This is, I believe, the very first attempt (with the exception of my own little book, _The Game of Logic_, published in 1886, a very incomplete performance) that has been made to _popularise_ this fascinating subject. It has cost me _years_ of hard work: but if it should prove, as I hope it may, to be of _real_ service to the young, and to be taken up, in High Schools and in private families, as a valuable addition to their stock of healthful mental recreations, such a result would more than repay ten times the labour that I have expended on it. L. C. 29, BEDFORD STREET, STRAND. _Christmas, 1896._ pg-xi INTRODUCTION. _TO LEARNERS._ [N.B. Some remarks, addressed to _Teachers_, will be found in the Appendix, at p. 165.] The Learner, who wishes to try the question _fairly_, whether this little book does, or does not, supply the materials for a most interesting mental recreation, is _earnestly_ advised to adopt the following Rules:-- (1) Begin at the _beginning_, and do not allow yourself to gratify a mere idle curiosity by dipping into the book, here and there. This would very likely lead to your throwing it aside, with the remark "This is _much_ too hard for me!", and thus losing the chance of adding a very _large_ item to your stock of mental delights. This Rule (of not _dipping_) is very _desirable_ with _other_ kinds of books----such as novels, for instance, where you may easily spoil much of the enjoyment you would otherwise get from the story, by dipping into it further on, so that what the author meant to be a pleasant surprise comes to you as a matter of course. Some people, I know, make a practice of looking into Vol. III first, just to see how the story ends: and perhaps it _is_ as well just to know that all ends _happily_----that the much-persecuted lovers _do_ marry after all, that he is proved to be quite innocent of the murder, that the wicked cousin is completely foiled in his plot and gets the punishment he deserves, and that the rich uncle in India (_Qu._ Why in _India_? _Ans._ Because, somehow, uncles never _can_ get rich anywhere else) dies at exactly the right moment----before taking the trouble to read Vol. I. This, I say, is _just_ permissible with a _novel_, where Vol. III has a _meaning_, even for those who have not read the earlier part of the story; but, with a _scientific_ book, it is sheer insanity: you will find the latter part _hopelessly_ unintelligible, if you read it before reaching it in regular course. pg-xii (2) Don't begin any fresh Chapter, or Section, until you are certain that you _thoroughly_ understand the whole book _up to that point_, and that you have worked, correctly, most if not all of the examples which have been set. So long as you are conscious that all the land you have