg was reading Prayers, and Bayne and I were the only M.A.’s in the stalls, I tried the experiment of going to the lectern and reading the lesson.  I did not hesitate much, but feel it too great a strain on the nerves to be tried often.  Then I went to the Latin Chapel for Holy Communion.  Only Paget (Dean) and Dr. Huntley came:  so, for the first time in my recollection, it had to be given up.  Then I returned to my rooms, and found in The Standard the very important communication from Gladstone denying the rumour that he has decided upon resigning the Premiership, but admitting that, owing to failing powers, it may come at any moment.  It will make a complete change in the position of politics!  Then I got, from Cook Wilson, what I have been so long trying for—­an accepted transcript of the fallacious argument over which we have had an (apparently) endless fight.  I think the end is near, now.

Feb. 4_th._—­The idea occurred to me that it might be a pleasant variation in Backgammon to throw three dice, and choose any two of the three numbers.  The average quality of the throws would be much raised.  I reckon that the chance of “6, 6” would be about two and a half what it now is.  It would also furnish a means, similar to giving