be wearisome for me to describe, and equally wearisome for you to read, the processes of reasoning by means of which the above deductions have been arrived at.  But in order to satisfy you that my assumptions are not entirely fanciful or destitute of sober sense, I will describe to you, as briefly as may be, the process by means of which I have come to the conclusion that the book used as the basis of the cryptogram was not a dictionary or other work in which the words come in alphabetical rotation; and such a conclusion is very easy of proof.

“In a document so lengthy as the Ms. of your friend the Scotch laird there must of necessity be many repetitions of what may be called ’indispensable words’—­words one or more of which are used in the composition of almost every long sentence.  I allude to such words as a, an, and, as, of, by, the, their, them, these, they, you, I, it, etc.  The first thing to do was to analyse the MS. and classify the different groups of figures for the purpose of ascertaining the number of repetitions of any one group.  My analysis showed me that these repetitions were surprisingly few.  Forty groups were repeated twice, fifteen three times, and nine groups four times.  Now, according to my calculation, the MS. contains one thousand two hundred and eighty-three words.  Out of those one thousand two hundred and eighty-three words there must have been more than the number of repetitions shown by my analysis, and not of one only, but of several of what I have called ‘indispensable words.’  Had a dictionary been made use of by the writer of the MS. all such repetitions would have been referred to one particular page, and to one particular line of that page:  that is to say, in every case where a word repeated itself in the MS. the same group of numbers would in every case have been its valeur.  As the repetitions were so few I could only conclude that some book of an ordinary kind had been made use of, and that the writer of the cryptogram had been sufficiently ingenious not to repeat his numbers very frequently in the case of ‘indispensable words,’ but had in the majority of cases given a fresh group of numbers at each repetition of such a word.  I might, perhaps, go further and say that in the majority of cases where a group of figures is repeated such group refers to some word less frequently used than any of those specified above, and that one group was obliged to do duty on two or more occasions, simply because the writer was unable to find the word more than once in the book on which his cryptogram was based.

“Having once arrived at the conclusion that some book had been used as the basis of the cryptogram, my next supposition that each group of three sets of numbers showed the page of the book, the number of the line from the top, and the position of the required word in that line,